An ideal, or Carnot, heat pump is used to heat a house to a temperature of 294 K (21 oC). How much work must the pump do to deliver 3000 J of heat into the house (a) on a day when the outdoor temperature is 273 K (0 oC) and (b) on another day when the outdoor temperature is 252 K (-21 oC)

a) , b)

Explanation:

a) The performance of a Carnot heat pump is determined by the Coefficient of Performance, which is equal to the following ratio:

Where:

- Temperature of surroundings, measured in Kelvin.

- Temperature of the house, measured in Kelvin.

Given that and . The Coefficient of Performance is:

Besides, the performance of real heat pumps are determined by the following form of the Coefficient of Performance, that is, the ratio of heat received by the house to input work.

The input work to deliver a determined amount of heat to the house:

If and , the input work that is needed is:

b) The performance of a Carnot heat pump is determined by the Coefficient of Performance, which is equal to the following ratio:

Where:

- Temperature of surroundings, measured in Kelvin.

- Temperature of the house, measured in Kelvin.

Given that and . The Coefficient of Performance is:

Besides, the performance of real heat pumps are determined by the following form of the Coefficient of Performance, that is, the ratio of heat received by the house to input work.

The input work to deliver a determined amount of heat to the house:

If and , the input work that is needed is:

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