A single$-$acting compressor is required to deliver air at $70$ bar from an induction pressure of $\frac{1}{b}ar,$ at the rate of $2\mathrm{.}4\frac{m^3}{m}in$ measured at free air conditions of $\frac{1\mathrm{.}013}{b}ar$ and $15C.$ The compression is carried out in two stages with an ideal intermediate pressure and complete intercooling. The clearance volume is $3\%$ of the swept volume in each cylinder and the compressor speed is $750rpm.$ The index of compression and re$-$expansion is $1\mathrm{.}25$ for both cylinders and the temperature at the end of the induction stroke in each cylinder is $32C.$ The mechanical efficiency of the compressor is $85\%.$ Calculate

a$.$ The individual power required $(22\mathrm{.}74kW)$

b$.$ The saving in power over single$-$stage compression between the same pressure $(5\mathrm{.}98kW)$

c$.$ The swept volume of each cylinder $(0\mathrm{.}00396m^3,0\mathrm{.}000474m^3)$

d$.$ The required power output of the drive motor $(26\mathrm{.}75kW)$

e$.$ The heat rejection per minutes to the jacket of the cooling water of each stage, and the heat rejected per minute to the intercooler. Assume that $50\%$ of the friction power in each stage is transferred to the jacket cooling water. $(264k\frac{J}{m}in,478k\frac{J}{m}in)$