Carnot Refrigerator and Carnot Heat Pump

Reversing the Carnot cycle does reverse the directions of heat and work interactions. A refrigerator or heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump.

A heat pump is a machine or device that moves heat from one location (the "source") at a lower temperature to another location (the "sink" or "heat sink") at a higher temperature using mechanical work or a high-temperature heat source. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink (as when warming the inside of a home on a cold day), or a "refrigerator" if the objective is to cool the heat source (as in the normal operation of a freezer). In either case, the operating principles are identical. Heat is moved from a cold place to a warm place.

Refrigerators and heat pumps are essentially the same device; they only differ in their objectives.

The Reversed Carnot Cycle

Reversed Carnot cycle is an ideal refrigeration cycle for constant temperature external heat source and heat sinks. The figure below shows the schematic of a reversed Carnot refrigeration system using a gas as the working fluid along with the cycle diagram on T-s and P-v coordinates. As shown, the cycle consists of the following four processes:

Process 1-2: Reversible, adiabatic compression in a compressor

Process 2-3: Reversible, isothermal heat rejection in a compressor

Process 3-4: Reversible, adiabatic expansion in a turbine

Process 4-1: Reversible, isothermal heat absorption in a turbine

Coefficient of Performance (COP)

The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP):

The reversed Carnot cycle is the most efficient refrigeration cycle operating between two specified temperature levels. It sets the highest theoretical COP. The coefficient of performance for Carnot refrigerators and heat pumps are:

Limitations of Carnot cycle:

Carnot cycle is an idealization and it suffers from several practical limitations.

One of the main difficulties with Carnot cycle employing a gas is the difficulty of achieving isothermal heat transfer during processes 2-3 and 4-1. For a gas to have heat transfer isothermally, it is essential to carry out work transfer from or to the system when heat is transferred to the system (process 4-1) or from the system (process 2-3). This is difficult to achieve in practice.

Another difficulty that arises is that the cycle requires a compressor and turbine that can handle two-phases, i.e. two-phase flow.

In addition, the volumetric refrigeration capacity of the Carnot system is very small leading to large compressor displacement, which gives rise to large frictional effects.

Why is COP of Carnot refrigerator in winter higher than the COP in summer?

According to the equation of COP, if temperature cooling water or available heat rejection is low, the COP will be high. In winter season the temperature of cooling water Th is low, so the COP will be higher. Similarly, in the summer season the temperature Th is greater than that in the winter. So the COP of refrigerator in summer is less than COP in winter. I.e. the Carnot refrigerator works more efficiently in winter than in summer.

Why is the Carnot COP of domestic refrigerator less than that of domestic air-conditioner?

From above equation of COP, at constant higher temperature Th, COP of refrigerator increases with increasing lower temperature Tl. Generally, for refrigerator the Tl is around 0°C and for air-conditioner, Tl is around 20°C. Since Tl for air-conditioner is greater than that of refrigerator, the COP of air-conditioner is higher than that of the domestic refrigerator.