Q111 · 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 $(\partial \mathrm{U} / \partial \mathrm{V})_{\mathrm{T}}$ of a real gas is related to the compressibility factor $\mathrm{Z}=\mathrm{p} \tilde{\mathrm{V}} / \mathrm{RT}$ by [where, $\tilde{\mathrm{V}}$ is the molar volume]
(a)$(\partial \mathrm{U} / \partial \mathrm{V})_{\mathrm{T}}=\mathrm{RT}(\partial \mathrm{Z} / \partial \mathrm{V})_{\mathrm{T}}$
(b)$(\partial \mathrm{U} / \partial \mathrm{V})_{\mathrm{T}}=\mathrm{RT}(\tilde{\mathrm{V}} \mathrm{Z})$
(c)$(\partial \mathrm{U} / \partial \mathrm{V})_{\mathrm{T}}=\left(\mathrm{RT}^{2} / \tilde{\mathrm{V}}\right)(\partial \mathrm{Z} / \partial \mathrm{T})_{\mathrm{V}}$
(d)$(\partial \mathrm{U} / \partial \mathrm{V})_{\mathrm{T}}=\left(\tilde{\mathrm{V}} / \mathrm{RT}^{2}\right)(\partial \mathrm{Z} / \partial \mathrm{T})_{\mathrm{V}}$
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
(∂U/∂V)_T = T(∂p/∂T)_V − p; with p = ZRT/V this gives (RT²/V)(∂Z/∂T)_V (c).

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