$(30)$a$)$ Show that T$.$dS $=c_v*dT+(T\frac{}{}).dV$ using generalized method. $dS=c\frac{p}{T}*dT-V*dP$ and $dV=V*dT-V*dP$

b$)$ Calculate the entropy change as the temperature and volume of the one mole of ideal gas were taken from $273K$ and $22\mathrm{.}41$ ts to $373K$ and $44\mathrm{.}8$ lis.

$R=8\mathrm{.}314\frac{J}{m}ol.K=0\mathrm{.}082lt.at\frac{m}{m}ol.K$