An ideal gas at pressure P and temperature T is expanding such that PT 3 = constant . The coefficient of volume expansion of the gas is .

Physics · Thermodynamics

JEE Main 2026 — 5 April, Evening Shift — Question 9

An ideal gas at pressure P and temperature T is expanding such that $PT^3 = \text{constant}$ . The coefficient of volume expansion of the gas is ____.

Option A:
$\frac{2}{T}$
Option B:
$\frac{3}{T}$
Option C:
$\frac{4}{T}$
Correct
Option D:
$\frac{3}{T}$

Answer: C

Step-by-step solution

From $PT^3 = C$ and ideal gas $PV = nRT$ , eliminate P: $(nRT/V) T^3 = C \Rightarrow V \propto T^4$ . Then $\beta = \frac{1}{V}\frac{dV}{dT} = \frac{4}{T}$ .

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 5 April, Evening Shift
Subject: Physics
Chapter: Thermodynamics
Topic: First Law of Thermodynamics