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 `Delta Q =Delta u + Delta W` Since gas expands freely therefore `Delta W =0,` since no heat is given to gas `Delta Q=0`
`implies Delta u =0` and temperature remains constant.
Since the process is isothermal therefore
`P_(0) xx V_(0) = P_("fnal") xx 2V_(0)`
`implies P _("final") = P_(0)//2`