Answer:
[tex]Q_{L} = 11.442\times 10^{6}\,J[/tex]
Explanation:
The ideal efficiency of a refrigerator is given by the model of a Carnot refrigerator, whose indicator is known as Coefficient of Performance:
[tex]COP_{R} = \frac{T_{H}}{T_{H}-T_{L}}[/tex]
[tex]COP_{R} = \frac{310\,K}{310\,K-271\,K}[/tex]
[tex]COP_{R}=7.949[/tex]
Heat rate extracted from the freezing compartment is:
[tex]\dot Q_{L} = COP_{R}\cdot \dot W[/tex]
[tex]\dot Q_{L} = 7.949\cdot 294\,W[/tex]
[tex]\dot Q_{L} = 2337.01\,W[/tex]
The heat that can be extracted in abovementioned period of time is:
[tex]Q_{L} = \dot Q_{L}\cdot \Delta t[/tex]
[tex]Q_{L} = (2337.01\,W)\cdot (81.6\,min)\cdot (\frac{60\,s}{1\,min} )[/tex]
[tex]Q_{L} = 11.442\times 10^{6}\,J[/tex]
