Reversed heat engines use work to transfer heat from cold to hot

How reversed heat engines work

• A reversed heat engine transfers heat energy from a cold space to a hot space by inputting work.
• Work needs to be done because heat energy naturally flows from a warmer to a colder space (as required by the second law). To reverse this flow, external energy must be supplied.
• Reversed heat engines are used for:
  • Refrigerators or air-conditioning units
  • Heat pumps (used to heat a building)

The reversed source-sink diagram

• In the source-sink diagram for a reversed heat engine, all the arrows are reversed compared to a normal heat engine:
  • $Q_C$ = energy extracted from the cold space (J)
  • $Q_H$ = energy delivered to the hot space (J)
  • $W$ = work inputted (J)
• Applying the first law of thermodynamics gives:

• $Q_H$ will always be greater than $Q_C$ because of the additional work input.

Refrigerators vs heat pumps

• A refrigerator extracts as much energy as possible from the cold space per joule of work done. A refrigerator wants to stay cold, so it is taking the heat out of the system. The inside of the fridge is the cold space, and the outside is the hot space.
• A heat pump (e.g. to heat a house) provides as much energy as possible to the hot space per joule of work done. A heat pump wants to make a room warm, so it puts heat into the system. The outside of the house is the cold space, and the inside is the hot space.
• They are both identical in principle, and it is possible to use one to fulfil the function of the other, but it would not work as well. A domestic refrigerator keeps its contents cool but simultaneously acts as a heater, warming the room it is placed in.