A Carnot air conditioner maintains the temperature in a house at 298 K on a day when the temperature outside is 310 K. What is the coefficient of performance of the air conditioner?

The maximum COP= Tcool/(Thot-Tcool)

actual COPS are much less.

would it be 310/(298-310) im just makeing sure let me know please thank you

To find the coefficient of performance of the Carnot air conditioner, we need to know the temperatures of the hot reservoir (outside temperature) and the cold reservoir (house temperature).

The coefficient of performance (COP) is defined as the ratio of cooling provided to the work done by the air conditioner. In this case, the COP can be calculated using the following formula:

COP = Th / (Th - Tc)

Where:
COP: Coefficient of Performance
Th: Temperature of the hot reservoir (outside temperature)
Tc: Temperature of the cold reservoir (house temperature)

Given:
Th = 310 K (outside temperature)
Tc = 298 K (house temperature)

Substituting the given values into the formula:

COP = 310 K / (310 K - 298 K)
COP = 310 K / 12 K
COP = 25.83

Therefore, the coefficient of performance of the Carnot air conditioner is approximately 25.83.