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 90RP
To determine
To show that the position of the Joule-Thomson coefficient inversion curve on the
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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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- Q3: In a closed vessel with a volume of 50 dm3 there are 2 moles of an ideal monoatomic gas with cv, m = 12.471 J K-1 mol-1 at 25°C. The vessel was heated to 125°C. Calculate the values of Q, W, AU, AH in Joules and the initial and final pressure in the system. R = 8,314 J K-1 mol-1. Cp,m = 20,785 J K-1 mol-1arrow_forwardA rigid vessel as shown in figure below contain three different gases separated by diaphragms. If diaphragms are removed and gases allowed to be mixed together adiabatically, find the final temperature and pressure of the mixture. CO2 m = 24 kg T = 77 °C P = 1.5 bar N2 m = 6 kg T = 52 °C P = 0.5 bar O2 m = 12 kg T = 27 °C P = 2.0 bararrow_forwardDerive a relation for the volume expansivity β and the isothermal compressibility κ (a) for an ideal gas and (b) for a gas whose equation of state is P(v - a) = RT and (c) calculate β and κ for nitrogen at T=175K, v = 0.00375 m3 /kg, and a = 0.00138 m3 /kg and compare the results obtained from ideal gas law and from P(v - a) = RT.arrow_forward
- A cylinder contains oxygen at a pressure of 2.00 atm. The volume is 4.00 L, and the temperature is 300 K. Assume that the oxygen may be treated as an ideal gas. The oxygen is carried through the following processes: (i) Heated at constant pressure from the initial state (state 1) to state 2, which has T = 450 K. (ii) Cooled at constant volume to 250 K (state 3). (iii) Compressed at constant temperature to a volume of 4.00 L (state 4). (iv) Heated at constant volume to 300 K, which takes the system back to state 1. (a) Show these four processes in a pV-diagram, giving the numerical values of p and V in each of the four states. (b) Calculate Q and W for each of the four processes. (c) Calculate the net work done by the oxygen in the complete cycle. (d) What is the efficiency of this device as a heat engine? How does this compare to the efficiency of a Carnot-cycle engine operating between the same minimum and maximum temperatures of 250 K and 450 K?arrow_forwardAt low pressures, the compressibility factor of a van der Waals gas is given by the equation: Z = PV/RT = 1+(b- a/RT) P/RT Calculate the fugacity of nitrogen gas at 3000 K and 0.05 bar. The van der Waals constants of nitrogen gas are a = 1.408 L^2-bar-mol^2 and b = 0.03913 L-mol^-1. By investigating the fugacity coefficient, what can be said about nitrogen at this temperature and pressure? *final answer in 4 decimalsarrow_forwardAt the critical Temperature T-Te, the first and second partial derivative of P with respect to Vm at a fixed temperature is 0 (inflection point). Use this information to determine a and b in the van der Waals equation of state in terms of the experimentally determined values Tc and Pc.arrow_forward
- A piston- cylinder device contains 0.1m ^ 3 of liquid water and 0.9m ^ 3 of water vapor in equilibrium at 800 kPa. Heat is transferred at constant pressure until the temperature reaches 350 degrees * C . i. What is the initial temperature of the water? ii Determine the total mass of the water. iii. Calculate the final volume. iv. Show the process on a P-v diagram with respect to saturation linesarrow_forwardHelium at 20 bar and 40o is contained in a small cylinder having a volume of 15 cm3. The cylinder is placed in a large container having a volume of 1500 cm3.The large container is perfectly insulated and evacuated.Now helium is allowed to discharge and fill the large container.Calculate final pressure after entire assembly reches equilibrium.arrow_forward= B- Find an expression for Cp - Cv if the equation of state is p for an ideal gas. RT v-b and Show that CP - Cv=Rarrow_forward
- Question 1: Derive the thermodynamic equation of state (dH/dP)_T = V-T(dV/dT)_P Derive an expression for (dH/dP)_T for an ideal gas and for a van der Waals gas. For the van der waals gas, estimate its value for 1.0 mol of Ar(g) at 298K and 10 atm. Question 2: Show that the slope of compressibility factor Z as a function of pressure as P ---> 0; at isothermal conditions is related to the van der waals parameters by: Limit (P-->0) dz/dP = (b-a/RT)/RTarrow_forwardThe isothermal compressibility, κT, of water at 293 K is 4.96 × 10−5 atm−1. Calculate the pressure that must be applied in order to increase its density by 0.10 per cent.arrow_forwardCarbon Dioxide (M=44) is being stored at 46°C, 80 bar. The critical temperature and pressure are 31°C and 72.8 bar. Calculate the specific volume. (0.004 m³/kg)arrow_forward
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