Problem $3)$

Starting from Gibb's equation $dh=Tds+vdP$

a$)$ Show that for an isothermal process, $dh$ can be written as:

$\{$:$dh{)}_T=(v-T\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$

b$)$ Find $h$ for the isothermal compression of $N_2$ from $P_1$ to $P_2$ assuming that $N_2$ follows

$Pv=RT$

c$)$ Find $h$ for the isothermal compression of $N_2$ from $P_1$ to $P_2$ assuming that $N_2$ follows

$Pv=RT+bP,$ where $b=A+\frac{B}{T}+\frac{C}{T^2}$