Q156 · CSIR-NET Chemistry, December 2019

Paper: CSIR-NET December 2019 · Subject: Physical Chemistry · Chapter: Thermodynamics · Topic: Thermodynamics – General · Marks: 2 · Difficulty: Medium

$\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)$ for a non-ideal gas differs from $\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)$ for a perfect gas by the expression
(a)$\left(\frac{\partial \mathrm{P}}{\partial \mathrm{T}}\right)_{\mathrm{V}}\left(\frac{\partial \mathrm{U}}{\partial \mathrm{P}}\right)_{\mathrm{S}}$
(b)$\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\mathrm{P}}\left(\frac{\partial \mathrm{U}}{\partial \mathrm{V}}\right)_{\mathrm{T}}$
(c)$-\frac{1}{\mathrm{T}}\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\mathrm{P}}\left(\frac{\partial \mathrm{U}}{\partial \mathrm{V}}\right)_{\mathrm{T}}$
(d)$\left(\frac{\partial \mathrm{P}}{\partial \mathrm{T}}\right)_{\mathrm{V}}\left(\frac{\partial \mathrm{U}}{\partial \mathrm{T}}\right)_{\mathrm{P}}$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
Cp − Cv = (∂V/∂T)_P[P + (∂U/∂V)_T]. The extra term over the perfect gas, where (∂U/∂V)_T = 0, is (∂V/∂T)_P(∂U/∂V)_T, which is expression 2, option (b).

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