A closed, adiabatic system is divided in two subsystems by a separator. The first subsystem has a volume of $0\mathrm{.}01$ m$\mathrm{^{\; 3}}$ and contains $1$ mol of monoatomic gas at the temperature of $400$ K$.$ The second subsystem, containing $2$ mol of the same gas, is at the same pressure of the first, but its volume is three times the one of the first subsystem. If the separator is removed, calculate the equilibrium temperature and the variation of entropy of the system.