$12\mathrm{.}5$ A single$-$acting compressor is required to deliver air at $70$ bar from an induction pressure of $1$ bar $,$ at the rate of $2\mathrm{.}4\frac{m^3}{m}in$ measured at free air conditions of $1\mathrm{.}013$ bar 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 $750re\frac{v}{m}in.$ 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:

$($i$)$ the indicated power required;

$($ii$)$ the saving in power over single$-$stage compression between the same pressures;

$($iii$)$ the swept volume of each cylinder;

$($iv$)$ the required power output of the drive motor.