JEE Advanced 2026 · Paper 1, Physics question 11

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition $(P_1)$ and a freely movable but thermally insulated piston $(P_2)$. The partition $P_1$ with thermal conductivity $K$, cross sectional area $A$ and width $x$ divides the container into two sections, $S_1$ and $S_2$, each containing one mole of a monoatomic gas. The piston $P_2$ moves freely such that the gas in $S_2$ is always at the atmospheric pressure. Initially, the difference between the temperatures of $S_1$ and $S_2$ is $\Delta T_0$. The time it takes for the temperature difference to become $\dfrac{\Delta T_0}2$ is $nxR/KA$, where $R$ is the universal gas constant. The value of $n$ is:
[Given: $\ln2\approx0.7$]