Q 11-11-036JEE MainJEE Main 2026 (6 Apr, Shift 1)Medium
A certain gas is isothermally compressed to $\left(\dfrac{1}{3}\right)^{\text{rd}}$ of its initial volume ($V_0 = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5\ \text{N/m}^2$, the magnitude of work done on the gas is ______ J.
Numerical value type. Enter your answer.
Answer: 989
For an isothermal process the bulk modulus equals the pressure, so the initial pressure is $p_0 = 3 \times 10^5$ Pa.
$$|W| = p_0V_0\ln\frac{V_0}{V} = 3 \times 10^5 \times 3 \times 10^{-3} \times \ln 3 = 900 \times 1.0986 \approx 989\ \text{J}$$
Solution by Sreeraj P, M.Sc Physics