Calculate the change in internal energy, enthalpy, entropy and free energy when one kmol an ideal gas at $300K$ and $\frac{1}{b}ar$ is heated and compressed to $500K$ and $100$ bar. The entropy of the gas in the initial state is $131\mathrm{.}5k\frac{J}{k}$molK. Enthalpy at $273K$ may be taken to be zero. Assume $C_P=27\mathrm{.}3+4\mathrm{.}2{10}^{-3}T$ at $1$ bar where $C_P$ is in $k\frac{J}{k}$molK and $T$ is in $K.$