To determine The derivation of relation c p = − T ( ∂ 2 g ∂ T 2 ) p . Explanation Write the expression for differential equation of change in specific enthalpy h ( T , p ) . d h = ( ∂ h ∂ T ) p d T + ( ∂ h ∂ p ) T d p = ( c p ) d T + ( ∂ h ∂ p ) T d p = c p d T + ( ∂ h ∂ p ) T d p (I) Here, change in the temperature is d T , specific heat at constant pressure is c p , and change in the pressure is d p . Write the expression for differential equation of change in specific entropy s ( T , p ) . d s = ( ∂ s ∂ T ) p d T + ( ∂ s ∂ p ) T d p (II) Write the expression for T d s equation. d h = T d s + v d p (III) Write the expression for differential equation Gibb’s function. − ( ∂ s ∂ T ) p = ( ∂ 2 g ∂ T 2 ) p (IV) Here, Gibb’s function is g . Conclusion: Substituting c p d T + ( ∂ T ∂ p ) d p for d h and ( ∂ s ∂ T ) p d T + ( ∂ s ∂ p ) T d p for d s in the 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 31P

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The derivation of relation cp=−T(∂2g∂T2)p.

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Chapter 11.9, Problem 30P

Chapter 11.9, Problem 32P

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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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