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11 REFRIGERATION Chapter CYCLES major application area of thermodynamics is refrigeration, which is the transfer of heat from a lower temperature region to a higher temperature one. Devices that produce refrigeration are called refrigerators, and the cycles on which they operate are called refrigeration cycles. The most frequently used refrigeration cycle is the vapor-compression refrigeration cycle in which the refrigerant is vaporized and condensed alternately and is compressed in the vapor phase. Another well-known refrigeration cycle is the gas refrigeration cycle in which the refrigerant remains in the gaseous phase throughout. Other refrigeration cycles discussed in this chapter are cascade refrigeration, where more than one refrigeration cycle is used; absorption refrigeration, where the refrigerant is dissolved in a liquid before it is compressed; and, as a Topic of Special Interest, thermoelectric refrigeration, where refrigeration is produced by the passage of electric current through two dissimilar materials. A Objectives The objectives of Chapter 11 are to: Introduce the concepts of refrigerators and heat pumps and the measure of their performance. Analyze the ideal vapor-compression refrigeration cycle. Analyze the actual vapor-compression refrigeration cycle. Review the factors involved in selecting the right refrigerant for an application. Discuss the operation of refrigeration and heat pump systems. Evaluate the performance of innovative vapor-compression refrigeration systems. Analyze gas refrigeration systems. Introduce the concepts of absorption-refrigeration systems. Review the concepts of thermoelectric power generation and refrigeration. | 607 608 | Thermodynamics INTERACTIVE TUTORIAL 111 REFRIGERATORS AND HEAT PUMPS SEE TUTORIAL CH. 11, SEC. 1 ON THE DVD. WARM environment WARM house QH QH (desired output) Wnet,in (required input) Wnet,in (required input) HP R QL (desired output) COLD refrigerated space (a) Refrigerator QL COLD environment We all know from experience that heat flows in the direction of decreasing temperature, that is, from high-temperature regions to low-temperature ones. This heat-transfer process occurs in nature without requiring any devices. The reverse process, however, cannot occur by itself. The transfer of heat from a low-temperature region to a high-temperature one requires special devices called refrigerators. Refrigerators are cyclic devices, and the working fluids used in the refrigeration cycles are called refrigerants. A refrigerator is shown schematically in Fig. 111a. Here QL is the magnitude of the heat removed from the refrigerated space at temperature TL ,QH is the magnitude of the heat rejected to the warm space at temperature TH , and Wnet,in is the net work input to the refrigerator. As discussed in Chap. 6, QL and QH represent magnitudes and thus are positive quantities. Another device that transfers heat from a low-temperature medium to a high-temperature one is the heat pump. Refrigerators and heat pumps are essentially the same devices; they differ in their objectives only. The objective of a refrigerator is to maintain the refrigerated space at a low temperature by removing heat from it. Discharging this heat to a higher-temperature medium is merely a necessary part of the operation, not the purpose. The objective of a heat pump, however, is to maintain a heated space at a high temperature. This is accomplished by absorbing heat from a low-temperature source, such as well water or cold outside air in winter, and supplying this heat to a warmer medium such as a house (Fig. 111b). The performance of refrigerators and heat pumps is expressed in terms of the coefficient of performance (COP), defined as COPR COPHP Desired output Required input Desired output Required input Cooling effect Work input Heating effect Work input QL Wnet,in QH Wnet,in (111) (b) Heat pump FIGURE 111 The objective of a refrigerator is to remove heat (QL) from the cold medium; the objective of a heat pump is to supply heat (QH) to a warm medium. (112) These relations can also be expressed in the rate form by replacing the . . . quantities QL, QH, and Wnet,in by QL, QH, and Wnet,in, respectively. Notice that both COPR and COPHP can be greater than 1. A comparison of Eqs. 111 and 112 reveals that COPHP COPR 1 (113) for fixed values of QL and QH. This relation implies that COPHP 1 since COPR is a positive quantity. That is, a heat pump functions, at worst, as a resistance heater, supplying as much energy to the house as it consumes. In reality, however, part of QH is lost to the outside air through piping and other devices, and COPHP may drop below unity when the outside air temperature is too low. When this happens, the system normally switches to the fuel (natural gas, propane, oil, etc.) or resistance-heating mode. The cooling capacity of a refrigeration system--that is, the rate of heat removal from the refrigerated space--is often expressed in terms of tons of refrigeration. The capacity of a refrigeration system that can freeze 1 ton (2000 lbm) of liquid water at 0C (32F) into ice at 0C in 24 h is said to be Chapter 11 1 ton. One ton of refrigeration is equivalent to 211 kJ/min or 200 Btu/min. The cooling load of a typical 200-m2 residence is in the 3-ton (10-kW) range. | 609 112 THE REVERSED CARNOT CYCLE Recall from Chap. 6 that the Carnot cycle is a totally reversible cycle that consists of two reversible isothermal and two isentropic processes. It has the maximum thermal efficiency for given temperature limits, and it serves as a standard against which actual power cycles can be compared. Since it is a reversible cycle, all four processes that comprise the Carnot cycle can be reversed. Reversing the cycle does also reverse the directions of any heat and work interactions. The result is a cycle that operates in the counterclockwise direction on a T-s diagram, which is called the reversed Carnot cycle. A refrigerator or heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump. Consider a reversed Carnot cycle executed within the saturation dome of a refrigerant, as shown in Fig. 112. The refrigerant absorbs heat isothermally from a low-temperature source at TL in the amount of QL (process 1-2), is compressed isentropically to state 3 (temperature rises to TH), rejects heat isothermally to a high-temperature sink at TH in the amount of QH (process 3-4), and expands isentropically to state 1 (temperature drops to TL). The refrigerant changes from a saturated vapor state to a saturated liquid state in the condenser during process 3-4. WARM medium at TH QH 4 TH Condenser 3 T QH 4 Turbine Compressor 3 1 Evaporator TL QL 2 1 QL 2 s COLD medium at TL FIGURE 112 Schematic of a Carnot refrigerator and T-s diagram of the reversed Carnot cycle. 610 | Thermodynamics The coefficients of performance of Carnot refrigerators and heat pumps are expressed in terms of temperatures as COPR,Carnot 1 TH>TL 1 (114) and COPHP,Carnot 1 1 TL >TH (115) Notice that both COPs increase as the difference between the two temperatures decreases, that is, as TL rises or TH falls. The reversed Carnot cycle is the most efficient refrigeration cycle operating between two specified temperature levels. Therefore, it is natural to look at it first as a prospective ideal cycle for refrigerators and heat pumps. If we could, we certainly would adapt it as the ideal cycle. As explained below, however, the reversed Carnot cycle is not a suitable model for refrigeration cycles. The two isothermal heat transfer processes are not difficult to achieve in practice since maintaining a constant pressure automatically fixes the temperature of a two-phase mixture at the saturation value. Therefore, processes 1-2 and 3-4 can be approached closely in actual evaporators and condensers. However, processes 2-3 and 4-1 cannot be approximated closely in practice. This is because process 2-3 involves the compression of a liquidvapor mixture, which requires a compressor that will handle two phases, and process 4-1 involves the expansion of high-moisture-content refrigerant in a turbine. It seems as if these problems could be eliminated by executing the reversed Carnot cycle outside the saturation region. But in this case we have difficulty in maintaining isothermal conditions during the heat-absorption and heat-rejection processes. Therefore, we conclude that the reversed Carnot cycle cannot be approximated in actual devices and is not a realistic model for refrigeration cycles. However, the reversed Carnot cycle can serve as a standard against which actual refrigeration cycles are compared. INTERACTIVE TUTORIAL SEE TUTORIAL CH. 11, SEC. 2 ON THE DVD. 113 THE IDEAL VAPOR-COMPRESSION REFRIGERATION CYCLE Many of the impracticalities associated with the reversed Carnot cycle can be eliminated by vaporizing the refrigerant completely before it is compressed and by replacing the turbine with a throttling device, such as an expansion valve or capillary tube. The cycle that results is called the ideal vapor-compression refrigeration cycle, and it is shown schematically and on a T-s diagram in Fig. 113. The vapor-compression refrigeration cycle is the most widely used cycle for refrigerators, air-conditioning systems, and heat pumps. It consists of four processes: 1-2 2-3 3-4 4-1 Isentropic compression in a compressor Constant-pressure heat rejection in a condenser Throttling in an expansion device Constant-pressure heat absorption in an evaporator In an ideal vapor-compression refrigeration cycle, the refrigerant enters the compressor at state 1 as saturated vapor and is compressed isentropically to the condenser pressure. The temperature of the refrigerant increases during Chapter 11 | 611 WARM environment QH Condenser 3 Expansion valve Compressor 4 Evaporator 1 2 T Saturated liquid QH Win 3 2 Win 4' QL COLD refrigerated space 4 1 QL Saturated vapor s FIGURE 113 Schematic and T-s diagram for the ideal vapor-compression refrigeration cycle. this isentropic compression process to well above the temperature of the surrounding medium. The refrigerant then enters the condenser as superheated vapor at state 2 and leaves as saturated liquid at state 3 as a result of heat rejection to the surroundings. The temperature of the refrigerant at this state is still above the temperature of the surroundings. The saturated liquid refrigerant at state 3 is throttled to the evaporator pressure by passing it through an expansion valve or capillary tube. The temperature of the refrigerant drops below the temperature of the refrigerated space during this process. The refrigerant enters the evaporator at state 4 as a low-quality saturated mixture, and it completely evaporates by absorbing heat from the refrigerated space. The refrigerant leaves the evaporator as saturated vapor and reenters the compressor, completing the cycle. In a household refrigerator, the tubes in the freezer compartment where heat is absorbed by the refrigerant serves as the evaporator. The coils behind the refrigerator, where heat is dissipated to the kitchen air, serve as the condenser (Fig. 114). Remember that the area under the process curve on a T-s diagram represents the heat transfer for internally reversible processes. The area under the process curve 4-1 represents the heat absorbed by the refrigerant in the evaporator, and the area under the process curve 2-3 represents the heat rejected in the condenser. A rule of thumb is that the COP improves by 2 to 4 percent for each C the evaporating temperature is raised or the condensing temperature is lowered. Kitchen air 25C Freezer compartment QL Evaporator coils Capillary tube 18C QH Condenser coils 3C Compressor FIGURE 114 An ordinary household refrigerator. 612 P | Thermodynamics Another diagram frequently used in the analysis of vapor-compression refrigeration cycles is the P-h diagram, as shown in Fig. 115. On this diagram, three of the four processes appear as straight lines, and the heat transfer in the condenser and the evaporator is proportional to the lengths of the corresponding process curves. Notice that unlike the ideal cycles discussed before, the ideal vaporcompression refrigeration cycle is not an internally reversible cycle since it involves an irreversible (throttling) process. This process is maintained in the cycle to make it a more realistic model for the actual vapor-compression refrigeration cycle. If the throttling device were replaced by an isentropic turbine, the refrigerant would enter the evaporator at state 4 instead of state 4. As a result, the refrigeration capacity would increase (by the area under process curve 4 -4 in Fig. 113) and the net work input would decrease (by the amount of work output of the turbine). Replacing the expansion valve by a turbine is not practical, however, since the added benefits cannot justify the added cost and complexity. All four components associated with the vapor-compression refrigeration cycle are steady-flow devices, and thus all four processes that make up the cycle can be analyzed as steady-flow processes. The kinetic and potential energy changes of the refrigerant are usually small relative to the work and heat transfer terms, and therefore they can be neglected. Then the steadyflow energy equation on a unitmass basis reduces to 1qin qout 2 1win wout 2 he hi (116) QH 3 QL 4 1 Win 2 h FIGURE 115 The P-h diagram of an ideal vapor-compression refrigeration cycle. The condenser and the evaporator do not involve any work, and the compressor can be approximated as adiabatic. Then the COPs of refrigerators and heat pumps operating on the vapor-compression refrigeration cycle can be expressed as COPR qL wnet,in h1 h2 h4 h1 (117) and COPHP qH wnet,in h2 h2 h3 h1 (118) where h1 hg @ P1 and h3 hf @ P3 for the ideal case. Vapor-compression refrigeration dates back to 1834 when the Englishman Jacob Perkins received a patent for a closed-cycle ice machine using ether or other volatile fluids as refrigerants. A working model of this machine was built, but it was never produced commercially. In 1850, Alexander Twining began to design and build vapor-compression ice machines using ethyl ether, which is a commercially used refrigerant in vapor-compression systems. Initially, vapor-compression refrigeration systems were large and were mainly used for ice making, brewing, and cold storage. They lacked automatic controls and were steam-engine driven. In the 1890s, electric motordriven smaller machines equipped with automatic controls started to replace the older units, and refrigeration systems began to appear in butcher shops and households. By 1930, the continued improvements made it possible to have vapor-compression refrigeration systems that were relatively efficient, reliable, small, and inexpensive. Chapter 11 EXAMPLE 111 The Ideal Vapor-Compression Refrigeration Cycle | 613 A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.14 and 0.8 MPa. If the mass flow rate of the refrigerant is 0.05 kg/s, determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the rate of heat rejection to the environment, and (c) the COP of the refrigerator. Solution A refrigerator operates on an ideal vapor-compression refrigeration cycle between two specified pressure limits. The rate of refrigeration, the power input, the rate of heat rejection, and the COP are to be determined. Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. Analysis The T-s diagram of the refrigeration cycle is shown in Fig. 116. We note that this is an ideal vapor-compression refrigeration cycle, and thus the compressor is isentropic and the refrigerant leaves the condenser as a saturated liquid and enters the compressor as saturated vapor. From the refrigerant-134a tables, the enthalpies of the refrigerant at all four states are determined as follows: P1 0.14 MPa h1 s1 0.8 MPa f s1 hg @ 0.14 MPa sg @ 0.14 MPa 239.16 kJ>kg 0.94456 kJ>kg # K T P2 s2 P3 h4 h2 275.39 kJ>kg hf @ 0.8 MPa 95.47 kJ>kg 0.8 MPa h3 h3 1throttling2 h4 2 h1 2 h3 2 # QH h4 95.47 kJ>kg 3 0.8 MPa QH (a) The rate of heat removal from the refrigerated space and the power input to the compressor are determined from their definitions: 2 Win # QL and # m 1h 1 # m 1h 2 # m 1h 2 10.05 kg>s2 3 1239.16 10.05 kg>s2 3 1275.39 10.05 kg>s2 3 1275.39 # QL # Win # QL # Win 7.18 95.472 kJ>kg4 239.16 2 kJ>kg 4 95.472 kJ>kg4 8.99 kW 7.18 kW 0.14 MPa 4s 4 1 QL # Win # QH 1.81 kW (b) The rate of heat rejection from the refrigerant to the environment is 9.0 kW s It could also be determined from 1.81 (c) The coefficient of performance of the refrigerator is COPR 7.18 kW 1.81 kW FIGURE 116 T-s diagram of the ideal vapor-compression refrigeration cycle described in Example 111. 3.97 That is, this refrigerator removes about 4 units of thermal energy from the refrigerated space for each unit of electric energy it consumes. Discussion It would be interesting to see what happens if the throttling valve were replaced by an isentropic turbine. The enthalpy at state 4s (the turbine exit with P4s 0.14 MPa, and s4s s3 0.35404 kJ/kg K) is 88.94 kJ/kg, 614 | Thermodynamics and the turbine would produce 0.33 kW of power. This would decrease the power input to the refrigerator from 1.81 to 1.48 kW and increase the rate of heat removal from the refrigerated space from 7.18 to 7.51 kW. As a result, the COP of the refrigerator would increase from 3.97 to 5.07, an increase of 28 percent. INTERACTIVE TUTORIAL SEE TUTORIAL CH. 11, SEC. 3 ON THE DVD. 114 ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE An actual vapor-compression refrigeration cycle differs from the ideal one in several ways, owing mostly to the irreversibilities that occur in various components. Two common sources of irreversibilities are fluid friction (causes pressure drops) and heat transfer to or from the surroundings. The T-s diagram of an actual vapor-compression refrigeration cycle is shown in Fig. 117. In the ideal cycle, the refrigerant leaves the evaporator and enters the compressor as saturated vapor. In practice, however, it may not be possible to control the state of the refrigerant so precisely. Instead, it is easier to design the system so that the refrigerant is slightly superheated at the compressor inlet. This slight overdesign ensures that the refrigerant is completely vaporized when it enters the compressor. Also, the line connecting WARM environment QH T 2 3 3 2 2' Win 4 5 6 7 8 1 4 5 Condenser Expansion valve Compressor 6 7 Evaporator QL 8 1 s COLD refrigerated space FIGURE 117 Schematic and T-s diagram for the actual vapor-compression refrigeration cycle. Chapter 11 the evaporator to the compressor is usually very long; thus the pressure drop caused by fluid friction and heat transfer from the surroundings to the refrigerant can be very significant. The result of superheating, heat gain in the connecting line, and pressure drops in the evaporator and the connecting line is an increase in the specific volume, thus an increase in the power input requirements to the compressor since steady-flow work is proportional to the specific volume. The compression process in the ideal cycle is internally reversible and adiabatic, and thus isentropic. The actual compression process, however, involves frictional effects, which increase the entropy, and heat transfer, which may increase or decrease the entropy, depending on the direction. Therefore, the entropy of the refrigerant may increase (process 1-2) or decrease (process 1-2 ) during an actual compression process, depending on which effects dominate. The compression process 1-2 may be even more desirable than the isentropic compression process since the specific volume of the refrigerant and thus the work input requirement are smaller in this case. Therefore, the refrigerant should be cooled during the compression process whenever it is practical and economical to do so. In the ideal case, the refrigerant is assumed to leave the condenser as saturated liquid at the compressor exit pressure. In reality, however, it is unavoidable to have some pressure drop in the condenser as well as in the lines connecting the condenser to the compressor and to the throttling valve. Also, it is not easy to execute the condensation process with such precision that the refrigerant is a saturated liquid at the end, and it is undesirable to route the refrigerant to the throttling valve before the refrigerant is completely condensed. Therefore, the refrigerant is subcooled somewhat before it enters the throttling valve. We do not mind this at all, however, since the refrigerant in this case enters the evaporator with a lower enthalpy and thus can absorb more heat from the refrigerated space. The throttling valve and the evaporator are usually located very close to each other, so the pressure drop in the connecting line is small. | 615 EXAMPLE 112 The Actual Vapor-Compression Refrigeration Cycle Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 MPa and 10C at a rate of 0.05 kg/s and leaves at 0.8 MPa and 50C. The refrigerant is cooled in the condenser to 26C and 0.72 MPa and is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the isentropic efficiency of the compressor, and (c) the coefficient of performance of the refrigerator. Solution A refrigerator operating on a vapor-compression cycle is considered. The rate of refrigeration, the power input, the compressor efficiency, and the COP are to be determined. Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. 616 | Thermodynamics Analysis The T-s diagram of the refrigeration cycle is shown in Fig. 118. We note that the refrigerant leaves the condenser as a compressed liquid and enters the compressor as superheated vapor. The enthalpies of the refrigerant at various states are determined from the refrigerant tables to be P1 T1 P2 T2 P3 T3 h4 T 0.14 MPa f h1 10C 0.8 MPa f 50C h2 246.36 kJ/kg 286.69 kJ/kg 0.72 MPa f h3 h f @ 26C 87.83 kJ/kg 26C h3 (throttling) h4 87.83 kJ/kg (a) The rate of heat removal from the refrigerated space and the power input to the compressor are determined from their definitions: 2 QH 0.72 MPa 26C 3 0.15 MPa 4 QL 2s # QL 0.8 MPa 50C Win # m 1h 1 # m 1h 2 h4 2 h1 2 10.05 kg>s2 3 1246.36 10.05 kg>s 2 3 1286.69 h2s h2 h1 h1 87.832 kJ>kg4 246.36 2 kJ>kg 4 7.93 kW and # Win 2.02 kW (b) The isentropic efficiency of the compressor is determined from 0.14 MPa 1 10C hC where the enthalpy at state 2s (P2s kJ/kg K) is 284.21 kJ/kg. Thus, 0.8 MPa and s2s s1 0.9724 s FIGURE 118 T-s diagram for Example 112. hC 284.21 286.69 246.36 246.36 0.939 or 93.9% (c) The coefficient of performance of the refrigerator is COPR # QL # Win 7.93 kW 2.02 kW 3.93 Discussion This problem is identical to the one worked out in Example 111, except that the refrigerant is slightly superheated at the compressor inlet and subcooled at the condenser exit. Also, the compressor is not isentropic. As a result, the heat removal rate from the refrigerated space increases (by 10.4 percent), but the power input to the compressor increases even more (by 11.6 percent). Consequently, the COP of the refrigerator decreases from 3.97 to 3.93. 115 SELECTING THE RIGHT REFRIGERANT When designing a refrigeration system, there are several refrigerants from which to choose, such as chlorofluorocarbons (CFCs), ammonia, hydrocarbons (propane, ethane, ethylene, etc.), carbon dioxide, air (in the air-conditioning of aircraft), and even water (in applications above the freezing point). The right Chapter 11 choice of refrigerant depends on the situation at hand. Of these, refrigerants such as R-11, R-12, R-22, R-134a, and R-502 account for over 90 percent of the market in the United States. Ethyl ether was the first commercially used refrigerant in vapor-compression systems in 1850, followed by ammonia, carbon dioxide, methyl chloride, sulphur dioxide, butane, ethane, propane, isobutane, gasoline, and chlorofluorocarbons, among others. The industrial and heavy-commercial sectors were very satisfied with ammonia, and still are, although ammonia is toxic. The advantages of ammonia over other refrigerants are its low cost, higher COPs (and thus lower energy cost), more favorable thermodynamic and transport properties and thus higher heat transfer coefficients (requires smaller and lower-cost heat exchangers), greater detectability in the event of a leak, and no effect on the ozone layer. The major drawback of ammonia is its toxicity, which makes it unsuitable for domestic use. Ammonia is predominantly used in food refrigeration facilities such as the cooling of fresh fruits, vegetables, meat, and fish; refrigeration of beverages and dairy products such as beer, wine, milk, and cheese; freezing of ice cream and other foods; ice production; and low-temperature refrigeration in the pharmaceutical and other process industries. It is remarkable that the early refrigerants used in the light-commercial and household sectors such as sulfur dioxide, ethyl chloride, and methyl chloride were highly toxic. The widespread publicity of a few instances of leaks that resulted in serious illnesses and death in the 1920s caused a public cry to ban or limit the use of these refrigerants, creating a need for the development of a safe refrigerant for household use. At the request of Frigidaire Corporation, General Motors' research laboratory developed R-21, the first member of the CFC family of refrigerants, within three days in 1928. Of several CFCs developed, the research team settled on R-12 as the refrigerant most suitable for commercial use and gave the CFC family the trade name "Freon." Commercial production of R-11 and R-12 was started in 1931 by a company jointly formed by General Motors and E. I. du Pont de Nemours and Co., Inc. The versatility and low cost of CFCs made them the refrigerants of choice. CFCs were also widely used in aerosols, foam insulations, and the electronic industry as solvents to clean computer chips. R-11 is used primarily in large-capacity water chillers serving airconditioning systems in buildings. R-12 is used in domestic refrigerators and freezers, as well as automotive air conditioners. R-22 is used in window air conditioners, heat pumps, air conditioners of commercial buildings, and large industrial refrigeration systems, and offers strong competition to ammonia. R-502 (a blend of R-115 and R-22) is the dominant refrigerant used in commercial refrigeration systems such as those in supermarkets because it allows low temperatures at evaporators while operating at singlestage compression. The ozone crisis has caused a major stir in the refrigeration and airconditioning industry and has triggered a critical look at the refrigerants in use. It was realized in the mid-1970s that CFCs allow more ultraviolet radiation into the earth's atmosphere by destroying the protective ozone layer and thus contributing to the greenhouse effect that causes global warming. As a result, the use of some CFCs is banned by international treaties. Fully | 617 618 | Thermodynamics halogenated CFCs (such as R-11, R-12, and R-115) do the most damage to the ozone layer. The nonfully halogenated refrigerants such as R-22 have about 5 percent of the ozone-depleting capability of R-12. Refrigerants that are friendly to the ozone layer that protects the earth from harmful ultraviolet rays have been developed. The once popular refrigerant R-12 has largely been replaced by the recently developed chlorine-free R-134a. Two important parameters that need to be considered in the selection of a refrigerant are the temperatures of the two media (the refrigerated space and the environment) with which the refrigerant exchanges heat. To have heat transfer at a reasonable rate, a temperature difference of 5 to 10C should be maintained between the refrigerant and the medium with which it is exchanging heat. If a refrigerated space is to be maintained at 10C, for example, the temperature of the refrigerant should remain at about 20C while it absorbs heat in the evaporator. The lowest pressure in a refrigeration cycle occurs in the evaporator, and this pressure should be above atmospheric pressure to prevent any air leakage into the refrigeration system. Therefore, a refrigerant should have a saturation pressure of 1 atm or higher at 20C in this particular case. Ammonia and R-134a are two such substances. The temperature (and thus the pressure) of the refrigerant on the condenser side depends on the medium to which heat is rejected. Lower temperatures in the condenser (thus higher COPs) can be maintained if the refrigerant is cooled by liquid water instead of air. The use of water cooling cannot be justified economically, however, except in large industrial refrigeration systems. The temperature of the refrigerant in the condenser cannot fall below the temperature of the cooling medium (about 20C for a household refrigerator), and the saturation pressure of the refrigerant at this temperature should be well below its critical pressure if the heat rejection process is to be approximately isothermal. If no single refrigerant can meet the temperature requirements, then two or more refrigeration cycles with different refrigerants can be used in series. Such a refrigeration system is called a cascade system and is discussed later in this chapter. Other desirable characteristics of a refrigerant include being nontoxic, noncorrosive, nonflammable, and chemically stable; having a high enthalpy of vaporization (minimizes the mass flow rate); and, of course, being available at low cost. In the case of heat pumps, the minimum temperature (and pressure) for the refrigerant may be considerably higher since heat is usually extracted from media that are well above the temperatures encountered in refrigeration systems. 116 HEAT PUMP SYSTEMS Heat pumps are generally more expensive to purchase and install than other heating systems, but they save money in the long run in some areas because they lower the heating bills. Despite their relatively higher initial costs, the popularity of heat pumps is increasing. About one-third of all single-family homes built in the United States in the last decade are heated by heat pumps. The most common energy source for heat pumps is atmospheric air (airto-air systems), although water and soil are also used. The major problem with air-source systems is frosting, which occurs in humid climates when the temperature falls below 2 to 5C. The frost accumulation on the evapo- Chapter 11 rator coils is highly undesirable since it seriously disrupts heat transfer. The coils can be defrosted, however, by reversing the heat pump cycle (running it as an air conditioner). This results in a reduction in the efficiency of the system. Water-source systems usually use well water from depths of up to 80 m in the temperature range of 5 to 18C, and they do not have a frosting problem. They typically have higher COPs but are more complex and require easy access to a large body of water such as underground water. Ground-source systems are also rather involved since they require long tubing placed deep in the ground where the soil temperature is relatively constant. The COP of heat pumps usually ranges between 1.5 and 4, depending on the particular system used and the temperature of the source. A new class of recently developed heat pumps that use variable-speed electric motor drives are at least twice as energy efficient as their predecessors. Both the capacity and the efficiency of a heat pump fall significantly at low temperatures. Therefore, most air-source heat pumps require a supplementary heating system such as electric resistance heaters or an oil or gas furnace. Since water and soil temperatures do not fluctuate much, supplementary heating may not be required for water-source or ground-source systems. However, the heat pump system must be large enough to meet the maximum heating load. Heat pumps and air conditioners have the same mechanical components. Therefore, it is not economical to have two separate systems to meet the heating and cooling requirements of a building. One system can be used as a heat pump in winter and an air conditioner in summer. This is accomplished by adding a reversing valve to the cycle, as shown in Fig. 119. As HEAT PUMP OPERATION--HEATING MODE Outdoor coil Reversing valve Indoor coil Fan Fan Compressor Expansion valve High-pressure liquid Low-pressure liquidvapor Low-pressure vapor High-pressure vapor HEAT PUMP OPERATION--COOLING MODE Outdoor coil Reversing valve Indoor coil Fan Fan Compressor Expansion valve | 619 FIGURE 119 A heat pump can be used to heat a house in winter and to cool it in summer. 620 | Thermodynamics a result of this modification, the condenser of the heat pump (located indoors) functions as the evaporator of the air conditioner in summer. Also, the evaporator of the heat pump (located outdoors) serves as the condenser of the air conditioner. This feature increases the competitiveness of the heat pump. Such dual-purpose units are commonly used in motels. Heat pumps are most competitive in areas that have a large cooling load during the cooling season and a relatively small heating load during the heating season, such as in the southern parts of the United States. In these areas, the heat pump can meet the entire cooling and heating needs of residential or commercial buildings. The heat pump is least competitive in areas where the heating load is very large and the cooling load is small, such as in the northern parts of the United States. 117 INNOVATIVE VAPOR-COMPRESSION REFRIGERATION SYSTEMS The simple vapor-compression refrigeration cycle discussed above is the most widely used refrigeration cycle, and it is adequate for most refrigeration applications. The ordinary vapor-compression refrigeration systems are simple, inexpensive, reliable, and practically maintenance-free (when was the last time you serviced your household refrigerator?). However, for large industrial applications efficiency, not simplicity, is the major concern. Also, for some applications the simple vapor-compression refrigeration cycle is inadequate and needs to be modified. We now discuss a few such modifications and refinements. Cascade Refrigeration Systems Some industrial applications require moderately low temperatures, and the temperature range they involve may be too large for a single vaporcompression refrigeration cycle to be practical. A large temperature range also means a large pressure range in the cycle and a poor performance for a reciprocating compressor. One way of dealing with such situations is to perform the refrigeration process in stages, that is, to have two or more refrigeration cycles that operate in series. Such refrigeration cycles are called cascade refrigeration cycles. A two-stage cascade refrigeration cycle is shown in Fig. 1110. The two cycles are connected through the heat exchanger in the middle, which serves as the evaporator for the topping cycle (cycle A) and the condenser for the bottoming cycle (cycle B). Assuming the heat exchanger is well insulated and the kinetic and potential energies are negligible, the heat transfer from the fluid in the bottoming cycle should be equal to the heat transfer to the fluid in the topping cycle. Thus, the ratio of mass flow rates through each cycle should be # mA 1h5 h8 2 # mB 1h2 # QL # Wnet,in h3 2 # mA # mB # mB 1h1 h5 2 h2 h5 h3 h8 (119) Also, COPR,cascade # mA 1h 6 h4 2 # mB 1h2 h1 2 (1110) Chapter 11 WARM environment 7 QH Condenser 6 T Decrease in compressor work QH 7 A 3 Expansion valve Condenser QL B Compressor 4 2 8 3 B 1 QL Increase in refrigeration capacity s 5 6 | 621 Expansion A Compressor valve Heat exchanger Evaporator 8 Heat 5 2 Evaporator 4 QL COLD refrigerated space 1 FIGURE 1110 A two-stage cascade refrigeration system with the same refrigerant in both stages. In the cascade system shown in the figure, the refrigerants in both cycles are assumed to be the same. This is not necessary, however, since there is no mixing taking place in the heat exchanger. Therefore, refrigerants with more desirable characteristics can be used in each cycle. In this case, there would be a separate saturation dome for each fluid, and the T-s diagram for one of the cycles would be different. Also, in actual cascade refrigeration systems, the two cycles would overlap somewhat since a temperature difference between the two fluids is needed for any heat transfer to take place. It is evident from the T-s diagram in Fig. 1110 that the compressor work decreases and the amount of heat absorbed from the refrigerated space increases as a result of cascading. Therefore, cascading improves the COP of a refrigeration system. Some refrigeration systems use three or four stages of cascading. EXAMPLE 113 A Two-Stage Cascade Refrigeration Cycle Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. Each stage operates on an ideal vaporcompression refrigeration cycle with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about 0.32 MPa. 622 | Thermodynamics (In practice, the working fluid of the lower cycle is at a higher pressure and temperature in the heat exchanger for effective heat transfer.) If the mass flow rate of the refrigerant through the upper cycle is 0.05 kg/s, determine (a) the mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat removal from the refrigerated space and the power input to the compressor, and (c) the coefficient of performance of this cascade refrigerator. Solution A cascade refrigeration system operating between the specified pressure limits is considered. The mass flow rate of the refrigerant through the lower cycle, the rate of refrigeration, the power input, and the COP are to be determined. Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. 3 The heat exchanger is adiabatic. Properties The enthalpies of the refrigerant at all eight states are determined from the refrigerant tables and are indicated on the T-s diagram. Analysis The T-s diagram of the refrigeration cycle is shown in Fig. 1111. The topping cycle is labeled cycle A and the bottoming one, cycle B. For both cycles, the refrigerant leaves the condenser as a saturated liquid and enters the compressor as saturated vapor. (a) The mass flow rate of the refrigerant through the lower cycle is determined from the steady-flow energy balance on the adiabatic heat exchanger, # E out 10.05 kg>s2 3 1251.88 # # # E in m Ah5 mBh3 # m A 1h 5 h 8 2 95.47 2 kJ>kg4 # mB # # mAh8 mBh2 # mB 1h2 h 3 2 # mB 3 1255.93 55.16 2 kJ>kg 4 0.0390 kg/s (b) The rate of heat removal by a cascade cycle is the rate of heat absorption in the evaporator of the lowest stage. The power input to a cascade cycle is the sum of the power inputs to all of the compressors: # QL # Win # m B 1h 1 h 4 2 10.0390 kg>s2 3 1239.16 55.162 kJ>kg 4 # # # # Wcomp I,in Wcomp II,in mA 1h6 h 5 2 mB 1h 2 h 1 2 T h3 = 55.16 h7 = 95.47 6 h6 = 270.92 kJ/kg 2 0.8 MPa A 0.32 MPa 5 8 h8 = 95.47 B 0.14 MPa 4 h4 = 55.16 1 h2 = 255.93 7.18 kW 7 3 h5 = 251.88 h1 = 239.16 FIGURE 1111 T-s diagram of the cascade refrigeration cycle described in Example 113. s Chapter 11 10.05 kg>s2 3 1270.92 1.61 kW (c) The COP of a refrigeration system is the ratio of the refrigeration rate to the net power input: | 623 10.039 kg>s2 3 1255.93 251.88 2 kJ>kg4 239.162 kJ>kg4 COPR # QL # Wnet,in 7.18 kW 1.61 kW 4.46 Discussion This problem was worked out in Example 111 for a single-stage refrigeration system. Notice that the COP of the refrigeration system increases from 3.97 to 4.46 as a result of cascading. The COP of the system can be increased even more by increasing the number of cascade stages. Multistage Compression Refrigeration Systems When the fluid used throughout the cascade refrigeration system is the same, the heat exchanger between the stages can be replaced by a mixing chamber (called a flash chamber) since it has better heat transfer characteristics. Such systems are called multistage compression refrigeration systems. A twostage compression refrigeration system is shown in Fig. 1112. WARM environment QH 5 Condenser 4 T 4 Expansion valve 6 High-pressure compressor 5 9 2 Flash chamber 3 7 Expansion valve 8 Evaporator QL COLD refrigerated space s Low-pressure compressor 1 2 7 9 6 3 1 8 FIGURE 1112 A two-stage compression refrigeration system with a flash chamber. 624 | Thermodynamics In this system, the liquid refrigerant expands in the first expansion valve to the flash chamber pressure, which is the same as the compressor interstage pressure. Part of the liquid vaporizes during this process. This saturated vapor (state 3) is mixed with the superheated vapor from the low-pressure compressor (state 2), and the mixture enters the high-pressure compressor at state 9. This is, in essence, a regeneration process. The saturated liquid (state 7) expands through the second expansion valve into the evaporator, where it picks up heat from the refrigerated space. The compression process in this system resembles a two-stage compression with intercooling, and the compressor work decreases. Care should be exercised in the interpretations of the areas on the T-s diagram in this case since the mass flow rates are different in different parts of the cycle. EXAMPLE 114 A Two-Stage Refrigeration Cycle with a Flash Chamber Consider a two-stage compression refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. The working fluid is refrigerant-134a. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.32 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure and cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the evaporator as a saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the amount of heat removed from the refrigerated space and the compressor work per unit mass of refrigerant flowing through the condenser, and (c) the coefficient of performance. Solution A two-stage compression refrigeration system operating between specified pressure limits is considered. The fraction of the refrigerant that evaporates in the flash chamber, the refrigeration and work input per unit mass, and the COP are to be determined. Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. 3 The flash chamber is adiabatic. Properties The enthalpies of the refrigerant at various states are determined from the refrigerant tables and are indicated on the T-s diagram. Analysis The T-s diagram of the refrigeration cycle is shown in Fig. 1113. We note that the refrigerant leaves the condenser as saturated liquid and enters the low-pressure compressor as saturated vapor. (a) The fraction of the refrigerant that evaporates as it is throttled to the flash chamber is simply the quality at state 6, which is x6 h6 h fg hf 95.47 55.16 196.71 0.2049 (b) The amount of heat removed from the refrigerated space and the compressor work input per unit mass of refrigerant flowing through the condenser are qL 11 11 x6 2 1h1 0.20492 3 1239.16 h8 2 55.16 2 kJ>kg4 146.3 kJ/kg Chapter 11 T 4 h4 = 274.48 kJ/kg | 625 h5 = 95.47 5 h7 = 55.16 7 h6 = 95.47 6 h3 = 251.88 9 3 2 h2 = 255.93 h9 = 255.10 h1 = 239.16 8 h = 55.16 8 1 s FIGURE 1113 T-s diagram of the two-stage compression refrigeration cycle described in Example 114. and win wcomp I,in wcomp II,in 11 x6 2 1h2 h1 2 112 1h 4 h9 2 The enthalpy at state 9 is determined from an energy balance on the mixing chamber, 112 h9 h9 Also, s9 s9) is h4 # Eout # Ein x6h3 10.20492 1251.882 11 x6 2h2 11 0.20492 1255.932 1274.48 255.10 kJ>kg win 11 0.9416 kJ/kg K. Thus the enthalpy at state 4 (0.8 MPa, s4 274.48 kJ/kg. Substituting, 0.20492 3 1255.93 239.162 kJ>kg4 255.102 kJ>kg 32.71 kJ/kg (c) The coefficient of performance is COPR qL win 146.3 kJ>kg 32.71 kJ>kg 4.47 Discussion This problem was worked out in Example 111 for a single-stage refrigeration system (COP 3.97) and in Example 113 for a two-stage cascade refrigeration system (COP 4.46). Notice that the COP of the refrigeration system increased considerably relative to the single-stage compression but did not change much relative to the two-stage cascade compression. Multipurpose Refrigeration Systems with a Single Compressor Some applications require refrigeration at more than one temperature. This could be accomplished by using a separate throttling valve and a separate compressor for each evaporator operating at different temperatures. However, such a system is bulky and probably uneconomical. A more practical and 626 | Thermodynamics Kitchen air QH 3 Condenser 2 2 Compressor 5 QL,R Expansion valve 6 A (Alternative path) Freezer 1 3 4 QL,R A 6 QL,F 1 5 QH T Expansion valve 4 Refrigerator QL,F s FIGURE 1114 Schematic and T-s diagram for a refrigeratorfreezer unit with one compressor. economical approach would be to route all the exit streams from the evaporators to a single compressor and let it handle the compression process for the entire system. Consider, for example, an ordinary refrigeratorfreezer unit. A simplified schematic of the unit and the T-s diagram of the cycle are shown in Fig. 1114. Most refrigerated goods have a high water content, and the refrigerated space must be maintained above the ice point to prevent freezing. The freezer compartment, however, is maintained at about 18C. Therefore, the refrigerant should enter the freezer at about 25C to have heat transfer at a reasonable rate in the freezer. If a single expansion valve and evaporator were used, the refrigerant would have to circulate in both compartments at about 25C, which would cause ice formation in the neighborhood of the evaporator coils and dehydration of the produce. This problem can be eliminated by throttling the refrigerant to a higher pressure (hence temperature) for use in the refrigerated space and then throttling it to the minimum pressure for use in the freezer. The entire refrigerant leaving the freezer compartment is subsequently compressed by a single compressor to the condenser pressure. Liquefaction of Gases The liquefaction of gases has always been an important area of refrigeration since many important scientific and engineering processes at cryogenic temperatures (temperatures below about 100C) depend on liquefied gases. Some examples of such processes are the separation of oxygen and nitrogen from air, preparation of liquid propellants for rockets, the study of material properties at low temperatures, and the study of some exciting phenomena such as superconductivity. Chapter 11 At temperatures above the critical-point value, a substance exists in the gas phase only. The critical temperatures of helium, hydrogen, and nitrogen (three commonly used liquefied gases) are 268, 240, and 147C, respectively. Therefore, none of these substances exist in liquid form at atmospheric conditions. Furthermore, low temperatures of this magnitude cannot be obtained by ordinary refrigeration techniques. Then the question that needs to be answered in the liquefaction of gases is this: How can we lower the temperature of a gas below its critical-point value? Several cycles, some complex and others simple, are used successfully for the liquefaction of gases. Below we discuss the Linde-Hampson cycle, which is shown schematically and on a T-s diagram in Fig. 1115. Makeup gas is mixed with the uncondensed portion of the gas from the previous cycle, and the mixture at state 2 is compressed by a multistage compressor to state 3. The compression process approaches an isothermal process due to intercooling. The high-pressure gas is cooled in an aftercooler by a cooling medium or by a separate external refrigeration system to state 4. The gas is further cooled in a regenerative counter-flow heat exchanger by the uncondensed portion of gas from the previous cycle to state 5, and it is throttled to state 6, which is a saturated liquidvapor mixture state. The liquid (state 7) is collected as the desired product, and the vapor (state 8) is routed through the regenerator to cool the high-pressure gas approaching the throttling valve. Finally, the gas is mixed with fresh makeup gas, and the cycle is repeated. | 627 Heat exchanger 4 Multistage compressor 3 T 2 9 1 4 Q Regenerator 5 8 6 Vapor recirculated 7 6 Makeup gas 5 3 1 2 9 8 s 7 Liquid removed FIGURE 1115 Linde-Hampson system for liquefying gases. 628 | Thermodynamics This and other refrigeration cycles used for the liquefaction of gases can also be used for the solidification of gases. 118 GAS REFRIGERATION CYCLES As explained in Sec. 112, the Carnot cycle (the standard of comparison for power cycles) and the reversed Carnot cycle (the standard of comparison for refrigeration cycles) are identical, except that the reversed Carnot cycle operates in the reverse direction. This suggests that the power cycles discussed in earlier chapters can be used as refrigeration cycles by simply reversing them. In fact, the vapor-compression refrigeration cycle is essentially a modified Rankine cycle operating in reverse. Another example is the reversed Stirling cycle, which is the cycle on which Stirling refrigerators operate. In this section, we discuss the reversed Brayton cycle, better known as the gas refrigeration cycle. Consider the gas refrigeration cycle shown in Fig. 1116. The surroundings are at T0, and the refrigerated space is to be maintained at TL. The gas is compressed during process 1-2. The high-pressure, high-temperature gas at state 2 is then cooled at constant pressure to T0 by rejecting heat to the surroundings. This is followed by an expansion process in a turbine, during which the gas temperature drops to T4. (Can we achieve the cooling effect by using a throttling valve instead of a turbine?) Finally, the cool gas absorbs heat from the refrigerated space until its temperature rises to T1. WARM environment QH Heat exchanger 3 2 Wnet,in 3 Turbine Compressor 1 4 Heat exchanger QL COLD refrigerated space s 1 4 QL QH 2 T FIGURE 1116 Simple gas refrigeration cycle. Chapter 11 All the processes described are internally reversible, and the cycle executed is the ideal gas refrigeration cycle. In actual gas refrigeration cycles, the compression and expansion processes deviate from the isentropic ones, and T3 is higher than T0 unless the heat exchanger is infinitely large. On a T-s diagram, the area under process curve 4-1 represents the heat removed from the refrigerated space, and the enclosed area 1-2-3-4-1 represents the net work input. The ratio of these areas is the COP for the cycle, which may be expressed as COPR qL wnet,in qL wcomp,in wturb,out (1111) | 629 T 2 Gas refrigeration cycle 3 A 1 Reversed Carnot cycle where qL wturb,out wcomp,in h1 h3 h2 h4 h4 h1 B 4 The gas refrigeration cycle deviates from the reversed Carnot cycle because the heat transfer processes are not isothermal. In fact, the gas temperature varies considerably during heat transfer processes. Consequently, the gas refrigeration cycles have lower COPs relative to the vapor-compression refrigeration cycles or the reversed Carnot cycle. This is also evident from the T-s diagram in Fig. 1117. The reversed Carnot cycle consumes a fraction of the net work (rectangular area 1A3B) but produces a greater amount of refrigeration (triangular area under B1). Despite their relatively low COPs, the gas refrigeration cycles have two desirable characteristics: They involve simple, lighter components, which make them suitable for aircraft cooling, and they can incorporate regeneration, which makes them suitable for liquefaction of gases and cryogenic applications. An open-cycle aircraft cooling system is shown in Fig. 1118. Atmospheric air is compressed by a compressor, cooled by the surrounding air, and expanded in a turbine. The cool air leaving the turbine is then directly routed to the cabin. s FIGURE 1117 A reserved Carnot cycle produces more refrigeration (area under B1) with less work input (area 1A3B). Q Heat exchanger 3 2 Wnet,in Turbine Compressor 4 Cool air out 1 Warm air in FIGURE 1118 An open-cycle aircraft cooling system. 630 | Thermodynamics COLD refrigerated space Regenerator Heat exchanger 6 Q QH 3 Heat exchanger 1 2 3 1 2 T 5 4 WARM environment 4 6 Turbine Compressor W net,in 5 QL s FIGURE 1119 Gas refrigeration cycle with regeneration. The regenerative gas cycle is shown in Fig. 1119. Regenerative cooling is achieved by inserting a counter-flow heat exchanger into the cycle. Without regeneration, the lowest turbine inlet temperature is T0, the temperature of the surroundings or any other cooling medium. With regeneration, the high-pressure gas is further cooled to T4 before expanding in the turbine. Lowering the turbine inlet temperature automatically lowers the turbine exit temperature, which is the minimum temperature in the cycle. Extremely low temperatures can be achieved by repeating this process. T, F 2 Tmax QH 3 1 EXAMPLE 115 The Simple Ideal Gas Refrigeration Cycle 80 0 Tmin Q 4 L An ideal gas refrigeration cycle using air as the working medium is to maintain a refrigerated space at 0F while rejecting heat to the surrounding medium at 80F. The pressure ratio of the compressor is 4. Determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of performance, and (c) the rate of refrigeration for a mass flow rate of 0.1 lbm/s. Solution An ideal gas refrigeration cycle using air as the working fluid is s FIGURE 1120 T-s diagram of the ideal-gas refrigeration cycle described in Example 115. considered. The maximum and minimum temperatures, the COP, and the rate of refrigeration are to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with variable specific heats. 3 Kinetic and potential energy changes are negligible. Analysis The T-s diagram of the gas refrigeration cycle is shown in Fig. 1120. We note that this is an ideal gas-compression refrigeration cycle, and thus, both the compressor and the turbine are isentropic, and the air is cooled to the environment temperature before it enters the turbine. Chapter 11 (a) The maximum and minimum temperatures in the cycle are determined from the isentropic relations of ideal gases for the compression and expansion processes. From Table A17E, | 631 T1 Pr2 T3 Pr4 460 R h1 109.90 Btu/lbm and Pr1 0.7913 P2 163.5 Btu/lbm h P (4)(0.7913) 3.165 e 2 T2 683 R (or 223F) P1 r1 540 R h3 129.06 Btu/lbm and Pr3 1.3860 P4 86.7 Btu/lbm h P (0.25)(1.386) 0.3465 e 4 T4 363 R (or 97F) P3 r3 Therefore, the highest and the lowest temperatures in the cycle are 223 and 97F, respectively. (b) The COP of this ideal gas refrigeration cycle is COPR where qL wnet,in qL wcomp,in Wturb,out qL Wturb,out Wcomp,in Thus, h1 h3 h2 h4 h4 h1 109.9 129.06 163.5 86.7 86.7 109.9 23.2 Btu>lbm 42.36 Btu>lbm 53.6 Btu>lbm COPR (c) The rate of refrigeration is 53.6 23.2 42.36 2.06 # Q refrig # m 1qL 2 10.1 lbm>s2 123.2 Btu>lbm2 2.32 Btu/s Discussion It is worth noting that an ideal vapor-compression cycle working under similar conditions would have a COP greater than 3. 119 ABSORPTION REFRIGERATION SYSTEMS Another form of refrigeration that becomes economically attractive when there is a source of inexpensive thermal energy at a temperature of 100 to 200C is absorption refrigeration. Some examples of inexpensive thermal energy sources include geothermal energy, solar energy, and waste heat from cogeneration or process steam plants, and even natural gas when it is available at a relatively low price. As the name implies, absorption refrigeration systems involve the absorption of a refrigerant by a transport medium. The most widely used absorption refrigeration system is the ammoniawater system, where ammonia (NH3) serves as the refrigerant and water (H2O) as the transport medium. Other absorption refrigeration systems include waterlithium bromide and waterlithium chloride systems, where water serves as the refrigerant. The latter two systems are limited to applications such as air-conditioning where the minimum temperature is above the freezing point of water. 632 | Thermodynamics To understand the basic principles involved in absorption refrigeration, we examine the NH3H2O system shown in Fig. 1121. The ammoniawater refrigeration machine was patented by the Frenchman Ferdinand Carre in 1859. Within a few years, the machines based on this principle were being built in the United States primarily to make ice and store food. You will immediately notice from the figure that this system looks very much like the vapor-compression system, except that the compressor has been replaced by a complex absorption mechanism consisting of an absorber, a pump, a generator, a regenerator, a valve, and a rectifier. Once the pressure of NH3 is raised by the components in the box (this is the only thing they are set up to do), it is cooled and condensed in the condenser by rejecting heat to the surroundings, is throttled to the evaporator pressure, and absorbs heat from the refrigerated space as it flows through the evaporator. So, there is nothing new there. Here is what happens in the box: Ammonia vapor leaves the evaporator and enters the absorber, where it dissolves and reacts with water to form NH3 H2O. This is an exothermic reaction; thus heat is released during this process. The amount of NH3 that can be dissolved in H2O is inversely proportional to the temperature. Therefore, it is necessary to cool the absorber to maintain its temperature as low as possible, hence to maximize the amount of NH3 dissolved in water. The H2O solution, which is rich in NH3, is then pumped to the liquid NH3 generator. Heat is transferred to the solution from a source to vaporize some of the solution. The vapor, which is rich in NH3, passes through a rectifier, which separates the water and returns it to the generator. The high-pressure pure NH3 vapor then continues its journey through the rest of the cycle. The WARM environment Qgen QH Condenser Pure NH3 NH3 + H2O Rectifier Generator Solar energy H2O Q Expansion valve Expansion valve Regenerator Absorber Pure NH3 NH3 + H2O Evaporator QL Wpump Qcool Cooling water Pump FIGURE 1121 Ammonia absorption refrigeration cycle. COLD refrigerated space Chapter 11 hot NH3 H2O solution, which is weak in NH3, then passes through a regenerator, where it transfers some heat to the rich solution leaving the pump, and is throttled to the absorber pressure. Compared with vapor-compression systems, absorption refrigeration systems have one major advantage: A liquid is compressed instead of a vapor. The steady-flow work is proportional to the specific volume, and thus the work input for absorption refrigeration systems is very small (on the order of one percent of the heat supplied to the generator) and often neglected in the cycle analysis. The operation of these systems is based on heat transfer from an external source. Therefore, absorption refrigeration systems are often classified as heat-driven systems. The absorption refrigeration systems are much more expensive than the vapor-compression refrigeration systems. They are more complex and occupy more space, they are much less efficient thus requiring much larger cooling towers to reject the waste heat, and they are more difficult to service since they are less common. Therefore, absorption refrigeration systems should be considered only when the unit cost of thermal energy is low and is projected to remain low relative to electricity. Absorption refrigeration systems are primarily used in large commercial and industrial installations. The COP of absorption refrigeration systems is defined as COPabsorption Desired output Required input Q gen QL Wpump,in QL Q gen (1112) | 633 The maximum COP of an absorption refrigeration system is determined by assuming that the entire cycle is totally reversible (i.e., the cycle involves no irreversibilities and any heat transfer is through a differential temperature difference). The refrigeration system would be reversible if the heat from the source (Qgen) were transferred to a Carnot heat engine, and the work output of this heat engine (W hth,rev Qgen) is supplied to a Carnot refrigerator to W COPR,rev remove heat from the refrigerated space. Note that QL hth,rev QgenCOPR,rev. Then the overall COP of an absorption refrigeration system under reversible conditions becomes (Fig. 1122) COPrev,absorption QL Q gen hth,revCOPR,rev a1 T0 TL ba b Ts T0 TL (1113) Source Ts Qgen Environment T0 Reversible heat engine W = hrev Qgen Reversible refrigerator QL = COPR,rev W T0 environment TL Refrigerated space where TL, T0, and Ts are the thermodynamic temperatures of the refrigerated space, the environment, and the heat source, respectively. Any absorption refrigeration system that receives heat from a source at Ts and removes heat from the refrigerated space at TL while operating in an environment at T0 has a lower COP than the one determined from Eq. 1113. For example, when the source is at 120C, the refrigerated space is at 10C, and the environment is at 25C, the maximum COP that an absorption refrigeration system can have is 1.8. The COP of actual absorption refrigeration systems is usually less than 1. Air-conditioning systems based on absorption refrigeration, called absorption chillers, perform best when the heat source can supply heat at a high temperature with little temperature drop. The absorption chillers are typically rated at an input temperature of 116C (240F). The chillers perform at lower temperatures, but their cooling capacity decreases sharply with W = hrev Qgen = 1 QL = COPR,revW = COPrev,absorption = ( T0 Q Ts gen TL W T0 TL ) ( QL TL T = 1 0 Qgen Ts T0 TL ) ( )( ) FIGURE 1122 Determining the maximum COP of an absorption refrigeration system. 634 | Thermodynamics decreasing source temperature, about 12.5 percent for each 6C (10F) drop in the source temperature. For example, the capacity goes down to 50 percent when the supply water temperature drops to 93C (200F). In that case, one needs to double the size (and thus the cost) of the chiller to achieve the same cooling. The COP of the chiller is affected less by the decline of the source temperature. The COP drops by 2.5 percent for each 6C (10F) drop in the source temperature. The nominal COP of single-stage absorption at chillers 116C (240F) is 0.65 to 0.70. Therefore, for each ton of refrigeration, a heat input of (12,000 Btu/h)/0.65 18,460 Btu/h is required. At 88C (190F ), the COP drops by 12.5 percent and thus the heat input increases by 12.5 percent for the same cooling effect. Therefore, the economic aspects must be evaluated carefully before any absorption refrigeration system is considered, especially when the source temperature is below 93C (200F ). Another absorption refrigeration system that is quite popular with campers is a propane-fired system invented by two Swedish undergraduate students. In this system, the pump is replaced by a third fluid (hydrogen), which makes it a truly portable unit. TOPIC OF SPECIAL INTEREST* Metal A I I Thermoelectric Power Generation and Refrigeration Systems All the refrigeration systems discussed above involve many moving parts and bulky, complex components. Then this question comes to mind: Is it really necessary for a refrigeration system to be so complex? Can we not achieve the same effect in a more direct way? The answer to this question is yes. It is possible to use electric energy more directly to produce cooling without involving any refrigerants and moving parts. Below we discuss one such system, called thermoelectric refrigerator. Consider two wires made from different metals joined at both ends (junctions), forming a closed circuit. Ordinarily, nothing will happen. However, when one of the ends is heated, something interesting happens: A current flows continuously in the circuit, as shown in Fig. 1123. This is called the Seebeck effect, in honor of Thomas Seebeck, who made this discovery in 1821. The circuit that incorporates both thermal and electrical effects is called a thermoelectric circuit, and a device that operates on this circuit is called a thermoelectric device. The Seebeck effect has two major applications: temperature measurement and power generation. When the thermoelectric circuit is broken, as shown in Fig. 1124, the current ceases to flow, and we can measure the driving force (the electromotive force) or the voltage generated in the circuit by a voltmeter. The voltage generated is a function of the temperature difference and the materials of the two wires used. Therefore, temperature can be measured by simply measuring voltages. The two wires used to measure the temperature in *This section can be skipped without a loss in continuity. Metal B FIGURE 1123 When one of the junctions of two dissimilar metals is heated, a current I flows through the closed circuit. Metal A I=0 Metal B + V FIGURE 1124 When a thermoelectric circuit is broken, a potential difference is generated. Chapter 11 this manner form a thermocouple, which is the most versatile and most widely used temperature measurement device. A common T-type thermocouple, for example, consists of copper and constantan wires, and it produces about 40 mV per C difference. The Seebeck effect also forms the basis for thermoelectric power generation. The schematic diagram of a thermoelectric generator is shown in Fig. 1125. Heat is transferred from a high-temperature source to the hot junction in the amount of QH, and it is rejected to a low-temperature sink from the cold junction in the amount of QL. The difference between these two quantities is the net electrical work produced, that is, We QH QL. It is evident from Fig. 1125 that the thermoelectric power cycle closely resembles an ordinary heat engine cycle, with electrons serving as the working fluid. Therefore, the thermal efficiency of a thermoelectric generator operating between the temperature limits of TH and TL is limited by the efficiency of a Carnot cycle operating between the same temperature limits. Thus, in the absence of any irreversibilities (such as I 2R heating, where R is the total electrical resistance of the wires), the thermoelectric generator will have the Carnot efficiency. The major drawback of thermoelectric generators is their low efficiency. The future success of these devices depends on finding materials with more desirable characteristics. For example, the voltage output of thermoelectric devices has been increased several times by switching from metal pairs to semiconductors. A practical thermoelectric generator using n-type (heavily doped to create excess electrons) and p-type (heavily doped to create a deficiency of electrons) materials connected in series is shown in Fig. 1126. Despite their low efficiencies, thermoelectric generators have definite weight and reliability advantages and are presently used in rural areas and in space applications. For example, silicongermanium-based thermoelectric generators have been powering Voyager spacecraft since 1980 and are expected to continue generating power for many more years. If Seebeck had been fluent in thermodynamics, he would probably have tried reversing the direction of flow of electrons in the thermoelectric circuit (by externally applying a potential difference in the reverse direction) to create a refrigeration effect. But this honor belongs to Jean Charles Athanase Peltier, who discovered this phenomenon in 1834. He noticed during his experiments that when a small current was passed through the junction of two dissimilar wires, the junction was cooled, as shown in Fig. 1127. This is called the Peltier effect, and it forms the basis for thermoelectric refrigeration. A practical thermoelectric refrigeration circuit using semiconductor materials is shown in Fig. 1128. Heat is absorbed from the refrigerated space in the amount of QL and rejected to the warmer environment in the amount of QH. The difference between these two quantities is the net electrical work that needs to be supplied; that is, We QH QL. Thermoelectric refrigerators presently cannot compete with vapor-compression refrigeration systems because of their low coefficient of performance. They are available in the market, however, and are preferred in some applications because of their small size, simplicity, quietness, and reliability. | 635 High-temperature source TH QH Hot junction I Wnet I Cold junction QL Low-temperature sink TL FIGURE 1125 Schematic of a simple thermoelectric power generator. SOURCE QH Hot plate p + Cold plate QL SINK n p n p n I Wnet FIGURE 1126 A thermoelectric power generator. 636 Heat rejected | Thermodynamics Heat absorbed EXAMPLE 116 Cooling of a Canned Drink by a Thermoelectric Refrigerator + FIGURE 1127 When a current is passed through the junction of two dissimilar materials, the junction is cooled. WARM environment QH Hot plate p n p n p n A thermoelectric refrigerator that resembles a small ice chest is powered by a car battery and has a COP of 0.1. If the refrigerator cools a 0.350-L canned drink from 20 to 4C in 30 min, determine the average electric power consumed by the thermoelectric refrigerator. Solution A thermoelectric refrigerator with a specified COP is used to cool canned drinks. The power consumption of the refrigerator is to be determined. Assumptions Heat transfer through the walls of the refrigerator is negligible during operation. Properties The properties of canned drinks are the same as those of water at room temperature, r 1 kg/L and c 4.18 kJ/kg C (Table A3). Analysis The cooling rate of the refrigerator is simply the rate of decrease of the energy of the canned drinks, m Q cooling rV 11 kg>L2 10.350 L2 Qcooling t 0.350 kg 42C 13 W 23.4 kJ 10.350 kg 2 14.18 kJ>kg # C2 120 23.4 kJ 30 60 s # Q cooling COPR 0.0130 kW mc T # Qcooling Cold plate QL Refrigerated space + I Then the average power consumed by the refrigerator becomes # Win 13 W 0.10 130 W FIGURE 1128 A thermoelectric refrigerator. Discussion In reality, the power consumption will be larger because of the heat gain through the walls of the refrigerator. SUMMARY The transfer of heat from lower temperature regions to higher temperature ones is called refrigeration. Devices that produce refrigeration are called refrigerators, and the cycles on which they operate are called refrigeration cycles. The working fluids used in refrigerators are called refrigerants. Refrigerators used for the purpose of heating a space by transferring heat from a cooler medium are called heat pumps. The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP), defined as COPR Desired output Required output Desired output Required input Cooling effect Work input Heating effect Work input QL Wnet,in QH Wnet,in The standard of comparison for refrigeration cycles is the reversed Carnot cycle. A refrigerator or heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump, and their COPs are COPR,Carnot COPHP,Carnot 1 TH>TL 1 1 1 TL >TH COPHP The most widely used refrigeration cycle is the vaporcompression refrigeration cycle. In an ideal vapor-compression refrigeration cycle, the refrigerant enters the compressor as a saturated vapor and is cooled to the saturated liquid state in the condenser. It is then throttled to the evaporator pressure and vaporizes as it absorbs heat from the refrigerated space. Chapter 11 Very low temperatures can be achieved by operating two or more vapor-compression systems in series, called cascading. The COP of a refrigeration system also increases as a result of cascading. Another way of improving the performance of a vapor-compression refrigeration system is by using multistage compression with regenerative cooling. A refrigerator with a single compressor can provide refrigeration at several temperatures by throttling the refrigerant in stages. The vapor-compression refrigeration cycle can also be used to liquefy gases after some modifications. The power cycles can be used as refrigeration cycles by simply reversing them. Of these, the reversed Brayton cycle, which is also known as the gas refrigeration cycle, is used to cool aircraft and to obtain very low (cryogenic) temperatures after it is modified with regeneration. The work output of the turbine can be used to reduce the work input requirements to the compressor. Thus the COP of a gas refrigeration cycle is COPabsorption qL wnet,in qL wcomp,in wturb,out | 637 Another form of refrigeration that becomes economically attractive when there is a source of inexpensive thermal energy at a temperature of 100 to 200C is absorption refrigeration, where the refrigerant is absorbed by a transport medium and compressed in liquid form. The most widely used absorption refrigeration system is the ammoniawater system, where ammonia serves as the refrigerant and water as the transport medium. The work input to the pump is usually very small, and the COP of absorption refrigeration systems is defined as COPabsorption Desired output Required input Q gen QL Wpump,in QL Q gen The maximum COP an absorption refrigeration system can have is determined by assuming totally reversible conditions, which yields COPrev,absorption hth,rev COPR,rev a1 T0 TL ba b Ts T0 TL where T0, TL, and Ts are the thermodynamic temperatures of the environment, the refrigerated space, and the heat source, respectively. REFERENCES AND SUGGESTED READINGS 1. ASHRAE, Handbook of Fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1985. 2. Heat Pump Systems--A Technology Review. OECD Report, Paris, 1982. 3. B. Nagengast. "A Historical Look at CFC Refrigerants." ASHRAE Journal 30, no. 11 (November 1988), pp. 3739. 4. W. F. Stoecker. "Growing Opportunities for Ammonia Refrigeration." Proceedings of the Meeting of the International Institute of Ammonia Refrigeration, Austin, Texas, 1989. 5. W. F. Stoecker and J. W. Jones. Refrigeration and Air Conditioning. 2nd ed. New York: McGraw-Hill, 1982. 6. K. Wark and D. E. Richards. Thermodynamics. 6th ed. New York: McGraw-Hill, 1999. PROBLEMS* The Reversed Carnot Cycle 111C Why is the reversed Carnot cycle executed within the saturation dome not a realistic model for refrigeration cycles? *Problems designated by a "C" are concept questions, and students are encouraged to answer them all. Problems designated by an "E" are in English units, and the SI users can ignore them. Problems with a CD-EES icon are solved using EES, and complete solutions together with parametric studies are included on the enclosed DVD. Problems with a computer-EES icon are comprehensive in nature, and are intended to be solved with a computer, preferably using the EES software that accompanies this text. 112 A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the working fluid. The refrigerant changes from saturated vapor to saturated liquid at 30C in the condenser as it rejects heat. The evaporator pressure is 160 kPa. Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the amount of heat absorbed from the refrigerated space, and (c) the net work input. Answers: (a) 5.64, (b) 147 kJ/kg, (c) 26.1 kJ/kg 113E Refrigerant-134a enters the condenser of a steadyflow Carnot refrigerator as a saturated vapor at 90 psia, and it leaves with a quality of 0.05. The heat absorption from the refrigerated space takes place at a pressure of 30 psia. Show 638 | Thermodynamics the condenser at 18C at a rate of 0.25 kg/s and leaves at 26C. The refrigerant enters the condenser at 1.2 MPa and 65C and leaves at 42C. The inlet state of the compressor is 60 kPa and 34C and the compressor is estimated to gain a net heat of 450 W from the surroundings. Determine (a) the quality of the refrigerant at the evaporator inlet, (b) the refrigeration load, (c) the COP of the refrigerator, and (d) the theoretical maximum refrigeration load for the same power input to the compressor. 1112 A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.12 and 0.7 MPa. The mass flow rate of the refrigerant is 0.05 kg/s. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the rate of heat rejection to the environment, and (c) the coefficient of performance. Answers: (a) 7.41 kW, 1.83 kW, (b) 9.23 kW, (c) 4.06 the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the quality at the beginning of the heat-absorption process, and (c) the net work input. Ideal and Actual Vapor-Compression Refrigeration Cycles 114C Does the ideal vapor-compression refrigeration cycle involve any internal irreversibilities? 115C Why is the throttling valve not replaced by an isentropic turbine in the ideal vapor-compression refrigeration cycle? 116C It is proposed to use water instead of refrigerant134a as the working fluid in air-conditioning applications where the minimum temperature never falls below the freezing point. Would you support this proposal? Explain. 117C In a refrigeration system, would you recommend condensing the refrigerant-134a at a pressure of 0.7 or 1.0 MPa if heat is to be rejected to a cooling medium at 15C? Why? 118C Does the area enclosed by the cycle on a T-s diagram represent the net work input for the reversed Carnot cycle? How about for the ideal vapor-compression refrigeration cycle? 119C Consider two vapor-compression refrigeration cycles. The refrigerant enters the throttling valve as a saturated liquid at 30C in one cycle and as subcooled liquid at 30C in the other one. The evaporator pressure for both cycles is the same. Which cycle do you think will have a higher COP? 1110C The COP of vapor-compression refrigeration cycles improves when the refrigerant is subcooled before it enters the throttling valve. Can the refrigerant be subcooled indefinitely to maximize this effect, or is there a lower limit? Explain. 1111 A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at 30C by rejecting its waste heat to cooling water that enters 26C QH 42C 3 Condenser 2 Water 18C 1.2 MPa 65C Qin Win 1113 Repeat Prob. 1112 for a condenser pressure of 0.9 MPa. 1114 If the throttling valve in Prob. 1112 is replaced by an isentropic turbine, determine the percentage increase in the COP and in the rate of heat removal from the refrigerated space. Answers: 4.2 percent, 4.2 percent Consider a 300 kJ/min refrigeration system that operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 140 kPa and is compressed to 800 kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the quality of the refrigerant at the end of the throttling process, (b) the coefficient of performance, and (c) the power input to the compressor. 1116 Reconsider Prob. 1115. Using EES (or other) software, investigate the effect of evaporator pressure on the COP and the power input. Let the evaporator pressure vary from 100 to 400 kPa. Plot the COP and the power input as functions of evaporator pressure, and discuss the results. 1115 Expansion valve Compressor 1117 Repeat Prob. 1115 assuming an isentropic efficiency of 85 percent for the compressor. Also, determine the rate of exergy destruction associated with the compression process in this case. Take T0 298 K. 1118 Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 MPa and 10C at a rate of 0.12 kg/s, and it leaves at 0.7 MPa and 50C. The refrigerant is cooled in the condenser to 24C and 0.65 MPa, and it is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the rate of heat removal from the refrigerated 60 kPa 34C Evaporator 4 1 Q L FIGURE P1111 Chapter 11 space and the power input to the compressor, (b) the isentropic efficiency of the compressor, and (c) the COP of the refrigerator. Answers: (a) 19.4 kW, 5.06 kW, (b) 82.5 percent, (c) 3.83 1119E An ice-making machine operates on the ideal vapor-compression cycle, using refrigerant-134a. The refrigerant enters the compressor as saturated vapor at 20 psia and leaves the condenser as saturated liquid at 80 psia. Water enters the ice machine at 55F and leaves as ice at 25F. For an ice production rate of 15 lbm/h, determine the power input to the ice machine (169 Btu of heat needs to be removed from each lbm of water at 55F to turn it into ice at 25F). 1120 Refrigerant-134a enters the compressor of a refrigerator at 140 kPa and 10C at a rate of 0.3 m3/min and leaves at 1 MPa. The isentropic efficiency of the compressor is 78 percent. The refrigerant enters the throttling valve at 0.95 MPa and 30C and leaves the evaporator as saturated vapor at 18.5C. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the power input to the compressor, (b) the rate of heat removal from the refrigerated space, and (c) the pressure drop and rate of heat gain in the line between the evaporator and the compressor. Answers: (a) 1.88 kW, (b) 4.99 kW, (c) 1.65 kPa, 0.241 kW | 639 60C. If the compressor consumes 450 W of power, determine (a) the mass flow rate of the refrigerant, (b) the condenser pressure, and (c) the COP of the refrigerator. Answers: (a) 0.00727 kg/s, (b) 672 kPa, (c) 2.43 Selecting the Right Refrigerant 1123C When selecting a refrigerant for a certain application, what qualities would you look for in the refrigerant? 1124C Consider a refrigeration system using refrigerant134a as the working fluid. If this refrigerator is to operate in an environment at 30C, what is the minimum pressure to which the refrigerant should be compressed? Why? 1125C A refrigerant-134a refrigerator is to maintain the refrigerated space at 10C. Would you recommend an evaporator pressure of 0.12 or 0.14 MPa for this system? Why? 1126 A refrigerator that operates on the ideal vaporcompression cycle with refrigerant-134a is to maintain the refrigerated space at 10C while rejecting heat to the environment at 25C. Select reasonable pressures for the evaporator and the condenser, and explain why you chose those values. 1127 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house and maintain it at 22C by using underground water at 10C as the heat source. Select reasonable pressures for the evaporator and the condenser, and explain why you chose those values. Reconsider Prob. 1120. Using EES (or other) software, investigate the effects of varying the compressor isentropic efficiency over the range 60 to 100 percent and the compressor inlet volume flow rate from 0.1 to 1.0 m3/min on the power input and the rate of refrigeration. Plot the rate of refrigeration and the power input to the compressor as functions of compressor efficiency for compressor inlet volume flow rates of 0.1, 0.5, and 1.0 m3/min, and discuss the results. 1122 A refrigerator uses refrigerant-134a as the working fluid and operates on the ideal vapor-compression refrigeration cycle. The refrigerant enters the evaporator at 120 kPa with a quality of 30 percent and leaves the compressor at 1121 Heat Pump Systems 1128C Do you think a heat pump system will be more cost-effective in New York or in Miami? Why? 1129C What is a water-source heat pump? How does the COP of a water-source heat pump system compare to that of an air-source system? 1130E A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house and maintain it at 75F by using underground water at 50F as the heat source. The house is losing heat at a rate of 60,000 Btu/h. The evaporator and condenser pressures are 50 and 120 psia, respectively. Determine the power input to the heat pump and the electric power saved by using a heat pump instead of a resistance heater. Answers: 2.46 hp, 21.1 hp 1131 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat water from 15 to 45C at a rate of 0.12 kg/s. The condenser and evaporator pressures are 1.4 and 0.32 MPa, respectively. Determine the power input to the heat pump. 1132 A heat pump using refrigerant-134a heats a house by using underground water at 8C as the heat source. The house is losing heat at a rate of 60,000 kJ/h. The refrigerant enters the compressor at 280 kPa and 0C, and it leaves at 1 MPa Q H Condenser 3 60C 2 Expansion valve Compressor Win Evaporator 4 120 kPa x = 0.3 QL 1 FIGURE P1122 640 | Thermodynamics QH Condenser 3 2 Expansion valve and 60C. The refrigerant exits the condenser at 30C. Determine (a) the power input to the heat pump, (b) the rate of heat absorption from the water, and (c) the increase in electric power input if an electric resistance heater is used instead of a heat pump. Answers: (a) 3.55 kW, (b) 13.12 kW, (c) 13.12 kW 1133 Reconsider Prob. 1132. Using EES (or other) software, investigate the effect of varying the compressor isentropic efficiency over the range 60 to 100 percent. Plot the power input to the compressor and the electric power saved by using a heat pump rather than electric resistance heating as functions of compressor efficiency, and discuss the results. 1.4 MPa s2 = s1 Win Compressor Evaporator 4 20C x = 0.23 Water 50C 1134 Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 55C at a rate of 0.018 kg/s and leaves at 750 kPa subcooled by 3C. The refrigerant enters the compressor at 200 kPa superheated by 4C. Determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the COP of the heat pump. Also, determine (d ) the COP and the rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kPa. Q 1 Sat. 40C L FIGURE P1135 750 kPa QH Condenser subcooling of the refrigerant in the condenser, (b) the mass flow rate of the refrigerant, (c) the heating load and the COP of the heat pump, and (d) the theoretical minimum power input to the compressor for the same heating load. Answers: 800 kPa 55C 2 (a) 3.8C, (b) 0.0194 kg/s, (c) 3.07 kW, 4.68, (d) 0.238 kW Innovative Refrigeration Systems 1136C What is cascade refrigeration? What are the advantages and disadvantages of cascade refrigeration? 1137C How does the COP of a cascade refrigeration system compare to the COP of a simple vapor-compression cycle operating between the same pressure limits? 1138C A certain application requires maintaining the refrigerated space at 32C. Would you recommend a simple refrigeration cycle with refrigerant-134a or a two-stage cascade refrigeration cycle with a different refrigerant at the bottoming cycle? Why? 1139C Consider a two-stage cascade refrigeration cycle and a two-stage compression refrigeration cycle with a flash chamber. Both cycles operate between the same pressure limits and use the same refrigerant. Which system would you favor? Why? 1140C Can a vapor-compression refrigeration system with a single compressor handle several evaporators operating at different pressures? How? 1141C In the liquefaction process, why are gases compressed to very high pressures? 1142 Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. 3 Expansion valve Compressor Win Evaporator 4 QL 1 FIGURE P1134 1135 A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25C by absorbing heat from geothermal water that enters the evaporator at 50C at a rate of 0.065 kg/s and leaves at 40C. The refrigerant enters the evaporator at 20C with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. The refrigerant loses 300 W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor at 1.4 MPa at the same entropy as the inlet. Determine (a) the degrees of Chapter 11 Each stage operates on the ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about 0.4 MPa. If the mass flow rate of the refrigerant through the upper cycle is 0.24 kg/s, determine (a) the mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat removal from the refrigerated space and the power input to the compressor, and (c) the coefficient of performance of this cascade refrigerator. Answers: (a) 0.195 kg/s, (b) 34.2 kW, 7.63 kW, (c) 4.49 QH 7 Condenser 6 Expansion valve Win | 641 Compressor 8 Evaporator Heat Condenser 5 1143 Repeat Prob. 1142 for a heat exchanger pressure of 0.55 MPa. A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1 and 0.14 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.5 MPa. The refrigerant leaving the low-pressure compressor at 0.5 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 0.25 kg/s through the condenser, and (c) the coefficient of performance. 1145 Reconsider Prob. 1144. Using EES (or other) software, investigate the effect of the various refrigerants for compressor efficiencies of 80, 90, and 100 percent. Compare the performance of the refrigeration system with different refrigerants. Repeat Prob. 1144 for a flash chamber pressure of 0.32 MPa. 1144 3 2 Win Expansion valve Compressor Evaporator 4 QL 1 FIGURE P1147 1146 1147 Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where the pressure in the upper and lower cycles are 0.4 and 0.5 MPa, respectively. In both cycles, the refrigerant is a saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the isentropic efficiency of the compressor is 80 percent. If the mass flow rate of the refrigerant through the lower cycle is 0.15 kg/s, determine (a) the mass flow rate of the refrigerant through the upper cycle, (b) the rate of heat removal from the refrigerated space, and (c) the COP of this refrigerator. Answers: (a) 0.212 kg/s, (b) 25.7 kW, (c) 2.68 1148 Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the working fluid. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.45 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure and cools the refrigerated space as it vaporizes in the evaporator. The mass flow rate of the refrigerant through the low-pressure compressor is 0.15 kg/s. Assuming the refrigerant leaves the evaporator as a saturated vapor and the isentropic efficiency is 80 percent for both compressors, determine (a) the mass flow rate of the refrigerant through the high-pressure compressor, (b) the rate of heat removal from the refrigerated space, and (c) the COP of this refrigerator. Also, determine (d) the rate of heat removal and the COP if this refrigerator operated on a single-stage cycle between the same pressure limits with the same compressor efficiency and the same flow rate as in part (a). 642 | Thermodynamics QH 5 Condenser 4 Expansion valve 6 Flash chamber 7 High-pressure compressor 9 heats for air, determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Answers: (a) 6.67 kW, (b) 3.88 kW, (c) 1.72 Reconsider Prob. 1156. Using EES (or other) software, study the effects of compressor and turbine isentropic efficiencies as they are varied from 70 to 100 percent on the rate of refrigeration, the net power input, and the COP. Plot the T-s diagram of the cycle for the isentropic case. 1157 3 2 Expansion valve Low-pressure compressor 1158E Air enters the compressor of an ideal gas refrigeration cycle at 40F and 10 psia and the turbine at 120F and 30 psia. The mass flow rate of air through the cycle is 0.5 lbm/s. Determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Repeat Prob. 1156 for a compressor isentropic efficiency of 80 percent and a turbine isentropic efficiency of 85 percent. 1160 A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is 10C at the compressor inlet and 50C at the turbine inlet. Assuming adiabatic efficiencies of 80 percent for both the turbine and the compressor, determine (a) the minimum temperature in the cycle, (b) the coefficient of performance, and (c) the mass flow rate of the helium for a refrigeration rate of 18 kW. 1161 A gas refrigeration system using air as the working fluid has a pressure ratio of 4. Air enters the compressor at 7C. The high-pressure air is cooled to 27C by rejecting heat to the surroundings. It is further cooled to 15C by regenerative cooling before it enters the turbine. Assuming both the turbine and the compressor to be isentropic and using constant specific heats at room temperature, determine (a) the lowest temperature that can be obtained by this cycle, (b) the coefficient of performance of the cycle, and (c) the mass flow rate of air for a refrigeration rate of 12 kW. Answers: (a) 99.4C, (b) 1.12, (c) 0.237 kg/s 1159 Evaporator 8 QL 1 FIGURE P1148 Gas Refrigeration Cycle 1149C How does the ideal-gas refrigeration cycle differ from the Brayton cycle? 1150C Devise a refrigeration cycle that works on the reversed Stirling cycle. Also, determine the COP for this cycle. 1151C How does the ideal-gas refrigeration cycle differ from the Carnot refrigeration cycle? 1152C How is the ideal-gas refrigeration cycle modified for aircraft cooling? 1153C In gas refrigeration cycles, can we replace the turbine by an expansion valve as we did in vapor-compression refrigeration cycles? Why? 1154C How do we achieve very low temperatures with gas refrigeration cycles? 1155 An ideal gas refrigeration cycle using air as the working fluid is to maintain a refrigerated space at 23C while rejecting heat to the surrounding medium at 27C. If the pressure ratio of the compressor is 3, determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of performance, and (c) the rate of refrigeration for a mass flow rate of 0.08 kg/s. Air enters the compressor of an ideal gas refrigeration cycle at 12C and 50 kPa and the turbine at 47C and 250 kPa. The mass flow rate of air through the cycle is 0.08 kg/s. Assuming variable specific 1156 1162 Repeat Prob. 1161 assuming isentropic efficiencies of 75 percent for the compressor and 80 percent for the turbine. 1163 A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0C. The high-pressure air is cooled to 35C by rejecting heat to the surroundings. The refrigerant leaves the turbine at 80C and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using constant specific heats at room temperature, determine (a) the effectiveness of the regenerator, (b) the rate of heat removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the Chapter 11 QL Heat exch. 5 4 6 Regenerator 3 Heat exch. QH | 643 1 2 1173E Heat is supplied to an absorption refrigeration system from a geothermal well at 250F at a rate of 105 Btu/h. The environment is at 80F, and the refrigerated space is maintained at 0F. If the COP of the system is 0.55, determine the rate at which this system can remove heat from the refrigerated space. 1174 A reversible absorption refrigerator consists of a reversible heat engine and a reversible refrigerator. The system removes heat from a cooled space at 10C at a rate of 22 kW. The refrigerator operates in an environment at 25C. If the heat is supplied to the cycle by condensing saturated steam at 200C, determine (a) the rate at which the steam condenses and (b) the power input to the reversible refrigerator. (c) If the COP of an actual absorption chiller at the same temperature limits has a COP of 0.7, determine the second law efficiency of this chiller. Answers: (a) 0.00408 kg/s, (b) 2.93 kW, (c) 0.252 Turbine Compressor FIGURE P1163 same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies. Answers: (a) 0.434, (b) 21.4 kW, (c) 0.478, (d) 24.7 kW, 0.599 Ts T0 Absorption Refrigeration Systems 1164C What is absorption refrigeration? How does an absorption refrigeration system differ from a vapor-compression refrigeration system? 1165C What are the advantages and disadvantages of absorption refrigeration? 1166C Can water be used as a refrigerant in air-conditioning applications? Explain. 1167C In absorption refrigeration cycles, why is the fluid in the absorber cooled and the fluid in the generator heated? 1168C How is the coefficient of performance of an absorption refrigeration system defined? 1169C What are the functions of the rectifier and the regenerator in an absorption refrigeration system? 1170 An absorption refrigeration system that receives heat from a source at 130C and maintains the refrigerated space at 5C is claimed to have a COP of 2. If the environment temperature is 27C, can this claim be valid? Justify your answer. 1171 An absorption refrigeration system receives heat from a source at 120C and maintains the refrigerated space at 0C. If the temperature of the environment is 25C, what is the maximum COP this absorption refrigeration system can have? 1172 Heat is supplied to an absorption refrigeration system from a geothermal well at 130C at a rate of 5 105 kJ/h. The environment is at 25C, and the refrigerated space is maintained at 30C. Determine the maximum rate at which this system can remove heat from the refrigerated space. Answer: 5.75 105 kJ/h T0 TL Rev. HE Rev. Ref. FIGURE P1174 Special Topic: Thermoelectric Power Generation and Refrigeration Systems 1175C What is a thermoelectric circuit? 1176C Describe the Seebeck and the Peltier effects. 1177C Consider a circular copper wire formed by connecting the two ends of a copper wire. The connection point is now heated by a burning candle. Do you expect any current to flow through the wire? 1178C An iron and a constantan wire are formed into a closed circuit by connecting the ends. Now both junctions are heated and are maintained at the same temperature. Do you expect any electric current to flow through this circuit? 644 | Thermodynamics in the cooling mode, determine (a) the average rate of heat removal from the drink, (b) the average rate of heat supply to the coffee, and (c) the electric power drawn from the battery of the car, all in W. 1189 It is proposed to run a thermoelectric generator in conjunction with a solar pond that can supply heat at a rate of 106 kJ/h at 80C. The waste heat is to be rejected to the environment at 30C. What is the maximum power this thermoelectric generator can produce? 1179C A copper and a constantan wire are formed into a closed circuit by connecting the ends. Now one junction is heated by a burning candle while the other is maintained at room temperature. Do you expect any electric current to flow through this circuit? 1180C How does a thermocouple work as a temperature measurement device? 1181C Why are semiconductor materials preferable to metals in thermoelectric refrigerators? 1182C Is the efficiency of a thermoelectric generator limited by the Carnot efficiency? Why? 1183E A thermoelectric generator receives heat from a source at 340F and rejects the waste heat to the environment at 90F. What is the maximum thermal efficiency this thermoelectric generator can have? Answer: 31.3 percent 1184 A thermoelectric refrigerator removes heat from a refrigerated space at 5C at a rate of 130 W and rejects it to an environment at 20C. Determine the maximum coefficient of performance this thermoelectric refrigerator can have and the minimum required power input. Answers: 10.72, 12.1 W 1185 A thermoelectric cooler has a COP of 0.15 and removes heat from a refrigerated space at a rate of 180 W. Determine the required power input to the thermoelectric cooler, in W. 1186E A thermoelectric cooler has a COP of 0.15 and removes heat from a refrigerated space at a rate of 20 Btu/min. Determine the required power input to the thermoelectric cooler, in hp. 1187 A thermoelectric refrigerator is powered by a 12-V car battery that draws 3 A of current when running. The refrigerator resembles a small ice chest and is claimed to cool nine canned drinks, 0.350-L each, from 25 to 3C in 12 h. Determine the average COP of this refrigerator. Review Problems 1190 Consider a steady-flow Carnot refrigeration cycle that uses refrigerant-134a as the working fluid. The maximum and minimum temperatures in the cycle are 30 and 20C, respectively. The quality of the refrigerant is 0.15 at the beginning of the heat absorption process and 0.80 at the end. Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the condenser and evaporator pressures, and (c) the net work input. 1191 A large refrigeration plant is to be maintained at 15C, and it requires refrigeration at a rate of 100 kW. The condenser of the plant is to be cooled by liquid water, which experiences a temperature rise of 8C as it flows over the coils of the condenser. Assuming the plant operates on the ideal vapor-compression cycle using refrigerant-134a between the pressure limits of 120 and 700 kPa, determine (a) the mass flow rate of the refrigerant, (b) the power input to the compressor, and (c) the mass flow rate of the cooling water. 1192 Reconsider Prob. 1191. Using EES (or other) software, investigate the effect of evaporator pressure on the COP and the power input. Let the evaporator pressure vary from 120 to 380 kPa. Plot the COP and the power input as functions of evaporator pressure, and discuss the results. 1193 Repeat Prob. 1191 assuming the compressor has an isentropic efficiency of 75 percent. Also, determine the rate of exergy destruction associated with the compression process in this case. Take T0 25C. 1194 A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house. The mass flow rate of the refrigerant is 0.32 kg/s. The condenser and evaporator pressures are 900 and 200 kPa, respectively. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the rate of heat supply to the house, (b) the volume flow rate of the refrigerant at the compressor inlet, and (c) the COP of this heat pump. 1195 Derive a relation for the COP of the two-stage refrigeration system with a flash chamber as shown in Fig. 1112 in terms of the enthalpies and the quality at state 6. Consider a unit mass in the condenser. 1196 Consider a two-stage compression refrigeration system operating between the pressure limits of 0.8 and FIGURE P1187 1188E Thermoelectric coolers that plug into the cigarette lighter of a car are commonly available. One such cooler is claimed to cool a 12-oz (0.771-lbm) drink from 78 to 38F or to heat a cup of coffee from 75 to 130F in about 15 min in a well-insulated cup holder. Assuming an average COP of 0.2 Chapter 11 0.14 MPa. The working fluid is refrigerant-134a. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure, and it cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the amount of heat removed from the refrigerated space and the compressor work per unit mass of refrigerant flowing through the condenser, and (c) the coefficient of performance. Answers: (a) 0.165, (b) 146.4 kJ/kg, 32.6 kJ/kg, (c) 4.49 | 645 is 5000 Btu/h. Assuming the COP of the air conditioner to be 3.5, determine the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room temperature. 11103 A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0C. The high-pressure air is cooled to 35C by rejecting heat to the surroundings. The refrigerant leaves the turbine at 80C and enters the refrigerated space where it absorbs heat before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using variable specific heats, determine (a) the effectiveness of the regenerator, (b) the rate of heat removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies. 1197 An aircraft on the ground is to be cooled by a gas refrigeration cycle operating with air on an open cycle. Air enters the compressor at 30C and 100 kPa and is compressed to 250 kPa. Air is cooled to 70C before it enters the turbine. Assuming both the turbine and the compressor to be isentropic, determine the temperature of the air leaving the turbine and entering the cabin. Answer: 9C 1198 Consider a regenerative gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and 10C and is compressed to 300 kPa. Helium is then cooled to 20C by water. It then enters the regenerator where it is cooled further before it enters the turbine. Helium leaves the refrigerated space at 25C and enters the regenerator. Assuming both the turbine and the compressor to be isentropic, determine (a) the temperature of the helium at the turbine inlet, (b) the coefficient of performance of the cycle, and (c) the net power input required for a mass flow rate of 0.45 kg/s. 1199 An absorption refrigeration system is to remove heat from the refrigerated space at 10C at a rate of 12 kW while operating in an environment at 25C. Heat is to be supplied from a solar pond at 85C. What is the minimum rate of heat supply required? Answer: 9.53 kW 11100 Reconsider Prob. 1199. Using EES (or other) software, investigate the effect of the source temperature on the minimum rate of heat supply. Let the source temperature vary from 50 to 250C. Plot the minimum rate of heat supply as a function of source temperature, and discuss the results. QL Heat exch. 5 4 6 Regenerator 3 Heat exch. 1 2 Q H Turbine Compressor FIGURE P11103 11101 A typical 200-m2 house can be cooled adequately by a 3.5-ton air conditioner whose COP is 4.0. Determine the rate of heat gain of the house when the air conditioner is running continuously to maintain a constant temperature in the house. 11102 Rooms with floor areas of up to 15-m2 are cooled adequately by window air conditioners whose cooling capacity 11104 An air conditioner with refrigerant-134a as the working fluid is used to keep a room at 26C by rejecting the waste heat to the outside air at 34C. The room is gaining heat through the walls and the windows at a rate of 250 kJ/min while the heat generated by the computer, TV, and lights amounts to 900 W. An unknown amount of heat is also generated by the people in the room. The condenser and evaporator pressures are 1200 and 500 kPa, respectively. The refrigerant is saturated liquid at the condenser exit and saturated vapor at the compressor inlet. If the refrigerant enters the compressor at a rate of 100 L/min and the isentropic efficiency of the compressor is 75 percent, determine (a) the temperature of the refrigerant at the compressor exit, (b) the rate of heat generation by the people in the room, (c) the COP of the air 646 | Thermodynamics 34C QH 1200 kPa Condenser 3 2 Expansion valve Compressor Win Evaporator 4 QL 26C 1 500 kPa FIGURE P11104 conditioner, and (d ) the minimum volume flow rate of the refrigerant at the compressor inlet for the same compressor inlet and exit conditions. Answers: (a) 54.5C, (b) 670 W, (c) 5.87, (d) 15.7 L/min 11106 The vortex tube (also known as a Ranque or Hirsch tube) is a device that produces a refrigeration effect by expanding pressurized gas such as air in a tube (instead of a turbine as in the reversed Brayton cycle). It was invented and patented by Ranque in 1931 and improved by Hirsch in 1945, and is commercially available in various sizes. The vortex tube is simply a straight circular tube equipped with a nozzle, as shown in the figure. The compressed gas at temperature T1 and pressure P1 is accelerated in the nozzle by expanding it to nearly atmospheric pressure and is introduced into the tube tangentially at a very high (typically supersonic) velocity to produce a swirling motion (vortex) within the tube. The rotating gas is allowed to exit through the full-size tube that extends to the right, and the mass flow rate is controlled by a valve located about 30 diameters downstream. A smaller amount of air at the core region is allowed to escape to the left through a small aperture at the center. It is observed that the gas that is in the core region and escapes through the central aperture is cold while the gas that is in the peripheral region and escapes through the full-size tube is hot. If the temperature and the mass flow rate of the cold . stream are Tc and mc, respectively, the rate of refrigeration in the vortex tube can be expressed as # # # mccp 1T1 Tc 2 Q refrig,vortex tube mc 1h1 h c 2 where cp is the specific heat of the gas and T1 Tc is the temperature drop of the gas in the vortex tube (the cooling effect). Temperature drops as high as 60C (or 108F) are obtained at high pressure ratios of about 10. The coefficient of performance of a vortex tube can be defined as the ratio of the refrigeration rate as given above to the power used to compress the gas. It ranges from about 0.1 to 0.15, which is well below the COPs of ordinary vapor compression refrigerators. This interesting phenomenon can be explained as follows: the centrifugal force creates a radial pressure gradient in the vortex, and thus the gas at the periphery is pressurized and heated by the gas at the core region, which is cooled as a result. Also, energy is transferred from the inner layers toward the outer layers as the outer layers slow down the inner layers because of fluid viscosity that tends to produce a solid vortex. Both of these effects cause the energy and thus the temperature of the gas in the core region to decline. The conservation of energy requires the energy of the fluid at the outer layers to increase by an equivalent amount. The vortex tube has no moving parts, and thus it is inherently reliable and durable. The ready availability of the compressed air at pressures up to 10 atm in most industrial facilities makes the vortex tube particularly attractive in such settings. Despite its low efficiency, the vortex tube has found application in small-scale industrial spot-cooling operations such as cooling of soldered parts or critical electronic components, cooling drinking water, and cooling the suits of workers in hot environments. 11105 A heat pump water heater (HPWH) heats water by absorbing heat from the ambient air and transferring it to water. The heat pump has a COP of 2.2 and consumes 2 kW of electricity when running. Determine if this heat pump can be used to meet the cooling needs of a room most of the time for "free" by absorbing heat from the air in the room. The rate of heat gain of a room is usually less than 5000 kJ/h. Cold water in Cool air to the room Hot water out Water heater Warm air from the room FIGURE P11105 Chapter 11 Consider a vortex tube that receives compressed air at 500 kPa and 300 K and supplies 25 percent of it as cold air at 100 kPa and 278 K. The ambient air is at 300 K and 100 kPa, and the compressor has an isentropic efficiency of 80 percent. The air suffers a pressure drop of 35 kPa in the aftercooler and the compressed air lines between the compressor and the vortex tube. (a) Without performing any calculations, explain how the COP of the vortex tube would compare to the COP of an actual air refrigeration system based on the reversed Brayton cycle for the same pressure ratio. Also, compare the minimum temperatures that can be obtained by the two systems for the same inlet temperature and pressure. (b) Assuming the vortex tube to be adiabatic and using specific heats at room temperature, determine the exit temperature of the hot fluid stream. (c) Show, with calculations, that this process does not violate the second law of thermodynamics. (d ) Determine the coefficient of performance of this refrigeration system, and compare it to the COP of a Carnot refrigerator. | 647 Fundamentals of Engineering (FE) Exam Problems 11110 Consider a heat pump that operates on the reversed Carnot cycle with R-134a as the working fluid executed under the saturation dome between the pressure limits of 140 and 800 kPa. R-134a changes from saturated vapor to saturated liquid during the heat rejection process. The net work input for this cycle is (a) 28 kJ/kg (d) 144 kJ/kg (b) 34 kJ/kg (e) 275 kJ/kg (c) 49 kJ/kg 11111 A refrigerator removes heat from a refrigerated space at 5C at a rate of 0.35 kJ/s and rejects it to an environment at 20C. The minimum required power input is (a) 30 W (d) 124 W (b) 33 W (e) 350 W (c) 56 W 11112 A refrigerator operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 120 and 800 kPa. If the rate of heat removal from the refrigerated space is 32 kJ/s, the mass flow rate of the refrigerant is (a) 0.19 kg/s (d) 0.28 kg/s (b) 0.15 kg/s (e) 0.81 kg/s (c) 0.23 kg/s Compressed air 11113 A heat pump operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 0.32 and 1.2 MPa. If the mass flow rate of the refrigerant is 0.193 kg/s, the rate of heat supply by the heat pump to the heated space is (a) 3.3 kW (d) 31 kW (b) 23 kW (e) 45 kW (c) 26 kW Cold air Warm air FIGURE P11106 11107 Repeat Prob. 11106 for a pressure of 600 kPa at the vortex tube intake. 11108 Using EES (or other) software, investigate the effect of the evaporator pressure on the COP of an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Assume the condenser pressure is kept constant at 1 MPa while the evaporator pressure is varied from 100 kPa to 500 kPa. Plot the COP of the refrigeration cycle against the evaporator pressure, and discuss the results. Using EES (or other) software, investigate the effect of the condenser pressure on the COP of an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Assume the evaporator pressure is kept constant at 120 kPa while the condenser pressure is varied from 400 to 1400 kPa. Plot the COP of the refrigeration cycle against the condenser pressure, and discuss the results. 11114 An ideal vapor compression refrigeration cycle with R-134a as the working fluid operates between the pressure limits of 120 kPa and 1000 kPa. The mass fraction of the refrigerant that is in the liquid phase at the inlet of the evaporator is (a) 0.65 (d) 0.55 (b) 0.60 (e) 0.35 (c) 0.40 11115 Consider a heat pump that operates on the ideal vapor compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 0.32 and 1.2 MPa. The coefficient of performance of this heat pump is (a) 0.17 (d) 4.9 (b) 1.2 (e) 5.9 (c) 3.1 11109 11116 An ideal gas refrigeration cycle using air as the working fluid operates between the pressure limits of 80 and 280 kPa. Air is cooled to 35C before entering the turbine. The lowest temperature of this cycle is (a) 58C (d) 11C (b) 26C (e) 24C (c) 5C 11117 Consider an ideal gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and 10C and compressed to 250 kPa. Helium is 648 | Thermodynamics 11124 It is proposed to use a solar-powered thermoelectric system installed on the roof to cool residential buildings. The system consists of a thermoelectric refrigerator that is powered by a thermoelectric power generator whose top surface is a solar collector. Discuss the feasibility and the cost of such a system, and determine if the proposed system installed on one side of the roof can meet a significant portion of the cooling requirements of a typical house in your area. then cooled to 20C before it enters the turbine. For a mass flow rate of 0.2 kg/s, the net power input required is (a) 9.3 kW (d ) 93.5 kW (b) 27.6 kW (e) 119 kW (c) 48.8 kW 11118 An absorption air-conditioning system is to remove heat from the conditioned space at 20C at a rate of 150 kJ/s while operating in an environment at 35C. Heat is to be supplied from a geothermal source at 140C. The minimum rate of heat supply is (a) 86 kJ/s (d ) 61 kJ/s (b) 21 kJ/s (e) 150 kJ/s (c) 30 kJ/s Thermoelectric generator Waste heat SUN 11119 Consider a refrigerator that operates on the vapor compression refrigeration cycle with R-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 160 kPa, and exits at 800 kPa and 50C, and leaves the condenser as saturated liquid at 800 kPa. The coefficient of performance of this refrigerator is (a) 2.6 (d ) 3.2 (b) 1.0 (e) 4.4 (c) 4.2 Solar energy Design and Essay Problems 11120 Design a vapor-compression refrigeration system that will maintain the refrigerated space at 15C while operating in an environment at 20C using refrigerant-134a as the working fluid. 11121 Write an essay on air-, water-, and soil-based heat pumps. Discuss the advantages and the disadvantages of each system. For each system identify the conditions under which that system is preferable over the other two. In what situations would you not recommend a heat pump heating system? 11122 Consider a solar pond power plant operating on a closed Rankine cycle. Using refrigerant-134a as the working fluid, specify the operating temperatures and pressures in the cycle, and estimate the required mass flow rate of refrigerant134a for a net power output of 50 kW. Also, estimate the surface area of the pond for this level of continuous power production. Assume that the solar energy is incident on the pond at a rate of 500 W per m2 of pond area at noontime, and that the pond is capable of storing 15 percent of the incident solar energy in the storage zone. 11123 Design a thermoelectric refrigerator that is capable of cooling a canned drink in a car. The refrigerator is to be powered by the cigarette lighter of the car. Draw a sketch of your design. Semiconductor components for building thermoelectric power generators or refrigerators are available from several manufacturers. Using data from one of these manufacturers, determine how many of these components you need in your design, and estimate the coefficient of performance of your system. A critical problem in the design of thermoelectric refrigerators is the effective rejection of waste heat. Discuss how you can enhance the rate of heat rejection without using any devices with moving parts such as a fan. Thermoelectric refrigerator Electric current FIGURE P11124 11125 A refrigerator using R-12 as the working fluid keeps the refrigerated space at 15C in an environment at 30C. You are asked to redesign this refrigerator by replacing R-12 with the ozone-friendly R-134a. What changes in the pressure levels would you suggest in the new system? How do you think the COP of the new system will compare to the COP of the old system? 11126 In the 1800s, before the development of modern air-conditioning, it was proposed to cool air for buildings with the following procedure using a large pistoncylinder device ["John Gorrie: Pioneer of Cooling and Ice Making," ASHRAE Journal 33, no. 1 (Jan. 1991)]: 1. 2. 3. 4. 5. Pull in a charge of outdoor air. Compress it to a high pressure. Cool the charge of air using outdoor air. Expand it back to atmospheric pressure. Discharge the charge of air into the space to be cooled. Suppose the goal is to cool a room 6 m 10 m 2.5 m. Outdoor air is at 30C, and it has been determined that 10 air changes per hour supplied to the room at 10C could provide adequate cooling. Do a preliminary design of the system and Chapter 11 do calculations to see if it would be feasible. (You may make optimistic assumptions for the analysis.) (a) Sketch the system showing how you will drive it and how step 3 will be accomplished. (b) Determine what pressure will be required (step 2). (c) Estimate (guess) how long step 3 will take and what size will be needed for the pistoncylinder to provide the required air changes and temperature. (d ) Determine the work required in step 2 for one cycle and per hour. (e) Discuss any problems you see with the concept of your design. (Include discussion of any changes that may be required to offset optimistic assumptions.) 11127 Solar or photovoltaic (PV) cells convert sunlight to electricity and are commonly used to power calculators, satellites, remote communication systems, and even pumps. The conversion of light to electricity is called the photoelectric effect. It was first discovered in 1839 by Frenchman Edmond Becquerel, and the first PV module, which consisted of several cells connected to each other, was built in 1954 by Bell Laboratories. The PV modules today have conversion efficiencies of about 12 to 15 percent. Noting that the solar energy incident on a normal surface on earth at noontime is about 1000 W/m2 during a clear day, PV modules on a 1-m2 surface can provide as much as 150 W of electricity. The annual average daily solar energy incident on a horizontal surface in the United States ranges from about 2 to 6 kWh/m2. A PV-powered pump is to be used in Arizona to pump water for wildlife from a depth of 180 m at an average rate of 400 L/day. Assuming a reasonable efficiency for the pumping sys- | 649 tem, which can be defined as the ratio of the increase in the potential energy of the water to the electrical energy consumed by the pump, and taking the conversion efficiency of the PV cells to be 0.13 to be on the conservative side, determine the size of the PV module that needs to be installed, in m2. 11128 The temperature in a car parked in the sun can approach 100C when the outside air temperature is just 25C, and it is desirable to ventilate the parked car to avoid such high temperatures. However, the ventilating fans may run down the battery if they are powered by it. To avoid that happening, it is proposed to use the PV cells discussed in the preceding problem to power the fans. It is determined that the air in the car should be replaced once every minute to avoid excessive rise in the interior temperature. Determine if this can be accomplished by installing PV cells on part of the roof of the car. Also, find out if any car is currently ventilated this way. Solar energy Solar panels Solar-powered exhaust fan Sun PV panel FIGURE P11128 11129 A company owns a refrigeration system whose refrigeration capacity is 200 tons (1 ton of refrigeration 211 kJ/min), and you are to design a forced-air cooling system for fruits whose diameters do not exceed 7 cm under the following conditions: The fruits are to be cooled from 28C to an average temperature of 8C. The air temperature is to remain above 2C and below 10C at all times, and the velocity of air approaching the fruits must remain under 2 m/s. The cooling section can be as wide as 3.5 m and as high as 2 m. Assuming reasonable values for the average fruit density, specific heat, and porosity (the fraction of air volume in a box), recommend reasonable values for (a) the air velocity approaching the cooling section, (b) the product-cooling capacity of the system, in kg fruit/h, and (c) the volume flow rate of air. Water PV-powered pump FIGURE P11127 ... View Full Document

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