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10.15. If interfacial properties contribute to the bulk thermodynamic behavior of a system, the fundamental equation must be modified to include their effects. Generally, one can write for a single-component single-phase system dG -S dT + V dP udNy dA where A is the surface area of the system and y is the surface tension. Note that y is defined by the change in Gibbs free energy with area at constant T, P, and N. Generally, the surface tension is positive, which drives systems towards the minimization of interfacial areas by way of minimizing the Gibbs free energy (a) Show that the entropy of the system is independent of its area if the surface tension is constant with temperature (b) If the area is extensive (e.g., scales linearly with N), show that (ou/oy)Tp= -A/N.

10.15. If interfacial properties contribute to the bulk thermodynamic behavior of a system, the fundamental equation must be modified to include their effects. Generally, one can write for a single-component single-phase system dG -S dT + V dP udNy dA where A is the surface area of the system and y is the surface tension. Note that y is defined by the change in Gibbs free energy with area at constant T, P, and N. Generally, the surface tension is positive, which drives systems towards the minimization of interfacial areas by way of minimizing the Gibbs free energy (a) Show that the entropy of the system is independent of its area if the surface tension is constant with temperature (b) If the area is extensive (e.g., scales linearly with N), show that (ou/oy)Tp= -A/N.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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This problem is (10.15) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

10.15. If interfacial properties contribute to the bulk thermodynamic behavior of a system, the fundamental equation must be modified to include their effects. Generally, one can write for a single-component single-phase system dG -S dT + V dP udNy dA where A is the surface area of the system and y is the surface tension. Note that y is defined by the change in Gibbs free energy with area at constant T, P, and N. Generally, the surface tension is positive, which drives systems towards the minimization of interfacial areas by way of minimizing the Gibbs free energy (a) Show that the entropy of the system is independent of its area if the surface tension is constant with temperature (b) If the area is extensive (e.g., scales linearly with N), show that (ou/oy)Tp= -A/N.
Transcribed Image Text:10.15. If interfacial properties contribute to the bulk thermodynamic behavior of a system, the fundamental equation must be modified to include their effects. Generally, one can write for a single-component single-phase system dG -S dT + V dP udNy dA where A is the surface area of the system and y is the surface tension. Note that y is defined by the change in Gibbs free energy with area at constant T, P, and N. Generally, the surface tension is positive, which drives systems towards the minimization of interfacial areas by way of minimizing the Gibbs free energy (a) Show that the entropy of the system is independent of its area if the surface tension is constant with temperature (b) If the area is extensive (e.g., scales linearly with N), show that (ou/oy)Tp= -A/N.
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