Refrigerators and heat pumps

If the Carnot cycle is run backwards — anticlockwise in the $P$-$V$ diagram — the engine reverses all its flows: instead of producing work, it absorbs it, and uses this work to move heat from the cold source to the hot one, i.e. against the spontaneous direction of heat flow.

The physical intuition is simple: heat never rises on its own from cold to hot (second law), but we can pump it by paying with external work. This is exactly what the compressor of a refrigerator or a heat pump does.

The same device takes different names depending on what interests us:

• Refrigerator: we are interested in the heat $Q_C$ extracted from the cold compartment (cooling).
• Heat pump: we are interested in the heat $Q_H$ released to the hot environment (heating).

For these machines we do not speak of efficiency (it would be greater than $1$ and it would make no sense to compare it with the driving engine) but of coefficient of performance (COP), i.e. the ratio between the useful effect and the work spent.

Summary

$\begin{aligned} \textbf{Engine:}\quad & \eta = \frac{L}{Q_H} \\ \textbf{Refrigerator:}\quad & \text{COP}_\text{fr} = \frac{Q_C}{L} \\ \textbf{Heat pump:}\quad & \text{COP}_\text{pdc} = \frac{Q_H}{L} \end{aligned}$ The engine extracts work from heat; the refrigerator and the heat pump spend work to move heat. The COP is typically greater than $1$: with one joule of work, more joules of heat are moved.

Links

Topics: Macchine termiche Concepts: Frigorifero e pompa di calore · Secondo principio della termodinamica Objects: Frigorifero

Related exercises: Problema — Frigo con la porta aperta · Problema — Vero o falso su macchine e frigoriferi · Problema — Stanza con frigorifero aperto