Question

Being the ideal engine, the maximum COP of a Carnot cycle operated in reverse as a refrigerator is

A) 100.
B) (Tc/Th) ∙ (1 - Tc/Th)-1.
C) (1 - Tc/Th)-1.
D) (Th/Tc)(1 - Tc/Th)-1.

Answer 1

The maximum Coefficient of Performance (COP) of a Carnot refrigerator is (Th/Tc) - 1, which corresponds to option D in the provided question.

Step-by-step explanation:

The maximum Coefficient of Performance (COP) of a Carnot cycle operating in reverse as a refrigerator is given by the expression (Th/Tc) - 1, where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir, both expressed in kelvins. This formula is derived from the efficiency of a Carnot engine, which is Eff = 1 - (Tc/Th), and remembering that for a Carnot refrigerator or heat pump, COP = 1/Eff. Therefore, using the given option labels, the correct answer is D) (Th/Tc)(1 - Tc/Th)-1.

To apply this concept to specific examples, such as determining the energy needed by a Carnot engine to operate a refrigerator between certain temperatures, it is important to convert all Celsius temperatures to kelvins, and then use the COP formula to calculate the energy requirements.