Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781259822674
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 12.6, Problem 66P
To determine
To derive an equation for the Joule-Thomson coefficient inversion line.
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Define the van der Waals Equation of State.
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach
Ch. 12.6 - What is the difference between partial...Ch. 12.6 - Consider the function z(x, y). Plot a differential...Ch. 12.6 - Consider a function z(x, y) and its partial...Ch. 12.6 - Prob. 4PCh. 12.6 - Prob. 5PCh. 12.6 - Consider a function f(x) and its derivative df/dx....Ch. 12.6 - Conside the function z(x, y), its partial...Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Nitrogen gas at 800 R and 50 psia behaves as an...
Ch. 12.6 - Consider an ideal gas at 400 K and 100 kPa. As a...Ch. 12.6 - Using the equation of state P(v a) = RT, verify...Ch. 12.6 - Prove for an ideal gas that (a) the P = constant...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Show how you would evaluate T, v, u, a, and g from...Ch. 12.6 - Prob. 18PCh. 12.6 - Prob. 19PCh. 12.6 - Prob. 20PCh. 12.6 - Prove that (PT)=kk1(PT)v.Ch. 12.6 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Using the Clapeyron equation, estimate the...Ch. 12.6 - Prob. 26PCh. 12.6 - Determine the hfg of refrigerant-134a at 10F on...Ch. 12.6 - Prob. 28PCh. 12.6 - Prob. 29PCh. 12.6 - Two grams of a saturated liquid are converted to a...Ch. 12.6 - Prob. 31PCh. 12.6 - Prob. 32PCh. 12.6 - Prob. 33PCh. 12.6 - Prob. 34PCh. 12.6 - Prob. 35PCh. 12.6 - Prob. 36PCh. 12.6 - Determine the change in the internal energy of...Ch. 12.6 - Prob. 38PCh. 12.6 - Determine the change in the entropy of helium, in...Ch. 12.6 - Prob. 40PCh. 12.6 - Estimate the specific heat difference cp cv for...Ch. 12.6 - Derive expressions for (a) u, (b) h, and (c) s for...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the isothermal...Ch. 12.6 - Prob. 46PCh. 12.6 - Show that cpcv=T(PT)V(VT)P.Ch. 12.6 - Show that the enthalpy of an ideal gas is a...Ch. 12.6 - Prob. 49PCh. 12.6 - Show that = ( P/ T)v.Ch. 12.6 - Prob. 51PCh. 12.6 - Prob. 52PCh. 12.6 - Prob. 53PCh. 12.6 - Prob. 54PCh. 12.6 - Prob. 55PCh. 12.6 - Does the Joule-Thomson coefficient of a substance...Ch. 12.6 - The pressure of a fluid always decreases during an...Ch. 12.6 - Will the temperature of helium change if it is...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Prob. 61PCh. 12.6 - Steam is throttled slightly from 1 MPa and 300C....Ch. 12.6 - What is the most general equation of state for...Ch. 12.6 - Prob. 64PCh. 12.6 - Consider a gas whose equation of state is P(v a)...Ch. 12.6 - Prob. 66PCh. 12.6 - What is the enthalpy departure?Ch. 12.6 - On the generalized enthalpy departure chart, the...Ch. 12.6 - Why is the generalized enthalpy departure chart...Ch. 12.6 - What is the error involved in the (a) enthalpy and...Ch. 12.6 - Prob. 71PCh. 12.6 - Saturated water vapor at 300C is expanded while...Ch. 12.6 - Determine the enthalpy change and the entropy...Ch. 12.6 - Prob. 74PCh. 12.6 - Prob. 75PCh. 12.6 - Prob. 77PCh. 12.6 - Propane is compressed isothermally by a...Ch. 12.6 - Prob. 81PCh. 12.6 - Prob. 82RPCh. 12.6 - Starting with the relation dh = T ds + vdP, show...Ch. 12.6 - Using the cyclic relation and the first Maxwell...Ch. 12.6 - For ideal gases, the development of the...Ch. 12.6 - Show that cv=T(vT)s(PT)vandcp=T(PT)s(vT)PCh. 12.6 - Temperature and pressure may be defined as...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - Prob. 90RPCh. 12.6 - Prob. 91RPCh. 12.6 - Estimate the cpof nitrogen at 300 kPa and 400 K,...Ch. 12.6 - Prob. 93RPCh. 12.6 - Prob. 94RPCh. 12.6 - Prob. 95RPCh. 12.6 - Methane is to be adiabatically and reversibly...Ch. 12.6 - Prob. 97RPCh. 12.6 - Prob. 98RPCh. 12.6 - Prob. 99RPCh. 12.6 - An adiabatic 0.2-m3 storage tank that is initially...Ch. 12.6 - Prob. 102FEPCh. 12.6 - Consider the liquidvapor saturation curve of a...Ch. 12.6 - For a gas whose equation of state is P(v b) = RT,...Ch. 12.6 - Prob. 105FEPCh. 12.6 - Prob. 106FEP
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- In the project, the theoretical methods will be used to construct the property tables for ammonia using the Van der Waals Equation of state. You are required to find out the specific heats of the Van der Waals gas before performing the calculation. Consider the Van der Waals gas obeying the equation of state: Р C. RT a v-b v² where a and b are empirical constant to be determined assuming the critical point occur at inflection and stationary point on the p - v diagram. The critical pressure and temperature of ammonia are 11.35 MPa and 405.5 K respectively. Assume the universal gas constant, R = 8.314 J/mol K. Sketch the following graphs using reduced temperature as the parameter, T, = 0.85, 0.86, 0.88, 0.90, 0.95, 1.00, 1.10, 1.40, 2.00, and 5.00 for ammonia. a. Reduced pressure, p, versus reduced specific volume, v,.. b. Compressibility factor, Z versus reduced pressure, pr. Internal energy of departure, (u* -u)r/RT, versus reduced pressure, p,..arrow_forward1. The virial equation of state can be written as: Z = 1+ BP/(RT) Let B be given as : B = a – b/T? Derive the equation for the internal energy departure: U(T, P) – U(T, P=0). where a andb are constants.arrow_forwardA PV diagram below, Figure 1, shows two possible states of a system containing three moles of a monatomic ideal gas. (P,= P2 = 450 Pa, V, = 2m', V,= 8m²) c. Draw the process which depicts an isothermal expansion from state 1 to the volume V, followed by an isochoric increase in temperature to state 2 and label this process (B). d. Find the change in internal energy of the gas for the two-step process (B) Figure 1 (N/m²) 500 ! 400+ 300+ 200+ 100 - + + + + 4 6. 8 10 V (m³) 2 Copyright © 2005 Pearson Prentice Hall, Inc.arrow_forward
- Answer for J and Karrow_forward2. Consider a metal rod with the equation of state L- Lo = Lo +a(T YA %3D Here Lo, Y, A, To, and a are constants,T is the temperature, L is the length, and F is the tension. Work is given by dW a) Using the first law and the expression for dU in terms of it partial derivatives with respect to T and L, show that for this system -FdL. (). -). G). (4). - se, b) By differentiating the first of these equations with respect to L and the second with respect to T show that ), -r(器). =F-T ƏT c) Using the above result and the equation of state, find an expression for (0/aL). Then, assuming that C. the heat capacity at constant length is a Constant. find an expression for the internal energy, U, as a function of T and L.arrow_forwardts Suppose you have a gas that obeys the following modified van der Waals equation: P(V – nb) = nRT %3D a) In 1-2 sentences, provide a physical interpretation for this equation. HINT: Compare this with the octual van der Waais equation. What does the missing term represent? b) For a gas obeying this modified van der Waals equation, derive an expression for the work done by a reversible and isothermal change in volume. c) For this modified van der Waals equation (with n and b as constants), find the following two partial derivatives: i) ii) Tarrow_forward
- Derive an expression for the specific heat difference of a substance whose equation of state is: P=[(RT)/(v-b)]-[a/(v*(v+b)*T1/2)] Where a and b are empirical constantsarrow_forward(1) For a gas that follows equation of state pV = f (T), show that %3| др 1 df (ar), -var V dT' \ƏT, 1 df p dT * AƏT.arrow_forward2010Q5: Please answer all parts in specific detail and explain each step with reasoningarrow_forward
- Niloarrow_forwardThe simplest equation of state for liquid water is the so-called stiffened-gas equation of state in the form c(y – 1)T - II P = (9.129) where y = 4 – 7, II = 4 × 10° Pa, and c = 4200 kJkg¯'K!. (a) Determine the volumetric thermal expansion of this liquid at T = 100°C and P = 1 MPa.(b) De- termine the isothermal compressibility of this liquid at T = 100°C and P = 1 MPa.arrow_forwardCalculate AH, AU, w, and q for the reversible heating of 1 mol of liquid water from 273 K to 373 K at 1 atm. ΔΗΞ 1806.88 You are correct AU = -1065.729 You are incorrect W = -741.151 You are incorrect q= 1806.88 You are correct X cal cal X cal calarrow_forward
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