Explain mathematically whether the divergence of the curl of a vector field is solenoidal or not?

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.

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Acarnot refrigerator operates in a room in which the temperature is 21°c and of power when operating. if the food compartment of the refrigerator is consumes 3 kw to be maintained at 2°c, determine (a) the coefficient of performance of the cycle and (b) the rate of heat removal from the food compartment. refrigerator cycle that has a higher coefficient of performance than that of the discussed (e) is it possible to develop a carn ot refrigerator, operating between the same temperature limits? explain