CENGEL'S 9TH EDITION OF THERMODYNAMICS:
9th Edition
ISBN: 9781260917055
Author: CENGEL
Publisher: MCG
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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.
One mole of a monatomic ideal gas undergoes a cycle that has four steps. At point 1 it starts at a pressure of 3 × 105 Pa and a volume of 20 × 10-3 m3 It undergoes an isothermal expansion to point 2 to a new volume at of 8.0 × 10-3 m?. It then undergoes an isochoric process to point 3 until its pressure is half as much of what it was at point 2. It then goes through an isothermal compression to point 4 to a volume of 20 mL. It returns to point 1 via an isochoric step.
What is the temperature of the gas at point 1?
How much work is done by the gas in step 1 to 2?
What is the pressure of the gas at point 2?
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A monatomic ideal gas (y = 5/3) is contained within a perfectly insulated cylinder that
is fitted with a movable piston. The initial pressure of the gas is 1.5 x 105 Pa. The piston is pushed so as to compress the gas, with the result that the Kelvin temperature doubles. What is the final pressure of the gas?
a. 4.91 ×…
Q4 Show that for a gas obeying van der Walls equation of state,
2a
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Chapter 12 Solutions
CENGEL'S 9TH EDITION OF THERMODYNAMICS:
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
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