$($a$)$ An ideal gas expands adiabatically from a volume of $2\mathrm{.}0103$m$32\mathrm{.}0103$m$3$ to $2\mathrm{.}5103$m$32\mathrm{.}5103$m$3.$ If the initial pressure and temperature were $5\mathrm{.}0105$Pa$5\mathrm{.}0105$Pa and $300$ K$,$ respectively, what are the final pressure and temperature of the gas? Use $=5/3$$=5/3$ for the gas. $($b$)$ In an isothermal process, an ideal gas expands from a volume of $2\mathrm{.}0103$m$32\mathrm{.}0103$m$3$ to $2\mathrm{.}5103$m$32\mathrm{.}5103$m$3.$ If the initial pressure and temperature were $5\mathrm{.}0105$Pa$5\mathrm{.}0105$Pa and $300$ K$,$ respectively, what are the final pressure and temperature of the gas?