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*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. cen84959_ch12.qxd 4/5/05 3:58 PM Page 676 676 | Thermodynamics
12–17 Reconsider Prob. 12–16. Using EES (or other) software, verify the validity of the last Maxwell relation for refrigerant-134a at the specified state. 12–3C Consider the function z(x, y), its partial derivatives ( z/ x)y and ( z/ y)x, and the total derivative dz/dx. (a) How do the magnitudes ( x)y and dx compare? (b) How do the magnitudes ( z)y and dz compare? (c) Is there any relation among dz, ( z)x, and ( z)y? 12–4C Consider a function z(x, y) and its partial derivative ( z/ y)x. Under what conditions is this partial derivative equal to the total derivative dz/dy? 12–5C Consider a function z(x, y) and its partial derivative ( z/ y)x. If this partial derivative is equal to zero for all values of x, what does it indicate? 12–6C Consider a function z(x, y) and its partial derivative ( z/ y)x. Can this partial derivative still be a function of x? 12–7C Consider a function f (x) and its derivative df/dx. Can this derivative be determined by evaluating dx/df and taking its inverse? 12–8 Consider air at 400 K and 0.90 m3/kg. Using Eq. 12–3, determine the change in pressure corresponding to an increase of (a) 1 percent in temperature at constant specific volume, (b) 1 percent in specific volume at constant temperature, and (c) 1 percent in both the temperature and specific volume. 12–9 Repeat Problem 12–8 for helium. 12–10 Prove for an ideal gas that (a) the P constant lines on a T-v diagram are straight lines and (b) the high-pressure lines are steeper than the low-pressure lines. 12–11 Derive a relation for the slope of the v constant lines on a T-P diagram for a gas that obeys the van der Waals equation of state. Answer: (v b)/R 12–12 Nitrogen gas at 400 K and 300 kPa behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A–18, and compare them to the values listed in Table A–2b. 12–13E Nitrogen gas at 600 R and 30 psia behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A–18E, and compare them to the values listed in Table A–2Eb.
Answers: 0.249 Btu/lbm · R, 0.178 Btu/lbm · R 12–18E Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at 800°F and 400 psia. 12–19 Using the Maxwell relations, determine a relation for ( s/ P)T for a gas whose equation of state is P(v b) RT.
Answer: R/P 12–20 Using the Maxwell relations, determine a relation a/v...
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