$($a$)$ The compressor employed in a basic vapor compression refrigeration system is of the reciprocating type. The refrigeration load is $300$ kW and the evaporating and condensing temperatures are $\backslash (-10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ respectively. The refrigerant employed is ammonia. Calculate the electric power of the compressor motor, compressor displacement, number of cylinders, and bore and stroke. Assume that the refrigerant entering the compressor is superheated vapor with a $\backslash (7^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ of superheat and that the refrigerant leaving the condenser is subcooled liquid with a $\backslash (5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ of subcooling. Your calculations should include details of computing the volumetric efficiency from all causes. Show and justify $($when needed$)$ all assumptions. $($b$)$ For the system described in Part $($a$),$ calculate the refrigeration load if the evaporator and condenser temperatures were $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ respectively, with a degree of subcooling equals $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the same degree of superheat as Part $($a$).$ The refrigerant flow rate in Part $($b$)$ is the same as in Part $($a$).(12\mathrm{.}5$ Points$)$