JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Heat & Thermodynamics

Two thermodynamical process are shown in the figure. The molar heat capacity for process A and

B

are

C_{A}

and

C_{B}

. The molar heat capacity at constant pressure and constant volume are represented by

C_{P}

and

C_{V}

, respectively. Choose the correct statement.

(A) $C_{B} = \infty, C_{A} = 0$
(B) $C_{A} = 0$ and $C_{B} = \infty$
(C) $C_{P} > C_{V} > C_{A} = C_{B}$
(D) $C_{A} > C_{P} > C_{V}$

Solution

For process A, the relation

P V^{- γ} = constant

(with

γ > 1

) gives

C_{A} = C_{V} + \frac{R}{1 + γ}

. For process B,

P V^{- 1} = constant

gives

C_{B} = C_{V} + \frac{R}{2}

. Since

C_{P} = C_{V} + R

, we have

C_{P} > C_{B} > C_{A} > C_{V}

. None of the given options match this ordering.

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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