Explanation For pure substance: Write the expression for the chemical potential of the component using the equation ( 11.107 ) . μ t = ( ∂ G ∂ n t ) T , p , n i (I) Here, constant pressure, constant temperature, constant number of moles of the i th component are p , T , n i . Write the expression for the Gibbs function using the equation (14.12). G = n ⋅ g ¯ (II) Here, number of moles is n and Gibbs free energy is g ¯ . Differentiate the equation (I). ( ∂ G ∂ n t ) T , p = g ¯ (III) Comparing the equation (III) and equation (I), the chemical potential of pure substance is equal to the molar Gibbs free energy. For ideal gas mixture: Write the Gibbs function for the ideal gas mixture as follows. μ = G n G n = g ¯ (IV) Here, Gibbs function is G and number of moles is n . Write the expression for the enthalpy for the ideal gas mixture. H = ∑ i = 1 j n i − h ¯ ( T ) (V) Write the expression for the entropy for the ideal gas mixture. S = ∑ i = 1 j n i − s ¯ i ( T , p i ) (VI) Write the Gibbs function for the ideal mixture. G = H − T ⋅ s (VII) Substitute (III) and (II) in equation (IV) G = ∑ i = 1 j n i − h ¯ ( T ) − T ⋅ ∑ i = 1 j n i − s ¯ i ( T , p i ) G = ∑ i = 1 j n i ⋅ g ¯ ( T , p i ) (VIII) Here, molar Gibbs function of component i is g ¯ . Rearrange and Rewrite the equation (V) g ¯ ( T , p i ) = [ h ¯ i ( T ) − s ¯ i ( T , p i ) ] (IX) Write the Gibbs function using the equation 14

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Properties of Pure Substances

A substance with fixed chemical composition throughout is called a pure substance like water, air, and nitrogen. A pure substance does not have to be a single element or compound. A mixture of two or more phases of a pure substance is also a pure substan…

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Chapter 11.9, Problem 14E

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Reduce the equation 11.108 for system consisting a pure substance and ideal gas mixture.

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Chapter 11.9, Problem 13E

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