$3.($a$)0\mathrm{.}5$ mol ideal Ar gas has an initial state of T$1=298$ K and P$1=100$ kPa with an entropy of $250$ J $($K$$mol$)-1.($a$)$ It is expanded to reach a pressure of $31\mathrm{.}5$ kPa through reversible adiabatic expansion. Calculate $$U$,$H$,$A$,$G$.(6$ marks$)($b$)$ If the expansion is conducted through an adiabatic process under a constant external pressure of $31\mathrm{.}5$ kPa. Find again the $$U$,$H$,$A$,$G$.$