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(a) If a system undergoes a transformation in which it exchanges an amount of heat Q with a reservoir at temperature Tres, its entropy change satisfies the condition Tres This is essentially proving that Chandler's statement of the Second Law implies Gibbs' statement of the Second Law. ASZ (b) Maximum Work Theorem. The maximum amount of work that can be extracted from a system kept at constant temperature and composition is equal to −AA, where AA is the change in the Helmholtz free energy of the system, Wmax extracted|T,{n;} = −AA.

(a) If a system undergoes a transformation in which it exchanges an amount of heat Q with a reservoir at temperature Tres, its entropy change satisfies the condition Tres This is essentially proving that Chandler's statement of the Second Law implies Gibbs' statement of the Second Law. ASZ (b) Maximum Work Theorem. The maximum amount of work that can be extracted from a system kept at constant temperature and composition is equal to −AA, where AA is the change in the Helmholtz free energy of the system, Wmax extracted|T,{n;} = −AA.

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Consider a system which is in contact with a reservoir. The combination, system and the reservoir, is isolated: it does not exchange heat, mass or work with the rest of the universe. Use this setup, the First Law of Thermodynamics, and Chandler's statements of the Second Law of Thermodynamics, to prove the following: (a) If a system undergoes a transformation in which it exchanges an amount of heat Q with a reservoir at temperature Tres, its entropy change satisfies the condition ASZ Q Tres This is essentially proving that Chandler's statement of the Second Law implies Gibbs' statement of the Second Law. (b) Maximum Work Theorem. The maximum amount of work that can be extracted from a system kept at constant temperature and composition is equal to -AA, where AA is the change in the Helmholtz free energy of the system, Wmax extracted T,{n₁} -AA.
Transcribed Image Text:Consider a system which is in contact with a reservoir. The combination, system and the reservoir, is isolated: it does not exchange heat, mass or work with the rest of the universe. Use this setup, the First Law of Thermodynamics, and Chandler's statements of the Second Law of Thermodynamics, to prove the following: (a) If a system undergoes a transformation in which it exchanges an amount of heat Q with a reservoir at temperature Tres, its entropy change satisfies the condition ASZ Q Tres This is essentially proving that Chandler's statement of the Second Law implies Gibbs' statement of the Second Law. (b) Maximum Work Theorem. The maximum amount of work that can be extracted from a system kept at constant temperature and composition is equal to -AA, where AA is the change in the Helmholtz free energy of the system, Wmax extracted T,{n₁} -AA.
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