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 53P
To determine
To show how to obtain the expressions for
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The 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
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69 L
34 L
8.6 L
657°C-
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43.0 g of 40Ar gas are sealed in a container at an initial pressure of 1.50 atm and an initial volume of 0.0500 m3 (state 1). The gas is then made to expand very, very quickly until its volume doubles (state 2). Then it is compressed very, very slowly back to its initial volume (state 3).
Show the two processes on a pV diagram, and fill out the table below.
p1 =
p2 =
p3 =
V1 =
V2 =
V3 =
T1 =
T2 =
T3 =
4 kmol of oxygen (0₂) gas undergoes a process in a closed system from p₁ = 50 bar,
T₁ = 170 K to P2 = 25 bar, T₂ = 200 K.
Determine the change in volume, in m³.
AV = 1.52978
x m³
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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- Statistical physics, Overview of Classical Thermodynamics, The Maxwell relations?arrow_forward4 kmol of oxygen (O₂) gas undergoes a process in a closed system from p₁ = 50 bar, T₁ = 170 K to P2 = 25 bar, T₂ = 200 K. Determine the change in volume, in m³. m³ ΔV : =arrow_forwardTwo kilograms of gas with R = 0.218 kJ/(kg-K) undergoes a process and results to the following changes: ΔH = 3150 kJ, ΔU = 2450 kJ. Find the specific heat ratio, k.arrow_forward
- Carbon dioxide (molar mass 44 kg/kmol) expands reversibly in a perfectly thermally insulated cylinder from 3.7 bar, 220 0C to a volume of 0.085 m3. If the initial volume occupied was 0.02 m3, calculate the gas constant to 3 decimal places. Assume nitrogen to be a perfect gas and take cv = 0.63 k J / k g Karrow_forwardOxygen (molar mass 32 kg/kmol) expands reversibly in a cylinder behind a piston at a constant pressure of 3 bar. The volume initially is 0.01 m and finally is 0.03 m; the initial temperature is 18.32 C. Calculate the mass of oxvgen with the correct unit to four decimal places. Assume oxygen to be a perfect gas and take the specific heat at constant pressure as = 0.917kj/kg Kand molar gas constant as = 8,314 J / kmol Karrow_forwardPLEASE HELP ANSWER THIS THERMODYNAMICS PRACTICE QUESTIONarrow_forward
- 8- Air in a closed cylinder undergoes a polytropic process with a polytrophic index of 1.65. a- What is the work done during the process if the initial pressure, volume and temperature are 8 bar, 0.08 m' and 475°C respectively, the final pressure is 0.8 bar and air can be taken to be a perfect gas? b- What is the change in internal energy? e- What is the heat loss/gain during the process?arrow_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_forwardA mass of 12 kg of Oxygen occupying 3 m3 is heated from 25°C at a constant volume. Take gas constant is 0.297 kJ/kgK, then its initial pressure would be approximately 0.78 bar. Select one: O True O Falsearrow_forward
- In 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_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_forwardNEED IN RUSH PLEASE THANKS IN ADVANCEarrow_forward
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