Question

A heat pump in heating mode extracts 1,096 J from the cold reservoir while transferring 1,363 J to the hot reservoir. Calculate its coefficient of performance.

Answer 1

The coefficient of performance of the heat pump is 0.804

Step-by-step explanation:

The coefficient of performance of a heat pump is defined as the ratio of the heat transferred from the cold reservoir to the work supplied. In this case, the heat pump extracts 1,096 J from the cold reservoir and transfers 1,363 J to the hot reservoir. To calculate the coefficient of performance, we divide the heat transferred from the cold reservoir by the work supplied:

COP = Heat transferred from cold reservoir / Work supplied = 1096 J / 1363 J = 0.804

Answer 2

The coefficient of performance of the heat pump in heating mode is approximately 5.11, calculated by dividing the heat transferred to the hot reservoir by the work input.

Step-by-step explanation:

The coefficient of performance (COP) of a heat pump in heating mode is a measure of its efficiency. It is calculated as the ratio of heat transfer to the hot reservoir (Q_h) to the work input (W). The work input can be found by subtracting the heat extracted from the cold reservoir (Q_c) from the heat added to the hot reservoir (Q_h).

Using the provided values, the work input (W) is 1,363 J (heat transferred to hot reservoir) - 1,096 J (heat extracted from the cold reservoir) = 267 J.

Therefore, the COP is calculated as the heat transferred to the hot reservoir divided by the work input, which in this case is 1,363 J / 267 J = approximately 5.11.