Q36 · CSIR-NET Chemistry, December 2012
Paper: CSIR-NET December 2012 · Subject: Physical Chemistry · Chapter: Thermodynamics · Topic: Thermodynamics – General · Marks: 2 · Difficulty: Medium
The internal pressure $(\partial U / \partial V)_{T}$ of a real gas is related to the compressibility factor \[ \mathrm{Z}=\mathrm{p} \tilde{\mathrm{V}} / \mathrm{RT} \text { by } \]
[ where, $\tilde{\mathrm{V}}$ is the molar volume] (a)$(\partial U / \partial V)_{T}=RT(\partial Z / \partial V)_{T}$
(b)$(\partial U / \partial V)_{T}=RT/(\tilde{V} Z)$
(c)$(\partial U / \partial V)_{T}=(RT^{2}/\tilde{V})(\partial Z/\partial T)_{V}$
(d)$(\partial U / \partial V)_{T}=(\tilde{V}/RT^{2})(\partial Z/\partial T)_{V}$
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
π_T = T(∂p/∂T)_V − p with p = ZRT/V̄: T(∂p/∂T)_V = ZRT/V̄ + (RT²/V̄)(∂Z/∂T)_V, so π_T = (RT²/V̄)(∂Z/∂T)_V.
Study loop for Thermodynamics
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