$6-25.$ One mole of a gas is compressed at a constant temperature of $400K$ from $P=0\mathrm{.}1$ bar to $P=10$ bar. The gas is known to follow the equation of state:

$V_{?}=R\frac{T}{P}+a{P}^2$

where $a=()2.$

The ideal gas heat capacity at $T=400K$ is $C_P^{**}=3\mathrm{.}85R.$

A$.$ Find an equation for the residual $G_{?}$ for a gas that follows this equation of state.

B$.$ Find the change in Gibbs free energy for this process.