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Answer:
The Carnot heat pump must work 3.624 hours per day to keep the temperature constant inside the house.
Explanation:
The net heat daily loss of the house is:
In order to keep the house warm, given heat must be equal to heat losses:
Besides, the Coefficient of Performance for a Carnot heat pump is:
Where,
- Temperature of the cold reservoir (Outdoors), measured in Kelvin.
- Temperature of the hot reservoir (House), measured in Kelvin.
Given that and
, the Coefficient of Performance is:
For a real heat machine, the Coefficient of Performance is determined by the following expression:
Where:
- Heat received by the house, measured in kilojoules.
- Work consumed by the Carnot heat pump, measured in kilojoules.
The daily work consumed is now cleared in the previous expression:
The working time is calculated by dividing this result by input power. That is:
The Carnot heat pump must work 3.624 hours per day to keep the temperature constant inside the house.