Answer:
a) [tex]\dot W = 0.417\,kW[/tex], b) [tex]COP_{R} = 2.198[/tex], c) Irreversible.
Explanation:
a) The power input required by the refrigerator is:
[tex]\dot W = \dot Q_{H} - \dot Q_{L}[/tex]
[tex]\dot W = \left(4800\,\frac{kJ}{h} - 3300\,\frac{kJ}{h}\right)\cdot \left(\frac{1}{3600} \,\frac{h}{s} \right)[/tex]
[tex]\dot W = 0.417\,kW[/tex]
b) The Coefficient of Performance of the refrigerator is:
[tex]COP_{R} = \frac{\dot Q_{L}}{\dot W}[/tex]
[tex]COP_{R} = \frac{3300\,\frac{kJ}{h} }{(0.417\,kW)\cdot \left(3600\,\frac{s}{h} \right)}[/tex]
[tex]COP_{R} = 2.198[/tex]
c) The maximum ideal Coefficient of Performance of the refrigeration is given by the inverse Carnot's Cycle:
[tex]COP_{R,ideal} = \frac{T_{L}}{T_{H}-T_{L}}[/tex]
[tex]COP_{R,ideal} = \frac{261.15\,K}{303.15\,K - 261.15\,K}[/tex]
[tex]COP_{R,ideal} = 6.218[/tex]
The refrigeration cycle is irreversible, as [tex]COP_{R} < COP_{R,ideal}[/tex].
