A nonconducting cylinder having volume `2 V_(0)` is partitioned by a fixed non conducting wall in two equal part. Partition is attached with a valve. 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 valve is opened find the final pressure and temperature of the two parts.

Explanation

From the first law thermodynamics `DeltaQ = DeltaU +W`
Since gas expands freely therefore `w = 0`, since no heat is given to gas `DeltaQ = 0`
`rArr DeltaU = 0` and temperature remains constant.
`T_("final") = T_(0)`
Since the process is isothermal therefore `P_(0) xx V_(0) = P_("final") xx 2V_(0) rArr P_("final") = P_(0)//2`