JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Heat & Thermodynamics

For an adiabatic expansion of an ideal gas , the fractional change in its pressure is equal to ( where

γ

is the ratio of specific heats):

(A) $- γ \frac{d V}{V}$ ✓ Correct
(B) $\frac{d V}{V}$
(C) $- γ \frac{V}{d V}$
(D) $- \frac{1}{γ} \frac{d V}{V}$

Answer: (A)

Solution

In an adiabatic change

P V^{γ}

stays constant. Differentiating,

V^{γ} d P + γ P V^{γ - 1} d V = 0

Dividing throughout by

P V^{γ}

gives

\frac{d P}{P} + γ \frac{d V}{V} = 0

, so the fractional change in pressure is

\frac{d P}{P} = - γ \frac{d V}{V}

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option

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