4AB › Chemistry PYQ › CSIR-NET › June 2019 › Q84Q84 · CSIR-NET Chemistry, June 2019 Paper: CSIR-NET June 2019 · Subject: Physical Chemistry · Chapter: Thermodynamics · Topic: Laws State Functions · Marks: 2 · Difficulty: Medium
A non-ideal gas, follows the equation \[ P=\frac{R T}{V_{m}}\left[1+\frac{B}{V_{m}}\right] \]
where B is a function of temperature only. The deviation in internal energy from that of an ideal gas, $\mathrm{U}-\mathrm{U}_{\text {ideal }}$ ideal is given by (a) $-\frac{\mathrm{RT}}{\mathrm{V}_{\mathrm{m}}}\left(\frac{\partial \mathrm{B}}{\partial \mathrm{T}}\right)_{\mathrm{V}}$
(b) $-\frac{\mathrm{RT}^{2}}{\mathrm{V}_{\mathrm{m}}}\left(\frac{\partial \mathrm{B}}{\partial \mathrm{T}}\right)_{\mathrm{V}}$
(c) $-\frac{\mathrm{RT}^{2}}{\mathrm{V}_{\mathrm{m}}} \mathrm{B}$
(d) $-\frac{R T}{V_{m}} B$
Answer Answer: B ✓ checked by 4AB · confidence medium
Explanation (∂U/∂V)_T = T(∂p/∂T)_V − p = (RT²/V_m²)(dB/dT); integrating from V_m = ∞ gives U − U_ideal = −(RT²/V_m)(dB/dT).
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