A rigid, nonconducting tank with a volume of $3$ m$3$ is divided into two unequal parts by a thin membrane. One side of the membrane, representing $1/3$ of the tank, contains nitrogen gas at $6$ bar and $100\backslash$deg C$,$ and the other side, representing $2/3$ of the tank, is evacuated. The membrane ruptures and the gas fills the tank. Assume nitrogen is an ideal gas for which Cp $=(7/2)$R and Cv $=(5/2)$R$.$

Calculate the final temperature of the gas and the work done. $($You must provide an answer before moving to the next part.$)$