1. (70 pts total) A gas follows the equation of state:
$$P = \frac{RT}{\bar{V}-b}$$
and its ideal-gas heat capacity at constant pressure is $C_p^{10} = c + eT$. The constants $b$, $c$, and $e$ are independent of temperature.
1.1. (45 pts) Obtain analytical expressions for differences in molar properties $\Delta U$, $\Delta H$ and $\Delta S$ for a general change of state of this gas from $(T_1, P_1)$ to $(T_2, P_2)$.