A single$-$stage, single$-$acting air compressor running at $100rpm$ delivers air at $25$ bar. For this purpose the induction and free air conditions can be taken as $1\mathrm{.}013$ bar and $15C,$ and the FAD as $0\mathrm{.}25\frac{m^3}{m}in.$ The clearance volume is $3\%$ of the swept volume and the stroke$/$bore ratio $1\mathrm{.}2/1.$ Take the index of compression and re$-$expansion as $1\mathrm{.}3.$

a$.$ Calculate $($i$)$ The bore and stroke $($ii$)$ the volumetric efficiency $($iii$)$ The indicated power $($iv$)$ the isothermal efficiency $(73\mathrm{.}2$ mm$,87\mathrm{.}8mm,67\mathrm{.}7\%,2kW,67\mathrm{.}7\%)$

b$.$ If the compressor has actual conditions of $1$ bar and $40C$ and delivery pressure is $25$ bar. Taking the bore and stroke as previously calculated. Determine FAD referred to $1\mathrm{.}013$ bar and $15C$ and the indicated power required. Also calculate the volumetric efficiency. $(0\mathrm{.}226\frac{m^3}{m}in,1\mathrm{.}98(kW),61\mathrm{.}2\%,67\mathrm{.}7\%)$