JEE Advanced · 2020 · 27 Sep 2020 · Paper 1 · Heat & Thermodynamics

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4V_1$. After this, the gas expands adiabatically and its volume becomes $32V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text{iso }}$ and $W_{\text{adia }}$, respectively. If the ratio $\frac{{\mathrm{W}}_{\text{iso }}}{{\mathrm{W}}_{\text{adia }}}=f\ln 2$, then $f$ is ____.