JEE Main 2026 Apr 6 Shift 1, Physics Q25: Thermodynamic Processes

For an isothermal process on an ideal gas, the (initial) bulk modulus equals the initial pressure: $B=P_0$. Hence $P_0=3\times 10^5$ N/m${}^2$.

Work done by the gas in isothermal compression: $W_{\text{by}}=nRT\ln \frac{V_f}{V_i}=P_0{V}_0\ln \frac{1}{3}$.

$P_0{V}_0=(3\times 10^5)(3\times 10^{-3})=900$ J. $\ln (1/3)=-\ln 3\approx -1.0986$.

$W_{\text{by}}\approx -988.75$ J.

Magnitude of work done on the gas $=|W_{\text{by}}|\approx 989$ J.

Note: The bulk modulus of an ideal gas varies with state during an isothermal process; here it is taken at the initial state per the standard textbook treatment.