Problem $1$

A rigid vessel is divided into two compartments by a partition. The volume of each compartment is $0\mathrm{.}1m^3.$ One compartment initially contains $400$ moles of gas A at $300K,$ and the other compartment is initially evacuated. The partition is then removed, and the gas is allowed to expand to a final temperature of $200K.$ Gas A is not ideal under these circumstances but can be described well by the following equation of state:

$P=\frac{RT}{v-b}+\frac{a}{T{v}^2}$

Where $a=42\frac{lKm}{mo{l}^2}$ and, $b=3\mathrm{.}2{10}^{-5}\frac{m^3}{(mol)}$

Heat capacity of gas A can be assumed to be $C_V=\frac{3}{2}R$

Determine:

a$-$ The final pressure of the gas

b$-$ The amount of heat exchanged with the surrounding $($Q in $\frac{J}{m}ol)$