$($i$)$ Show the variation of compressor specific work input and power input to a compressor with the evaporator temperature while the condenser temperature is kept constant.

$($ii$)$ R $22$ is compressed in a reciprocating compressor from saturation pressure at $-10C$ to saturation pressure at $42C.$ Vapour entering into the compressor get super heated to $-5C$ outside the evaporator. Pressure drop across the suction and the discharge vale are $0\mathrm{.}1$ bar and $0\mathrm{.}12$ bar respectively. The clearance volume ratio is $0\mathrm{.}04.$ The refrigeration capacity of the system is $10$ TR $.$ The compressor has two cylinders with stroke to bore ratio of $1\mathrm{.}15.$

$1$

Determine $($i$)$ the volumetric efficiency, $($ii$)$ the swept volume flow rate, $($iii$)$ stroke and bore of the compressor cylinders, and $($iv$)$ the COP of the system.

$1+7=8$