Answer:
a) [tex]COP_{R} = 13.721[/tex], b) [tex]\dot W = 0.342\,kW[/tex], c) [tex]\dot Q_{H} = 18131.2\,\frac{kJ}{h}[/tex]
Explanation:
a) A Carnot refrigerator has the following Coefficient of Performance:
[tex]COP_{R} = \frac{T_{L}}{T_{H}-T_{L}}[/tex]
[tex]COP_{R} = \frac{288.15\,K}{309.15\,K - 288.15\,K}[/tex]
[tex]COP_{R} = 13.721[/tex]
b) The power input is:
[tex]\dot W = \frac{\dot Q_{L}}{COP_{R}}[/tex]
[tex]\dot W = \frac{(16900\,\frac{kJ}{h} )\cdot (\frac{1\,h}{3600\,s} )}{13.721}[/tex]
[tex]\dot W = 0.342\,kW[/tex]
c) The heat rejected to the high-temperature reservoir is:
[tex]\dot Q_{H} = \dot Q_{L} + \dot W[/tex]
[tex]\dot Q_{H} = 16900\,\frac{kJ}{h} + (0.342\,\frac{kJ}{s} )\cdot (\frac{3600\,s}{1\,h} )[/tex]
[tex]\dot Q_{H} = 18131.2\,\frac{kJ}{h}[/tex]
