TC$8\mathrm{.}2.$ Use refrigerant R$-134$a to be the working fluid in a vapor$-$compression refrigeration cycle. Saturated vapor enters the compressor at $2$ bar, and saturated liquid exits the condenser at $8$ bar. The compressor has an isentropic efficiency of $80\%.$ The mass flow rate of the refrigerant is $7k\frac{g}{m}in.$

condenser

$($a$)$ Determine the compressor power, in kW $.$

$($b$)$ Determine the exergy destruction in the compressor, in kW $.$

$($c$)$ Determine the refrigeration capacity, in tons.

$($d$)$ Determine the exergy destruction at the valve, in kW $.$

$($e$)$ Determine the coefficient of performance.

Note: $1$ ton of refrigeration $=200BT\frac{U}{m}in$ or $211k\frac{J}{m}in.$

$[$Answers: $($a$)40\mathrm{.}4kW,(e)4$ tons, $(d)0\mathrm{.}4kW,(e)40\mathrm{.}7kW,(c)4$ tons tons, $(d)0\mathrm{.}4kW,(e)44kW,(b)0\mathrm{.}7kW,(c)4$ tons tons, $(d)0\mathrm{.}4kW,(e)4$