A two$-$stage, single$-$acting, reciprocating air compressor takes in air at $1$ bar and $300$ K$.$ Air is discharged at $10$ bar. The intermediate pressure is ideal for minimum work and perfect intercooling. The law of compression is pV$1\mathrm{.}3=$ constant. The rate of discharge is $0\mathrm{.}1$ kg$/$s$.$ Calculate $($a$)$ power required to drive the compressor, $($b$)$ saving in work in comparison with single stage compression, $($c$)$ isothermal efficiency, and $($d$)$ heat transferred in intercooler. Take R $=0\mathrm{.}287$ kJ$/$kg$.$K and Cp $=1$ kJ$/$kg $$ K