Question

A non-conducting cylinder having volume $2V_0$ is partitioned by a fixed non conducting wall in two equal parts. Partition is attached with a valve. The right side of the partition is a vacuum and left part is filled with a gas having pressure and temperature $P_0$ and $T_0$ respectively. If the valve is opened, find the final pressure and temperature of the two parts

Answer 1

From the first law thermodynamics $\Delta Q=\Delta U+W$
Since gas expands freely therefore $W=0$, since no heat is given to gas $\Delta Q=0$
$\Rightarrow \Delta U=0$ and temperature remains constant.
$T_{final}=T_0$
Since the process is isothermal therefore $P_0\times V_0=P_{final}\times 2V_0\Rightarrow P_{final}=P_0/2$