A Carnot heat engine receives heat from a reservoir at 900∘C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27∘C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at -5∘C and transfers it to the same ambient air at 27∘C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

a) The maximum rate of heat removal is 4987.776 kilojoules per minute.

b) The total rate of heat rejection is 5787.776 kilojoules per minute.

Now we proceed to describe the entire procedure:

a) Maximum rate of heat removal from refrigerated space:

The efficiency of the Carnot heat engine is:

(1)

Where:

The power needed to drive the refrigerator (), in kilojoules per minute, is:

(2)

Where:

The Coefficient of Performance of a Carnot Refrigerator (), no unit, is:

(3)

The maximum rate of heat removal (), in kilojoules per minute, from the refrigerated space is:

(4)

The maximum rate of heat removal is 4987.776 kilojoules per minute.

b) Total rate of heat rejection to the ambient air:

This rate is the sum of the waste heat from heat engine (), in kilojoules per minute, and heat transferred from refrigerator (), in kilojoules per minute. That is to say:

(5)

The heat transferred from refrigerator is:

The waste heat from heat engine is:

Finally, the total rate of the heat rejection to the ambient air is:

The total rate of heat rejection is 5787.776 kilojoules per minute.

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