P$5\mathrm{.}121\mathrm{.}10$ moles of $N_2$ at $20\mathrm{.}5C$ and $6\mathrm{.}20$ bar undergoes a transformation to the state described by $215C$ and $1\mathrm{.}75$ bar $.$ Calculate $S$ if

$\frac{C_{P,m}}{Jmo{l}^{-1}{K}^{-1}}=30\mathrm{.}81-11\mathrm{.}87{10}^{-3}\frac{T}{(K)}+2\mathrm{.}3968{10}^{-5}\frac{T^2}{K^2}$

$-1\mathrm{.}0176{10}^{-8}\frac{T^3}{K^3}$