Answer:
Heat pump needs 1.965 megajoules each hour to run.
Explanation:
The Coefficient of Performance ([tex]COP[/tex]), no unit, of a Carnot's heat pump is:
[tex]COP = \frac{Q_{H}}{W}[/tex] (1)
Where:
[tex]Q_{H}[/tex] - Heat received by the building, measured in megajoules.
[tex]W[/tex] - Work needed to run the heat pump, measured in megajoules.
If heat pump is a Carnot engine working in reverse, then the amount of work needed to run the heat pump is the least possible work. If we know that [tex]Q_{H} = 7.27\,MJ[/tex] and [tex]COP = 3.70[/tex], then the amount needed by the heat pump each hour is:
[tex]W = \frac{Q_{H}}{COP}[/tex]
[tex]W = \frac{7.27\,MJ}{3.70}[/tex]
[tex]W = 1.965\,MJ[/tex]
Heat pump needs 1.965 megajoules each hour to run.
