Question

A heat pump operates on a Carnot heat pump cycle with a COP of 12.5. It keeps a space at 24°C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.

Answer 1

a)
`T_(L) = 273.378\,K\,(0.228\,^(\textdegree)C)`, b)
`\dot Q_(H) = 26.875\,kW`

Step-by-step explanation:

a) The Coefficient of Performance of the Carnot Heat Pump is:

`COP_(HP) = (T_(H))/(T_(H)-T_(L))`

After some algebraic handling, the temperature of the cold reservoir is determined:

`T_(H)-T_(L) = (T_(H))/(COP_(HP))`

`T_(L) = T_(H)\cdot \left(1-(1)/(COP_(HP)) \right)`

`T_(L) = (297.15\,K)\cdot \left(1-(1)/(12.5)\right)`

`T_(L) = 273.378\,K\,(0.228\,^(\textdegree)C)`

b) The heating load provided by the heat pump is:

`\dot Q_(H) = COP_(HP)\cdot \dot W`

`\dot Q_(H) = (12.5)\cdot (2.15\,kW)`

`\dot Q_(H) = 26.875\,kW`