A rigid, thermally insulated cylinder is divided into Compartment 1 and Compartment 2 by a thin, movable, thermally conducting partition that is initially locked in place.

Compartment 1 contains \(N_0\) molecules of an ideal monatomic gas at an initial temperature of \(2T_0\), and Compartment 2 contains \(2N_0\) molecules of an ideal monatomic gas at an initial temperature of \(T_0\). Each compartment initially has a volume of \(V_0\). The partition is unlocked and allowed to slide without friction while conducting thermal energy between the gases until the system reaches final mechanical and thermal equilibrium. What is the final equilibrium volume \(V_1\) of Compartment 1 in terms of \(V_0\)?