JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Heat & Thermodynamics

An ideal gas at pressure

P

and temperature

T

is expanding such that

P T^{3} =

constant. The coefficient of volume expansion of the gas is ______.

(A) $\frac{2}{T}$
(B) $\frac{1}{T}$
(C) $\frac{4}{T}$ ✓ Correct
(D) $\frac{3}{T}$

Answer: (C)

Solution

For an ideal gas

P V = n R T

, so

P = \frac{n R T}{V}

. Substituting into

P T^{3} = constant

gives

\frac{n R T}{V} T^{3} = constant

, hence

V = (\frac{n R}{constant}) T^{4}

, i.e.

V \propto T^{4}

. The coefficient of volume expansion is

γ = \frac{1}{V} \frac{d V}{d T} = \frac{1}{T ^{4}} (4 T^{3}) = \frac{4}{T}

. The coefficient of volume expansion of the gas is

\frac{4}{T}

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Single correct option

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