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Unformatted text preview: EML 5104 Classical Thermodynamics, Spring 2010 Practice Problems Psychrometry P1: An air ­conditioning system, consisting of a cooler and a heater, is shown schematically below. Moist air enters the cooler at location 1 with T1=38°C and relative humidity φ1=50%. At location 2, a saturated mixture leaves the cooler and enters the heater. At location 3, condensed water leaves the cooler. The saturated mixture and the condensed water leaving the cooler are at the same temperature (T3=T2). At location 4, moist air leaves the heater and enters the air ­conditioned space at T4=22°C, φ4=55%, and a volumetric flow rate . The total pressure throughout the system is 1 bar. a) Calculate the mass flow rate of dry air through the system. b) Calculate the mass flow rate of condensed water leaving the cooler at location 3. c) Derive an expression for the steam pressure pg2 as a function of the humidity ratio ω2 and the total pressure p at location 2. d) Calculate the steam pressure pg2 and the temperature T2 at location 2. e) Derive expressions for the steady-state energy balance on the cooler and on the heater. f) Calculate the rate of heat removed from the cooler , and the heat supplied to the heater . g) Indicate states 1, 2, and 4 in a psychrometric chart. Note: Assume ideal gases. Use attached tables for gas and liquid enthalpies. The air gas ideal constant is . 1: T1 = 38 °C φ1 = 50% 2: saturated mixture 4: T4 = 22 °C φ4 = 55% Air ­conditioned space 3: P2: A spray dryer is used to produce fine powder from slurry (solid ­water mixture). Slurry is sprayed into the system at (3), T3=20 °C. The mass flow rate of slurry is denoted . Ambient air enters the system at (1) T1=20 °C, φ1=50%; the volumetric flow rate supplied to the system is =1 m3/s. The air is preheated and enters the spraying tower at (2). While slurry droplets fall down the spraying tower water evaporates; steam is carried away by air. Saturated (φ4=100%) moist air at T4=25°C leaves the system at (4). Dry powder is recovered at the bottom of the spraying tower (5). Assumptions: i) The system is well insulated, ii) total pressure 1 bar throughout the system. EML 5104 Classical Thermodynamics, Spring 2010 a) Based on T1, φ1, and , calculate the volumetric flow rate of dry air through the system 3 in m /s and the mass flow rate in kg/s. b) f w=0.8 is the water mass fraction of the slurry; f p=0.2 is the fraction of solid powder material. State the mass balance over the system accounting for air and water in terms of humidity ratios ω1, ω4, , and . Hint: ignore solid powder mass flows. c) Based on b) calculate and the mass flow rate of powder recovered from the system at (5). d) State the energy balance in terms of T1, ω1, T4, ω4, , , and . Calculate . Hint: To calculate specific enthalpies of water vapor assume saturated conditions, to calculate specific enthalpies of air use constant cp,a=1005 J/(kg K) e) Use a psychrometric chart to estimate T2, Show state (2) and state (4) in chart. Hint: Assume adiabatic change. f) Three measures to increase the rate of product production are proposed: 1) Increase heating rate and increase , 2) increase flow rate and increase , 3) Change nozzle to obtain finer slurry droplets (increased evaporation rate) and increase . For each measure explain i) if it works, ii) why/why not. 3 Spraying tower 4 2 5 1 Powder Chemical Thermodynamics and Phase Equilibrium P1: Determine the change of the Gibbs function G0 at 25 °C, in kJ/mol for the complete combustion of Methane with the theoretical amount of pure O2 P2: Calculate the equilibrium constant K for the water gas shift reaction CO + H2O(g) ↔ CO2 + H2 at 298 K and at 1000 K. Compare with tabular data (M+S Table A ­ 27) P3: Determine the temperature at which 5 % of molecular Hydrogen (H2) dissociates into monatomic Hydrogen (2 H). P4: At high temperatures water dissociates to form an equilibrium of H2O(g), H2, and O2. Determine the temperature, at which the mole fraction of water vapor is 98 % for total pressures of 1 bar and 10 bar. P5: A mixture initially consisting of 0.4 mol O2 and 1.1 mol CO forms and equilibrium of O2, CO, and CO2 at 1 bar and 2500 K. Determine the equilibrium composition. EML 5104 Classical Thermodynamics, Spring 2010 P6: Estimate the enthalpy of reaction at 2000 K for CO2 ↔ CO + ½ O2 using the Van’t Hoff equation and equilibrium constant data (M+S Table A ­27). Compare with the value obtained using enthalpy data. P7: At 293 K log10K=8.9 for C+2H2↔CH4. Assume that the enthalpy of reaction is independent of temperature and estimate the value of log10K at 500 °C. P8: Butane burns with 200% of theoretical air to form an equilibrium mixture at 1400 °C, 10 bar consisting of CO2, O2, H2O(g), N2, NO, and NO2. Consider the two competing reactions: N2+2O2 ↔2NO2 (K(1400°C) = 8.4⋅10 ­10) and ½ O2 + ½ N2↔ NO (K(1400°C)=6.8⋅10 ­3) to calculate the balanced reaction equation. P9: Determine the number of degrees of freedom for systems composed of a) ice and liquid water b) ice, liquid water, and water vapor, c) liquid water and water vapor, d) water vapor only, e) water vapor and dry air, f) ice water vapor and dry air, g) N2 and O2 at 20 °C, 1 bar. Vapor Cycles P1: Steam enters the turbine of a simple vapor power plant with a pressure of 10 MPa and temperature T, and expands adiabatically to 6 kPa. The isentropic turbine efficiency is 85%. Saturated liquid exits the condenser at 6 kPa and the isentropic pump efficiency is 82%. a) for T=580 °C, determine the turbine exit quality and the cycle thermal efficiency. b) for T=680 °C, determine the turbine exit quality and the cycle thermal efficiency. P2: The temperature at the inlet of a vapor power plant may not exceed 520 °C. The condenser pressure is 0.06 bar. Determine the steam generator pressure if the isentropic turbine efficiency is 80% and the quality of the steam at the turbine must be at least 90%. P3: An ideal Rankine cycle with reheat uses water as the working fluid. The conditions at the inlet to the first ­stage turbine are 14 MPa, 600 °C and the steam is reheated between the turbine stages to 600 °C. For a condenser pressure of 6 kPa, calculate the cycle thermal efficiency for reheat pressures of 2 and 12 MPa. P4: Steam enters the turbine of a vapor power plant at 100 bar, 520 °C and expands adiabatically exiting at 0.08 bar with a quality of 90%. Condensate leaves the condenser as saturated liquid at 0.08 bar. Liquid exits the pump at 100 bar, 43 °C. The specific exergy fo the fuel entering the combustor unit of the steam generator is estimated to be 14700 kJ/kg. No exergy is carried in by the combustion air. The exergy of the stack gases leaving the steam generator is estimated P5: Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at 8 MPa, 480 °C. The condenser pressure is 8 kPa. The net power output of the cycle is 100 MW. Determine for the cycle EML 5104 Classical Thermodynamics, Spring 2010 P6: Modify the ideal Rankine cycle from P5 to include one open feedwater heater operating at 0.7 MPa. Answer the same questions about the modified cycle as in P5 and discuss the results. P7: Carry out an Exergy accounting of the ideal Rankine cycle P5, assume that heat is supplied in the boiler/superheater at an average temperature of 800 °C. T0=15 °C. P8: Carry out an Exergy accounting of the open feedwater heater in P6, determine the rate of lost Work. Gas Cycles P1: An air ­standard Otto cycle has a compression ratio of 7.5. At the beginning of the compression, p1 = 86 kPa, and T1 = 32 °C. The mass of air is 2 g, and the maximum temperature in the cycle is 960 K. Determine a) the heat rejection, in kJ. b) the net work, in kJ. c) the thermal efficiency. P2: Air enters the compressor of an ideal air ­standard Brayton cycle at 100 kPa, 300 K, with a volumetric flow rate of 5 m3/s. The compressor pressure ratio is 10. For turbine inlet temperatures ranging form 1000 to 1600 K, plot a) the thermal efficiency of the cycle, b) the back work ratio, c) the net power developed, in kW. P3: Air enters the compressor of a simple gas turbine at 100 kPa, 300 K with a volumetric flow rate of 5 m3/s. The compressor pressure ratio is 10 and its isentropic efficiency is 85%. At the inlet to the turbine, the pressure is 950 kPa, and the temperature is 1400 K. The turbine has an isentropic efficiency of 88% and the exit pressure is 100 kPa. On the basis of an air standard analysis, Develop a full accounting of the net exergy increase of the air passing through the gas turbine combustor in kW. T0 = 300 K, p0=100 kPa. P4: A combined gas turbine ­vapor power plant (M+S Fig. 9.23) has a net power output of 100 MW. Air enters the compressor of the gas turbine at 100 kPa, 300 K, and is compressed to 1200 kPa. The isentropic efficiency of the compressor is 84%. The conditions at the inlet to the turbine are 1200 kPa and 1400 K. air expands through the turbine, which has an isentropic efficiency of 88%, to a pressure of 100 kPa. The air then passes through the interconnecting heat exchanger, and is finally discharged at 480 K. Steam enters the turbine of the vapor power cycle at 8 MPa, 400 °C and expands to the condenser pressure of 8 kPa. The turbine and pump have isentropic efficiencies of 90 and 80% respectively. Determine a) the rate of heat transfer to the working fluid passing through the steam generator in kW. b) the thermal efficiency. c) the mass flow rate of condenser cooling water in kg/h if the cooling water enters the condenser at 15 °C and exits at 35 °C with negligible pressure change. EML 5104 Classical Thermodynamics, Spring 2010 a) the mass flow rate of air and steam, each in kg/s. b) the thermal efficiency of the combined cycle. c) a full accounting of the net exergy increase of the air passing through the combustor of the gas turbine. P5: Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed in two stages to 900 kPa, with intercooling to 300 K between the stages at a pressure of 300 kPa. The turbine inlet temperature is 1480 K and the expansion occurs in two stages with reheat to 1420 K between the stages at a pressure of 300 kPa. The compressor and turbine stage efficiencies are 84 and 82% respectively. The net power developed is 1.8 MW. Determine a) the volumetric flow rate in m3/s, at the inlet of each compressor stage. b) the thermal efficiency of the cycle. c) the back work ratio. ...
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