Explanation Write the expression for the Joule’s Thomson coefficient. μ j = T ( ∂ v ∂ T ) p − v c p (I) Here, Joule’s Thomson coefficient is μ j , rate of change of specific volume with temperature T at constant pressure p is ( ∂ v ∂ T ) p and specific heat at constant pressure is c p . Write the expression for the rate of change of specific volume with respect to temperature. ( ∂ v ∂ T ) p = − R ( v − b ) [ 2 a v 3 − R T ( v − b ) 3 ] = − R v 3 ( v − b ) 2 a ( v − b ) − R T (II) Here, rate of change of specific volume with respect to temperature is ( ∂ v ∂ T ) p , the characteristic gas constant is R and Vander Waals constants for a real gas are a and b . Write the expression for specific heat at constant pressure. c p = c v + T ( ∂ v ∂ T ) p ( ∂ p ∂ T ) v (III) Here, specific heat at constant pressure is c p and specific heat at constant volume is c v , the partial derivative of specific volume with respect to temperature at constant pressure is ( ∂ v ∂ T ) p and the rate of change of pressure with respect to change in temperature at constant volume is ( ∂ p ∂ T ) v . Write the expression for pressure. p = R T v ¯ − b − a v ¯ 2 (IV) Here, the finite volume occupied by the molecules is b , the forces of attraction between molecules is a v ¯ 2 and the pressure is p . Differentiate Equation (IV) with respect to temperature at constant volume. ( ∂ p ∂ T ) v = R ( v − b ) (V) Write the expression for the specific heat at constant volume. c v = A + B T + C T 2 (VII) Here, the specific heat at constant volume is c v , corresponding temperature is T and constants are A , B and C . Conclusion: Substitute − R v 3 ( v − b ) 2 a ( v − b ) − R T for ( ∂ v ∂ T ) p and R ( v − b ) for ( ∂ p ∂ T ) v in Equation (III)

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 11.9, Problem 71P

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The expression for Joule Thomson’s coefficient.

The expression for inversion temperature.

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Chapter 11.9, Problem 70P

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Chapter 11 Solutions

Fundamentals of Engineering Thermodynamics

Ch. 11.9 - Prob. 1E Ch. 11.9 - Prob. 2E Ch. 11.9 - 3. What is an advantage of using the Redlich–Kwong...Ch. 11.9 - To determine the specific volume of superheated...Ch. 11.9 - Prob. 5E Ch. 11.9 - Prob. 6E Ch. 11.9 - Prob. 7E Ch. 11.9 - Prob. 8E Ch. 11.9 - Prob. 9E Ch. 11.9 - Prob. 10E

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The expression for Joule Thomson’s coefficient. The expression for inversion temperature.