Answer:
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Explanation:
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Answer:
A) β_max = 20.64
B) TH = 68.25°C
C) TC = 54.27°C
Explanation:
A) We are given;
TH = 16°C = 16 + 273K = 289K
TC = 2°C = 2 + 273K = 275K
Formula for maximum cycle coefficient of performance is given as;
β_max = TH/(TH - TC)
β_max = 289/(288 - 275)
β_max = 20.64
B) We are given;
Heat rejected to system at hot reservoir; Q_H = 10.5 KW
Heat provided to system at cold reservoir; Q_C = 8.75 KW
Cold reservoir temperature; TC = 0°C = 0 + 273K = 273K
Formula for actual cycle COP is given as;
β_actual = Q_C/W_cycle
Where W_cycle is the work done and is given by;
W_cycle = Q_H - Q_C
W_cycle = 10.5 - 8.75 = 1.75 KW
Thus,
β_actual = 8.75/1.75
β_actual = 5
Actual cycle COP is defined as;
β_actual = TH/(TH - TC)
And we are looking for TH.
Thus,
TH = TC/(1 - (1/β_actual))
TH = 273/(1 - 1/5)
TH = 273/(4/5)
TH = 341.25K = 341.25 - 273°C = 68.25°C
C) We are given;
TH = 27°C = 27 + 273 = 300°C
β_max = 12
Thus, from,
β_max = TH/(TH - TC)
TC = TH(1 - (1/β_max))
TC = 300/(1 - 1/12)
TC = 327.27K = 327.27 - 273 °C = 54.27°C
