(a) Explanation Write the expression for fugacity at a fixed temperature T from ( p ' , v ¯ ' ) to ( p , v ¯ ) . R ¯ T [ ln f ] f ' f = ∫ p ' p v ¯ d p (I) Here, the universal gas constant is R ¯ , the temperature of the gas is T , the initial pressure of the gas is p , the final pressure is p ′ , the initial specific volume is v , the final specific volume v ¯ and the fugacity is f . The figure below shows the graph between the varying pressure and varying volume. Figure-(1) Write the expression for area under curve when the pressure and volume varying. ∫ p ' p v ¯ d p + p ' v ¯ ' = ∫ v ¯ v ¯ ' p d v + p v ¯ ∫ p ' p v ¯ d p = p v ¯ − p ' v ¯ ' + ∫ v ¯ v ¯ ' p d v ∫ p ' p v ¯ d p = p v ¯ − p ' v ¯ ' − ∫ v ¯ ' v ¯ p d v (II) Write the expression for Redlich-Kwong Equation. ∫ v ¯ ' v ¯ p d v = ∫ v ¯ ' v ¯ [ R ¯ T v ¯ − b − a T v ¯ ( v ¯ + b ) ] d v ¯ (III) Here, the constants are a and b . Conclusion: Substitute p v ¯ − p ' v ¯ ' − ∫ v ¯ ' v ¯ p d v for ∫ p ' p v ¯ d p in Equation (I). R ¯ T [ ln f ] f ' f = p v ¯ − p ' v ¯ ' − ∫ v ¯ ' v ¯ p d v (IV) Substitute ∫ v ¯ ' v ¯ [ R ¯ T v ¯ − b − a T v ¯ ( v ¯ + b ) ] d v ¯ for ∫ v ¯ ' v ¯ p d v in Equation (IV). R ¯ T [ ln f ] f ' f = p v ¯ − p ' v ¯ ' − ∫ v ¯ ' v ¯ [ R ¯ T v ¯ − b − a T v ¯ ( v ¯ + b ) ] d v ¯ ln f f ' = [ p v ¯ R ¯ T − p ' v ¯ ' R ¯ T − ln [ R ¯ T ( v ¯ − b ) ] − a R ¯ T 3 / 2 [ 1 ( v ¯ + b ) + 1 b ln ( ( v ¯ + b ) v ¯ ) (b) To determine The fugacity for refrigerant.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 11.9, Problem 114P

(a)

To determine

The value of lnf for a gas obeying Redlich-Kwong equation.

(b)

To determine

The fugacity for refrigerant.

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Chapter 11.9, Problem 113P

Chapter 11.9, Problem 115P

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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 value of ln f for a gas obeying Redlich-Kwong equation.