Explanation The following expression represents a fundamental thermodynamic function. u = u ( s , v ) Here, internal energy at specific entropy s and specific volume v is u ( s , v ) . Write the expression to calculate the temperature. T = ( ∂ u ∂ s ) v (I) Herer, the change in internal energy is ∂ u ∂ s . Write the expression to calculate the pressure. p = − ( ∂ u ∂ v ) s (II) Here, the change in internal energy wth respect to spevific volume is ∂ u ∂ v . Write the expression for the specific enthalpy. h = u + p v (III) Here, the specific volume is is v and internal energy is u . Write the expression to calculate the helmontz function. ψ = u − T s (IV) Here, the specific entropy is s . Write the expression to calculate the gibbs function. g = h − T s (V) Conclusion: Substitute u ( s , v ) for u in Equation (I). p = − ( ∂ ( u ( s , v ) ) ∂ v ) s Substitute u ( s , v ) for u in Equation (II). p = − ( ∂ ( u ( s , v ) ) ∂ v ) s Substitute − ( ∂ u ∂ v ) s for p in Equation (III). h = u + ( − ( ∂ u ∂ v ) s ) v (VI) Substitute u ( s , v ) for u in Equation (VI)

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 28P

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The functions T, p, h, ψ and g can be represented in a form of a fundamental thermodynamic function of the form u=(s,v).

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Chapter 11.9, Problem 27P

Chapter 11.9, Problem 29P

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The functions T , p , h , ψ and g can be represented in a form of a fundamental thermodynamic function of the form u = ( s , v ) .

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The functions T, p, h, ψ and g can be represented in a form of a fundamental thermodynamic function of the form u=(s,v).

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