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Unformatted text preview: ocess. By taking s s(P, v) and using the Maxwell relations, show that for this process Pv k constant, where k is the isentropic expansion exponent defined as k v 0P ab P 0v s 12–81E Argon gas enters a turbine at 1000 psia and 1000 R with a velocity of 300 ft/s and leaves at 150 psia and 500 R with a velocity of 450 ft/s at a rate of 12 lbm/s. Heat is being lost to the surroundings at 75°F at a rate of 80 Btu/s. Using the generalized charts, determine (a) the power output of the turbine and (b) the exergy destruction associated with the process. Answers: (a) 922 hp, (b) 121.5 Btu/s 12–82 An adiabatic 0.2m3 storage tank that is initially evacuated is connected to a supply line that carries nitrogen at 225 K and 10 MPa. A valve is opened, and nitrogen flows into the tank from the supply line. The valve is closed when the pressure in the tank reaches 10 MPa. Determine the final temperature in the tank (a) treating nitrogen as an ideal gas and (b) using generalized charts. Compare your results to the actual value of 293 K. N2 225 K 10 MPa Also, show that the isentropic expansion exponent k reduces to the specific heat ratio cp /cv for an ideal gas. 12–89 Refrigerant134a undergoes an isothermal process at 60°C from 3 to 0.1 MPa in a closed system. Determine the work done by the refrigerant134a by using the tabular (EES) data and the generalized charts, in kJ/kg. 0.2 m 3 Initially evacuated FIGURE P12–82
12–83 For a homogeneous (singlephase) simple pure substance, the pressure and temperature are independent properties, and any property can be expressed as a function of these two properties. Taking v v(P, T ), show that the change in specific volume can be expressed in terms of the volume expansivity b and isothermal compressibility a as dv v b dT a dP 12–90 Methane is contained in a piston–cylinder device and is heated at constant pressure of 4 MPa from 100 to 350°C. Determine the heat transfer, work and entropy change per unit mass of the methane using (a) the idealgas assumption, (b) the generalized charts, and (c) real fluid data from EES or other sources. Fundamentals of Engineering (FE) Exam Problems
12–91 A substance whose JouleThomson coefficient is negative is throttled to a lower pressure. During this process, (select the correct statement) (a) the temperature of the substance will increase. (b) the temperature of the substance will decrease. (c) the entropy of the substance will remain constant. (d ) the entropy of the substance will decrease. (e) the enthalpy of the substance will decrease. 12–92 Consider the liquid–vapor saturation curve of a pure substance on the PT diagram. The magnitude of the slope of the tangent line to this curve at a temperature T (in Kelvin) is Also, assuming constant average values for b and a, obtain a relation for the ratio of the specific volumes v2/v1 as a homogeneous system undergoes a process from state 1 to state 2. 12–84 Repeat Prob. 12–83 for an isobaric process. cen84959_ch12.qxd 4/5/05 3:58 PM Page 680 680  Thermodynamics
v
a T (a) proportional to the enthalpy of vaporization hfg at that temperature. (b) proportional to the temperature T. (c) proportional to the square of the temperature T. (d ) proportional to the volume change vfg at that temperature. (e) inversely proportional to the entropy change sfg at that temperature. 12–93 Based on the generalized charts, the error involved in the enthalpy of CO2 at 350 K and 8 MPa if it is assumed to be an ideal gas is (a) 0 (b) 20% (c) 35% (d ) 26% (e) 65% 12–94 Based on data from the refrigerant134a tables, the JouleThompson coefficient of refrigerant134a at 0.8 MPa and 100°C is approximately (a) 0 (d ) 8°C/MPa (b) 5°C/MPa (e) 26°C/MPa (c) 11°C/MPa b) RT, u g s h P FIGURE P12–97
being Koenig’s thermodynamic square shown in the figure. There is a systematic way of obtaining the four Maxwell relations as well as the four relations for du, dh, dg, and da from this figure. By comparing these relations to Koenig’s diagram, come up with the rules to obtain these eight thermodynamic relations from this diagram. 12–98 Several attempts have been made to express the partial derivatives of the most common thermodynamic properties in a compact and systematic manner in terms of measurable properties. The work of P. W. Bridgman is perhaps the most fruitful of all, and it resulted in the wellknown Bridgman’s table. The 28 entries in that table are sufficient to express the partial derivatives of the eight common properties P, T, v, s, u, h, f, and g in terms of the six properties P, v, T, cp, b, and a, which can be measured directly or indirectly with relative ease. Obtain a copy of Bridgman’s table and explain, with examples, how it is used. 12–95 For a gas whose equation of state is P(v the specified heat difference cp cv is equal to (a) R (b) R b (c) R b (d ) 0 (e) R(1 + v/b) Design and Essay Problems
12–96 Consider the function z z(x, y). Write an essay on the physical interpretation of the ordinary derivative dz /dx and the partial derivative ( z / x)y. Explain how these two derivatives are related to each other and when they become equivalent. 12–97 There have been several attempts to represent the thermodynamic relations geometrically, the best known of these...
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