$P=\frac{RT}{V-b}-\frac{a^2}{V^2}$

$dP=\frac{RdT}{V-b}+[\frac{2a^2}{V^3}-\frac{RT}{(V-b{)}^2}]dV$

$1$atmL$-=\frac{8\mathrm{.}3144}{0\mathrm{.}082057}J$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{V}{(V-b{)}^2}dV=\frac{-b}{V-b}+ln(V-b)$

Assume the nitrogen gas is behaving as a van der waals gas. a$=1\mathrm{.}39$L$^2.$atm$/$mol$^2$ and b$=39\mathrm{.}1$cm$^3/$mol $.$ At $400$K$,$ calculate the gibbs free energy change when the volume is increased from $1$L to $2$L$.$