Physics · Thermodynamics

JEE Main 2026 — 6 April, Morning Shift — Question 20

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\mathrm{nd}}$ of its initial volume $(V_0 = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3\times10^{5}\mathrm{N/m}^2$ , the magnitude of work done on the gas is ______ J.

Answer: 989

Numerical answer — enter this value.

Step-by-step solution

For isothermal process, bulk modulus B = P (initial pressure). Given B = 3×10^5 Pa, so P0 = 3×10^5 Pa. Work done on gas (W = -nRT \ln(V_f/V_i) = -P_0 V_0 \ln(1/3) = -3×10^5 × (3×10^{-3}) × (-1.0986) = 3×10^5×3×10^{-3}×1.0986 = 900×1.0986 = 988.74 ≈ 989 J.

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 6 April, Morning Shift
Subject: Physics
Chapter: Thermodynamics
Topic: Calculation of Work, Heat and Internal Energy