A completely reversible air conditioner provides 36,000 Btu/h of cooling for a space maintained at 70°F while rejecting heat to the environmental air at 110°F.

Calculate the rate at which the entropies of the two reservoirs change, and verify that this air conditioner satisfies the increase of entropy principle.

To calculate the rate at which the entropies of the two reservoirs change and verify if the air conditioner satisfies the increase of entropy principle, we can use the formula for change in entropy and compare the magnitudes of the entropy changes of the two reservoirs.

Explanation:

The rate at which the entropy of a reservoir changes can be calculated using the formula:

Change in entropy = Heat transfer / Temperature

For the space being cooled, the change in entropy can be calculated as:

Change in entropy of cooled space = Heat transfer / Temperature of cooled space

For the environmental air, the change in entropy can be calculated as:

Change in entropy of environmental air = Heat transfer / Temperature of environmental air

In order to verify if the air conditioner satisfies the increase of entropy principle, you can compare the magnitudes of the entropy changes of the two reservoirs. If the entropy change of the cooled space is greater than or equal to the entropy change of the environmental air, then the air conditioner satisfies the increase of entropy principle.