Operating Principle

Operating principle of refrigerators and heat pumps: reversed cycle and external work

Conceptual context

The refrigerator and heat pump are thermal machines that operate in the reverse direction of an engine. While an engine converts heat into work, these machines consume work to transfer heat from a cold body to a hot one. The second law of thermodynamics, in its Clausius formulation, establishes that this process never occurs spontaneously: heat flows naturally only from hot to cold. Therefore, a refrigerator needs an external energy input ($W$) to perform its function. Understanding this principle is fundamental before addressing coefficients of performance and the design of real cycles.

🟢 Essential level

A refrigerator extracts heat $Q_C$ from the cold interior and transfers it to the warm exterior. To achieve this, a compressor consumes work $W$. The hot reservoir receives heat $Q_H$ which is the sum of $Q_C$ plus $W$. The reason work is needed is that heat, on its own, never travels from cold to hot. The compressor compresses the refrigerant gas, raising its temperature above that of the hot reservoir, which allows heat to flow naturally from the compressed gas to the exterior.

Then the refrigerant expands, cooling below the cold reservoir temperature, and heat flows naturally from the refrigerator interior to the cold gas. The heat pump works identically but with the reversed objective: the useful effect is the heat $Q_H$ delivered to the space to be heated. In both cases, without external work $W$, heat transfer from cold to hot would be thermodynamically impossible.

The refrigerant itself never disappears or gets consumed: it simply cycles between these hot and cold states over and over, carrying a fixed parcel of heat on each loop while the compressor keeps paying the energy toll that makes the whole loop possible.

🔵 Formal level

Basic formulas

The first law of thermodynamics applied to the complete reversed cycle establishes the energy balance:

Reversed cycle energy balance

The second law imposes an additional fundamental constraint. The total entropy change of the universe must be non-negative:

Second law for the reversed cycle

Both laws act as a joint filter: the first fixes how much energy moves, while the second decides whether that movement is physically possible without an external work input.

Real student questions

Why does the refrigerator heat the kitchen? Because $Q_H$ is greater than $Q_C$: the refrigerator extracts heat from the interior and adds the compressor work, rejecting everything to the environment through the back. The kitchen receives more heat than is extracted from the refrigerator interior.

Is it possible to cool a room with an open refrigerator? No. With the door open, the refrigerator extracts $Q_C$ from the room but returns greater $Q_H$ to the same room. The net effect is heating the room by an amount equal to $W$, the consumed electrical energy.

Why is more work needed to cool to lower temperatures? Because the minimum work is proportional to the difference $T_H$ minus $T_C$ divided by $T_C$. The lower $T_C$ is, the larger this ratio and the more work is required for each joule of extracted heat.

Final synthesis

The operating principle of refrigerators and heat pumps is based on the thermodynamic impossibility of spontaneous heat transfer from cold to hot. External work $W$ allows reversing this natural flow, extracting $Q_C$ from the cold reservoir and delivering $Q_H$ to the hot reservoir, with $Q_H$ always greater than $Q_C$. The second law establishes the minimum necessary work (Carnot cycle) and $\Delta S_{\\text{total}}$ quantifies how far the real cycle is from that ideal. Mastering this principle is a prerequisite for understanding COP, designing efficient cycles and evaluating the performance of real systems.