The differential form of the Helmholtz free energy, for a closed, one-component system, is dA = -PdV - SdTStarting from A=U-TS, derive the above expression.Show that ΔA=ΔU-TΔS. The Helmholtz energy can be used to determine the spontaneity of a process in the same way as the Gibbs energy: dA = -PdV - SdT + ∑µi dNi which at equilibrium dA = 0 Under what conditions and/or for what types of systems would it be easier to use the Helmholtz free energy, as opposed to the Gibbs free energy?

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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

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Problem 1.1P

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The differential form of the Helmholtz free energy, for a closed, one-component system, is dA = -PdV - SdT

Starting from A=U-TS, derive the above expression.
Show that ΔA=ΔU-TΔS.
The Helmholtz energy can be used to determine the spontaneity of a process in the same way as the Gibbs energy:

dA = -PdV - SdT + ∑µ_i dN_i

which at equilibrium dA = 0

Under what conditions and/or for what types of systems would it be easier to use the Helmholtz free energy, as opposed to the Gibbs free energy?

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