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Unformatted text preview: 2) for ( s/ v)T for a gas whose equation of state is (P (v b) RT. 12–21 Using the Maxwell relations and the ideal-gas equation of state, determine a relation for ( s/ v)T for an ideal gas. Answer: R/v The Clapeyron Equation
12–22C What is the value of the Clapeyron equation in thermodynamics? 12–23C Does the Clapeyron equation involve any approximations, or is it exact? 12–24C What approximations are involved in the ClapeyronClausius equation? 12–25 Using the Clapeyron equation, estimate the enthalpy of vaporization of refrigerant-134a at 40°C, and compare it to the tabulated value. Reconsider Prob. 12–25. Using EES (or other) software, plot the enthalpy of vaporization of refrigerant-134a as a function of temperature over the temperature range 20 to 80°C by using the Clapeyron equation and the refrigerant-134a data in EES. Discuss your results. 12–27 Using the Clapeyron equation, estimate the enthalpy of vaporization of steam at 300 kPa, and compare it to the tabulated value. 12–28 Calculate the hfg and sfg of steam at 120°C from the Clapeyron equation, and compare them to the tabulated values. Determine the hfg of refrigerant-134a at 50°F on the basis of (a) the Clapeyron equation and (b) the Clapeyron-Clausius equation. Compare your results to the tabulated hfg value. 12–30 Plot the enthalpy of vaporization of steam as a function of temperature over the temperature range 10 to 200°C by using the Clapeyron equation and steam data in EES. 12–29E 12–26 12–14 Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and 96 kPa. Estimate the change in the specific volume of the gas using (a) Eq. 12–3 and (b) the ideal-gas relation at each state. 12–15 Using the equation of state P(v a) RT, verify (a) the cyclic relation and (b) the reciprocity relation at constant v. The Maxwell Relations
12–16 Verify the validity of the last Maxwell relation (Eq. 12–19) for refrigerant-134a at 80°C and 1.2 MPa. 12–31 Using the Clapeyron-Clausius equation and the triplepoint data of water, estimate the sublimation pressure of water at 30°C and compare to the value in Table A–8. cen84959_ch12.qxd 4/5/05 3:58 PM Page 677 Chapter 12
General Relations for du, dh, ds, cv, and cp
12–32C Can the variation of specific heat cp with pressure at a given temperature be determined from a knowledge of Pv-T data alone? 12–33 Show that the enthalpy of an ideal gas is a function of temperature only and that for an incompressible substance it also depends on pressure. 12–34 Derive expressions for (a) u, (b) h, and (c) s for a gas that obeys the van der Waals equation of state for an isothermal process. 12–35 Derive expressions for (a) u, (b) h, and (c) s for a gas whose equation of state is P(v a) RT for an isothermal process. Answers: (a) 0, (b) a(P2 P1), (c) R ln (P2/P1) 12–36 Derive expressions for ( u/ P)T and ( h/ v)T in terms of P, v, and T only. 12–37 Derive an expression for the specific-heat difference cv for (a) an ideal gas, (b) a van der Waals gas,...
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This note was uploaded on 03/09/2009 for the course ME 430 taught by Professor Y during the Spring '09 term at CUNY City.
- Spring '09