A gas is compressed isothermally to one-third of its initial volume. The initial volume is 3 litres, and the stated bulk modulus is 3×10⁵ N·m⁻². Following the interpretation used in the given solution, take this bulk modulus as the initial isothermal bulk modulus. Find the magnitude of the work done on the gas in joules, to the nearest integer.
Physics · Thermodyanmics · thermodynmic process and work done
JEE Mains 2026 6 April Morning Shift

Question

A gas is compressed isothermally to one-third of its initial volume. The initial volume is 3 litres, and the stated bulk modulus is 3×10⁵ N·m⁻². Following the interpretation used in the given solution, take this bulk modulus as the initial isothermal bulk modulus. Find the magnitude of the work done on the gas in joules, to the nearest integer.

Physics · Thermodyanmics · thermodynmic process and work done

JEE Mains 2026 6 April Morning Shift

G1 Physics · Accepted Answer

For an isothermal ideal-gas process, the isothermal bulk modulus equals the pressure at that state. Following the source solution, the given bulk modulus is treated as the initial pressure: P₀ = B = 3×10⁵ Pa. Initial volume: V₀ = 3 litres = 3×10⁻³ m³. The final volume is V₂ = V₀ ÷ 3. The magnitude of work done on the gas during isothermal compression is W(on) = P₀V₀ ln(V₀ ÷ V₂). Since V₀ ÷ V₂ = 3, W(on) = BV₀ ln3. Therefore, W(on) = (3×10⁵)(3×10⁻³)ln3 = 900×1.0986 ≈ 988.75 J. To the nearest int…