JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Heat & Thermodynamics

A certain gas is isothermally compressed to

(\frac{1}{3})^{rd}

of its initial volume (

V_{0} = 3

litre) by applying required pressure. If the bulk modulus of the gas is

3 \times 1 0^{5} N / m^{2}

, the magnitude of work done on the gas is ______ J.

Answer: 989

Solution

For an isothermal change

P V = P_{0} V_{0}

, and the given bulk modulus equals the initial pressure,

P_{0} = B = 3 \times 1 0^{5}

N/m

^{2}

. The work done on the gas compressed from

V_{0}

V_{0} /3

∣ W ∣ = \int_{V_{0}}^{V_{0} /3} P d V = P_{0} V_{0} ln \frac{V _{0}}{V _{0} /3} = P_{0} V_{0} ln 3

. With

V_{0} = 3 \times 1 0^{- 3}

^{3}

∣ W ∣ = 3 \times 1 0^{5} \times 3 \times 1 0^{- 3} \times ln 3 = 900 \times 1.0986 = 988.7

J. The magnitude of the work done is

989

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Integer answer

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