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Irreversible processes (a) Consider two substances, initially at temperatures T' and T,, coming to equilibrium at a final temperature T, through heat exchange. By relating the direction of heat flow to the temperature difference, show that the change in the total entropy, which can be written as Ts đQ, + T T, Tf đQ2 T-121Q, AS = AS¡ +AS,> T,T, must be positive. This is an example of the more general condition that “in a closed system, equilibrium is characterized by the maximum value of entropy S." (b) Now consider a gas with adjustable volume V, and diathermal walls, embedded in a heat bath of constant temperature T, and fixed pressure P. The change in the entropy of the bath is given by AQbath 1 (ΔΕ, + PAVeas) . gas ASbath gas T By considering the change in entropy of the combined system establish that "the equilibrium of a gas at fixed T and P is characterized by the minimum of the Gibbs free energy G = E+PV – TS."

Irreversible processes (a) Consider two substances, initially at temperatures T' and T,, coming to equilibrium at a final temperature T, through heat exchange. By relating the direction of heat flow to the temperature difference, show that the change in the total entropy, which can be written as Ts đQ, + T T, Tf đQ2 T-121Q, AS = AS¡ +AS,> T,T, must be positive. This is an example of the more general condition that “in a closed system, equilibrium is characterized by the maximum value of entropy S." (b) Now consider a gas with adjustable volume V, and diathermal walls, embedded in a heat bath of constant temperature T, and fixed pressure P. The change in the entropy of the bath is given by AQbath 1 (ΔΕ, + PAVeas) . gas ASbath gas T By considering the change in entropy of the combined system establish that "the equilibrium of a gas at fixed T and P is characterized by the minimum of the Gibbs free energy G = E+PV – TS."

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Irreversible processes (a) Consider two substances, initially at temperatures T' and T,, coming to equilibrium at a final temperature T, through heat exchange. By relating the direction of heat flow to the temperature difference, show that the change in the total entropy, which can be written as Ts đQ, + T T, Tf đQ2 T-121Q, AS = AS¡ +AS,> T,T, must be positive. This is an example of the more general condition that “in a closed system, equilibrium is characterized by the maximum value of entropy S." (b) Now consider a gas with adjustable volume V, and diathermal walls, embedded in a heat bath of constant temperature T, and fixed pressure P. The change in the entropy of the bath is given by AQbath 1 (ΔΕ, + PAVeas) . gas ASbath gas T By considering the change in entropy of the combined system establish that "the equilibrium of a gas at fixed T and P is characterized by the minimum of the Gibbs free energy G = E+PV – TS."
Transcribed Image Text:Irreversible processes (a) Consider two substances, initially at temperatures T' and T,, coming to equilibrium at a final temperature T, through heat exchange. By relating the direction of heat flow to the temperature difference, show that the change in the total entropy, which can be written as Ts đQ, + T T, Tf đQ2 T-121Q, AS = AS¡ +AS,> T,T, must be positive. This is an example of the more general condition that “in a closed system, equilibrium is characterized by the maximum value of entropy S." (b) Now consider a gas with adjustable volume V, and diathermal walls, embedded in a heat bath of constant temperature T, and fixed pressure P. The change in the entropy of the bath is given by AQbath 1 (ΔΕ, + PAVeas) . gas ASbath gas T By considering the change in entropy of the combined system establish that "the equilibrium of a gas at fixed T and P is characterized by the minimum of the Gibbs free energy G = E+PV – TS."
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