A membrane divides a rigid, well$-$insulated $6m^3$ vessel into two equal parts. The left side contains an ideal gas $(c_P=30\frac{J}{\text{m}\text{o}\text{l}\text{K}}$ at $15$ bar and $270K.$ The right side contains nothing $($vacuum$).$ A small hole forms in the membrane, gas slowly leaks out from the left side, and eventually the temperature in the tank equalizes. What is the final temperature? What is the final pressure?