$($a$)$ How much work is required to compress $4\mathrm{.}97$ mol of air at $20\mathrm{.}7$C and $1\mathrm{.}00$ atm to one$-$eighth of the original volume by an isothermal process? kJ $($b$)$ How much work is required to produce the same compression in an adiabatic process? kJ $($c$)$ What is the final pressure in part $($a$)?$ atm $($d$)$ What is the final pressure in part $($b$)?$