$3\mathrm{.}17.$ A rigid, nonconducting tank with a volume of $4m^3$ is divided into two unequal parts

by a thin membrane. One side of the membrane, representing $\frac{1}{3}$ of the tank, contains

nitrogen gas at $6$ bar and $100C,$ and the other side, representing $\frac{2}{3}$ of the tank, is

evacuated. The membrane ruptures and the gas fills the tank.

$($a$)$ What is the final temperature of the gas? How much work is done? Is the process

reversible?

$($b$)$ Describe a reversible process by which the gas can be returned to its initial state.

How moch work is done?

Assume nitrogen is an ideal gas for which $C_P=(\frac{7}{2})R$ and $C_V=(\frac{5}{2})R.$