A heat pump driven by a 0.4 kW electric motor provides heating for a building on a day when the outside air is at –10°C. The energy lost through the walls and roof at steady state is estimated to be at a rate of 16,200 kJ/h. Starting with the Carnot expression for the coefficient of performance, obtain an expression for the building temperature (T1) in terms of the power input to the pump (W), the outside ambient temperature (T2) and the heat released by the working fluid flowing through radiators in the room (Q1).

(a) What is the maximum theoretical temperature that can be maintained within the building, and would this temperature be suitable for office workers?

(b) After an extensive renovation programme, the new insulation results in the energy loss being reduced to 14,400 kJ/h. Calculate the new (maximum) theoretical temperature for the building.

(c) If the temperature calculated in (b) is still not great enough, how would it be increased even further?