$(25$P$)$ A $2-$m$3$ rigid tank contains hydrogen at $250$ kPa and $550$ K $.$ The gas is now cooled until its temperature drops to $350$ K $.$ Determine $($a$)$ the final pressure in the tank and $($b$)$ the amount of heat transfer kJ$.$

$R=4\mathrm{.}1240$;$Cp=14\mathrm{.}307$;$Cv=10\mathrm{.}183k\frac{J}{k}gK$