A heat pump is used to heat a building. The external temperature is lower than the internal temperature. The pump's coefficient of performance is 3.70, and the heat pump delivers 7.27 MJ as heat to the building each hour. If the heat pump is a Carnot engine working in reverse, at what rate must work be done to run it

Heat pump needs 1.965 megajoules each hour to run.

Explanation:

The Coefficient of Performance (), no unit, of a Carnot's heat pump is:

(1)

Where:

- Heat received by the building, measured in megajoules.

- 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 and , then the amount needed by the heat pump each hour is:

Heat pump needs 1.965 megajoules each hour to run.

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form