Explanation Write the given equation of state. v = R T p + B − A R T Partially differentiate the equation of state with respect to temperature by keeping the pressure as constant. ( ∂ v ∂ T ) p = R p + A R T 2 (I) Here, the change in the specific volume with respect to change in the temperature at constant pressure is ( ∂ v ∂ T ) p . the specific volume is v , the gas constant is R , the temperature is T , the pressure of the gas is p and the constant are A and B . Write the expression for change in entropy. s ( p 2 , T ) − s ( p 1 , T ) = − ∫ p 1 p 2 ( ∂ v ∂ T ) p d p (II) Here, the specific entropy at state 2 is s ( p 2 , T ) , the specific entropy at state 1 is s ( p 1 , T ) , the final pressure is p 2 and the initial pressure is p 1 . Write the expression for the change in enthalpy. h ( p 2 , T ) − h ( p 1 , T ) = ∫ p 1 p 2 ( v − T ( ∂ v ∂ T ) p ) d p (III) Here, the specific enthalpy at state 2 is h ( p 2 , T ) and the specific enthalpy at state 1 is h ( p 1 , T ) . Write the expression for difference in the specific enthalpy. h ( p 2 , T ) − h ( p 1 , T ) = u ( p 2 , T ) − u ( p 1 , T ) − ( p 2 v 2 − p 1 v 1 ) (IV) Here, the change in internal energy at state 1 is u ( p 2 , T ) , the change in internal energy at state 2 is u ( p 1 , T ) , the change in specific enthalpy at state 1 is h ( p 2 , T ) and the change in specific at state 2 is u ( p 1 , T ) . Conclusion: Substitute R p + A R T 2 for ( ∂ v ∂ T ) p in the Equation (II). s ( p 2 , T ) − s ( p 1 , T ) = − ∫ p 1 p 2 ( R p + A R T 2 ) d p = − R ln ( p 2 p 1 ) − A R T 2 ( p 2 − p 1 ) Thus, the expression for entropy change is s ( p 2 , T ) − s ( p 1 , T ) = − R ln ( p 2 p 1 ) − A R T 2 ( p 2 − p 1 )

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 11.9, Problem 48P

To determine

The expression for the change in specific enthalpy.

The expression for the change in internal energy.

The expression for the change in the entropy

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Chapter 11.9, Problem 47P

Chapter 11.9, Problem 49P

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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