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The differential for the Internal energy, U, at constant composition is ?U = −P?V + T?S (a) What...

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Chemistry

The differential for the Internal energy, U, at constantcomposition is
?U = −P?V + T?S
(a) What are the natural independent variables of U? [2]
(b) Derive an expression for the change in internal energy atconstant Volume starting with the
above differential for the internal function, U, at constantcomposition. [3]
(c) Using the criterion for exact differentials, write the Maxwellrelation that is derived from this
equation. [2]
(d) Based on your answer in part (a), write the total differentialof U in terms of partial
differentials. [2]
(e) By comparison of the above equation (equation at the beginningof the question) and the total
differential of U written in part (d), obtain appropriateexpressions (partial differentials) for −P
and T.

Answer & Explanation Solved by verified expert
3.6 Ratings (544 Votes)
The differential for the Internal energy U at constantcomposition isU PV TSa What are the natural independent variables ofUAns Fundamental equations of Thermodynamics1 The combined first and second law From the first law dU dq dWFrom the second law T dq dS Where for irreversible system Tdq dS andfor reversible system dq dS T dq dS For a closed system inwhich only reversible pV work is    See Answer
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