The specific heat at constant pressure of a real gas obeying $\mathrm{PV}^{2}=\mathrm{RT}$ equation is:

(D) $\mathrm{C}_{\mathrm{V}}+\frac{\mathrm{R}}{2 \mathrm{~V}}$

(A) $\mathrm{C}_{\mathrm{V}}+\mathrm{R}$

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Heat & Thermodynamics

The specific heat at constant pressure of a real gas obeying

PV^{2} = RT

equation is:

(A) $C_{V} + R$
(B) $\frac{R}{3} + C_{V}$
(C)R
(D) $C_{V} + \frac{R}{2 V}$ ✓ Correct

Answer: (D)

Solution

By the first law of thermodynamics (per mole):

C d T = C_{V} d T + P d V

.
Differentiating the state relation

P V^{2} = R T

(with

P

treated as constant along the process):

P (2 V d V) = R d T

, so

P d V = \frac{R d T}{2 V}

.
Substituting,

C = C_{V} + \frac{R}{2 V} .

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Single correct option

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