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Refrigerant $134$a enters an air conditioner compressor at $\frac{4}{b}ar,20C,$ and is compressed at steady state to $\frac{12}{b}ar,80C.$ The volumetric flow rate of the refrigerant entering is $6\frac{m^3}{m}in.$ The work input to the compressor is $90$ kJ per kg of refrigerant flowing.

Neglecting kinetic and potential energy effects, determine the magnitude of the heat transfer rate from the compressor, in kW$.$

$Q_{cv}^{}=,kW$