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 \( \dfrac{n x R}{K A} \), where \( R \) is the universal gas constant. The value of \( n \) is: [Given: \( \ln 2 \approx 0.7 \)] 
