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# ENG_sgwhk10 - -10th lecture 3.7 Helmholtz function F and...

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1 3.7 Helmholtz function ( 亥姆霍茨函数 ) F and Gibbs function ( 吉布斯函数 ) G -10 th lecture-

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2 1. Combination formula of the 1 st and the 2 nd laws of thermodynamics T sur d S -d U - δ W exp - δ W’ { } > irreversible = reversible 2. Helmholtz function For isothermal process T is constant T sys = T sur = T we have T d S U = -d( U - TS ) - δ W exp - δ W’ { } > irreversible = reversible Definition Helmholtz function F U - TS Because U T S are all state functions and U and T S have energy dimension, as a consequence F is a state function with energy dimension.
3 For processes of constant T( d T =0) , V (d V =0 Æ W exp =0), then -d F - δ W’ { } > irreversible = reversible For processes of constant T, V , and without other work -d F 0 { } > irreversible = reversible or d F 0 { } > irreversible = reversible Principium of helmholtz function decreasing ( 亥姆霍茨函数减少原 ) For a closed system without other work and at constant T and V conditions, the helmholtz function remains unchanged in reversible processes; and decreases always in irreversible processes till minimum at which the system reaches its equilibrium. Criterion of Helmholtz function ( 亥姆霍茨函数判据 ) : At constant T, V and W ′＝ 0, the system can be solely carried through spontaneously towards the direction of F decreasing, till Δ F T,V 0, then the system reaches its equilibrium.

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4 The work done by system in a reversible isothermal process ( W T is equal, by value, to the decrease of Helmholtz function. The work done by system in an irreversible isothermal process ( W T is always smaller than the decrease in Helmholtz function. Generalized work done in an isothermal process δ W T = δ W exp + δ W’ From - Δ F - δ W T { } > irreversible = reversible -d F - δ W T { } > irreversible = reversible or From the deduction of Clausius inequality The system does the biggest work in reversible isothermal process)
5 A closed system undergoes isothermal T = T sur and isobaric p = p ex ) process, the volume work done by system is δ W exp = - p d V From the combination equation of the 1 st and the 2 nd laws 3. Gibbs Function ( 吉布斯函数 ) (or Gibbs Energy) T d S -d U - p d V - δ W’ { } >irreversible = reversible - d (U -TS + pV ) - δ W’ { } > irreversible = reversible Since T, p are constant T sur d S U - δ W exp - δ W’ { } > irreversible = reversible

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6 Definition : G U pV TS H TS F pV G Gibbs function or Gibbs energy is a state function. It is an extensive quantity of the same dimension of H . - d G - δ W’ { } >irreversible = reversible That is The decrease in Gibbs function of a closed system in a reversible isothermal and isobaric process equals the non-volume work done by the system, and that in an irreversible isothermal and isobaric process it is bigger than the non-volume work done by the system.
7 When at constant temperature, constant pressure, and without other work - d G 0 { } >irreversible = reversible or d G 0 { } >irreversible = reversible Principium of Gibbs function decreasing ( 吉布斯 函数减 少原理 )

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ENG_sgwhk10 - -10th lecture 3.7 Helmholtz function F and...

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