Helium gas $)=(5\mathrm{.}2(kJ)*K{g}^{-1}*K^{-1}$ undergoes a change of state from $100$kPa and $25C$ to $500$kPa and $250C.$ Assuming the gas obeys the following equation of state: $P(V-a)=RT$; where $a=0\mathrm{.}01m^3*k{g}^{-1},$ determine the change in the enthalpy $($in $kJ*k{g}^{-1}),$ and entropy $($in $kJk{g}^{-1}*K^{-1})$ by:

a$-$ Using $($eq$.6\mathrm{.}21)$ and $($eq$.6\mathrm{.}22)$

b$-$ Using the ideal gas state combined with $($eq$.6\mathrm{.}46)$ and $($eq$.6\mathrm{.}48)$