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 82RP
To determine
Develop the expressions for
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A 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.
5. A certain gas with Cp = 2.215
kg K
KJ
KJ
expand from 0.142 m³
and R = 0.518
%3D
%3D
kg K
and 300 °K to 0.425m³while the pressure remains constant at 106.869 KPa'
Determine: a. T2
b. mass of gas
C. Δh
d. Δυ
A certain ideal gas has the following properties:
Molecular Mass, M = 24.943416 kg/kmole and Cvo = 1.000 kJ/ºK/kg.
Determine Cpo in kJ / °K / kg.
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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- 2.00-mol of a monatomic ideal gas goes from State A to State D via the path A→B→C→D: State A PA=10.5atm, VA=11.00L State B PB=10.5atm, VB=6.00L State C PC=24.0atm, VC=6.00L State D PD=24.0atm, VD=23.50L Assume that the external pressure is constant during each step and equals the final pressure of the gas for that step. Calculate q for this process. Calculate w for this process. Calculate ΔE for this process Calculate ΔH for this process.arrow_forwardFor an ideal gas undergoing a polytropic process with n = 1, the temperature remains constant throughout the entire process. True Falsearrow_forwardQ3: 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_forward
- 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 JK-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-1 (15 Marks) %3Darrow_forwardOne kilogram on a diatomic ideal gas undergoes the following four step process starting at Point A (100 kPa, 300K, 5 m³) A => B Isothermal compression to 1 m³. B=> C Isobaric expansion to 900K. C=> D Adiabatic expansion to the original volume of 5 m³. D=> Alsochoric process to the original pressure of 100 kPa. ● ● ● (a) Determine P, V, and T, for points A, B, C & D. (b) What is AU, Q, W, AH & AS for each process of the cycle? (c) What is the efficiency of this cycle? d) Sketch a P-V diagram and T-S diagram, indicating P, V, T, for all points & AU, Q, W, AH & AS for each leg. Repeat problem one for a monoatomic ideal gas. Compare the Thermal Efficiency of a monoatomic ideal gas to the Thermal Efficiency of a diatomic ideaf gas for this same cyclearrow_forwardIn general, when a system undergoes a change from state 1 to state 2, the change in enthalpy is given by: deltaH = deltaU + PdeltaV + VdeltaP + deltaPdeltaV Derive this equation from the First Law of Thermodynamics, indicating the conditions assumed for the derivation.arrow_forward
- An ideal gas contained in a piston-and-cylinder device undergoes a thermodynamic cycle made up of three quasi-equilibrium processes. Step 1-2: Adiabatic compression from 330 K and 9.35 atm to 12.58 atm Step 2-3: Isobaric cooling Step 3-1: Isothermal expansion c.) Calculate Q, W, ΔU and ΔH, in J/mole, for each step in the process and for the entire cycle. Assume that CP = (5/2) R. d.) Is this cycle a power cycle or a refrigeration cycle? Explain. Calculate the thermal efficiency or COP of the cycle, whichever is appropriate.arrow_forward7. A perfect gas has a value of R = 0.3192 kJ/kg and k = 1.26. If 150 kJ are added to 3 kg of this gas at constant pressure when the initial temperature is 32.2°C, find T2, AH, AU, and Wnf.arrow_forwardThe figure shows a pV diagram for 1.8 g of helium gas (He) that undergoes the process from the state 1 to the state 2 to the state 3. Find the value of V3. P2 2.0 atm 0 17 L 69 L 34 L 8.6 L 657°C- 37°C 1 Isothermal 3 V(L)arrow_forward
- Calculate 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_forwardp/atm 2.0 1.0 EXERCISE 3 (c) 3 1 thermal (b) Ⓡ One mole of an ideal gas undergoes a cyclic three-step process according to Figure 2: (a) 1->2: reversible and adiabatic expansion starting at T₁, and pressure = 2 atm. pl (b) 2->3: reversible isothermal compression up to p3 = 1 atm and (c) 3->1: heating under constant volume, at final temperature Ti, and pressure p1 = 2 atm. Calculate the entropy changes of the gas for the three steps and for the cycle. The heat capacity under constant volume is given: cx= 12.47 J mol-¹ K-¹. V Enter your results (with units) in the Table below AS₁1+2 AS2+3 AS3+1 AS1+2+3+1arrow_forwardV. W. Th To %3D Room temperature T = 293 K V V. Vp The gas volume changes from Vp to Va at constant temperature T. The cartoon on the right shows a piston of gas undergoing this compression while submerged in a container of room temperature water, which acts as a reservoir. The initial state of this process is a piston containing 2 moles of a monatomic gas at Tc = 293 K (room temperature water) and volume V = a 1.0 m. The gas is compressed until V, = 0.2 m. During the compression, the heat bath of room temperature water maintains the temperature of the gas at T 293 K. Calculate the work done in joules by the gas during this process. Do not include units in your answer. Be careful to use the standard sign convention for work done by the gas. Write your numerical answer in normal form as described above in the instructions to this worksheet.arrow_forward
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