A fluid fits the following equation of state.

$P(V_{-}b)=RT+(\frac{a{P}^2}{T}),a={10}^{-3}{m}^3\frac{K}{\text{b}\text{a}\text{r}*\text{m}\text{o}\text{l}}veb=8^{***}{10}^{-5}\frac{m^3}{m}ol$

For this fluid, the average $Cp$ value between $0-300C$ at $1$ bar is $33\mathrm{.}5\frac{J}{m}ol.K.$

a$)$ Calculate the average $C_p$ value in the $0-300C$ temperature range for $12$ bar pressure.

b$)$ Calculate the enthalpy and entropy change when the fluid is brought from $4$ bar and $300K$ to $12$ bar and $400K.$