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Now, show that for any adiabatic operation (T, X) → (T', X') to be possible, we must ensure the condition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables.

Now, show that for any adiabatic operation (T, X) → (T', X') to be possible, we must ensure the condition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables.

Chemistry: The Molecular Science
Chemistry: The Molecular Science
5th Edition
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:John W. Moore, Conrad L. Stanitski
Chapter16: Thermodynamics: Directionality Of Chemical Reactions
Section16.3: Measuring Dispersal Of Energy: Entropy
Problem 16.3CE
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We know that Entropy S is a mathematical quantity that gives us information on the direction of possible thermodynamic processes. You can use the following assumptions and facts without proving: I. Entropy is an increasing function of temperature II. Second Law of Thermodynamics III. There exist adiabatic processes that had the sole effect of increasing the temperature of the system. In other words, if T < T', the process (T, X) → (T', X) is possible. Planck's Principle: For any extensive variables X and temperatures T < T', adiabatic processes (T,X) → (T'', X) that do not change X is irreversible. Now, show that for any adiabatic operation (T, X) → (T',X') to be possible, we must ensure the condition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables. IV.
Transcribed Image Text:We know that Entropy S is a mathematical quantity that gives us information on the direction of possible thermodynamic processes. You can use the following assumptions and facts without proving: I. Entropy is an increasing function of temperature II. Second Law of Thermodynamics III. There exist adiabatic processes that had the sole effect of increasing the temperature of the system. In other words, if T < T', the process (T, X) → (T', X) is possible. Planck's Principle: For any extensive variables X and temperatures T < T', adiabatic processes (T,X) → (T'', X) that do not change X is irreversible. Now, show that for any adiabatic operation (T, X) → (T',X') to be possible, we must ensure the condition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables. IV.
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