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 temperature difference of \(S_1\) and \(S_2\) is
\[
\Delta T_0
\]
The time it takes for the temperature difference to become
\[
\frac{\Delta T_0}{2}
\]
is
\[
\frac{nRx}{KA}
\]
where \(R\) is the universal gas constant. The value of \(n\) is _______.
\[
[\text{Given: }\ln2\approx0.7]
\]
