Q54 · CSIR-NET Chemistry, December 2019

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

$(C_P - C_V)$ for a non-ideal gas differs from $(C_P - C_V)$ for a perfect gas by the expression
(a)$\left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial U}{\partial P}\right)_S$
(b)$\left(\frac{\partial V}{\partial T}\right)_P \left(\frac{\partial U}{\partial V}\right)_T$
(c)$-\frac{1}{T}\left(\frac{\partial V}{\partial T}\right)_P \left(\frac{\partial U}{\partial V}\right)_T$
(d)$\left(\frac{\partial P}{\partial T}\right)_V \left(\frac{\partial U}{\partial T}\right)_P$
Answer
Answer: B ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Key was empty although the correct expression is printed as option (b): C_P − C_V = (∂V/∂T)_P[P + (∂U/∂V)_T], and the excess over a perfect gas is (∂V/∂T)_P(∂U/∂V)_T.

Explanation
C_P − C_V = (∂V/∂T)_P [P + (∂U/∂V)_T]. For a perfect gas (∂U/∂V)_T = 0, so C_P − C_V = P(∂V/∂T)_P = R. For a non-ideal gas the extra term is (∂V/∂T)_P(∂U/∂V)_T, which is option (b).

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