Question

In a heat pump, heat from the outdoors at –5C is transferred to a room at 17C, energy being supplied by an electric motor. How many joules of heat will be delivered to the room for each joule of electric energy consumed, ideally?

Answer 1

$$\frac{Q_h}{T_h}=\frac{Q_l}{T_l}$$

From the conservation of energy:

$$W+Q_l=Q_h$$

$$Q_h=(Q_h-W)\frac{T_h}{T_l}$$

$$Q_h=(Q_h-1)\frac{290.15}{268.15}$$

$$Q_h=13\ J$$