A cylindrical container of volume `V_(0)` is divided into two parts by a thin conducting separator of negligible mass. The walls of the container are adiabatic. Ideal gases are filled in the two parts such that the pressures are `P_(0) " and " 2 P_(0)` when the separator is held in the middle of the container (see figure). Now the separator is slowly slid and released in a position where it stays in equilibrium. Find the volume of the two parts.

Answer

`(2V_(0))/(3) " and " (V_(0))/(3)`