Figure of Merit for Working Fluids

Georg Alefeld introduced a figure of merit to assess and compare the performance potential of working fluids for vapor compression and absorption systems [Alefred and Radermacher 1994]. It is the latent heat of the fluid l divided by the specific heat capacity c_p . The latent heat is a measure for the cooling capacity provided. The specific heat is a measure for how much the cooling capacity is reduced, as some of the refrigerant evaporates as it cools itself from the condenser temperature to the evaporator temperature. To make this ratio dimensionless, c_p is multiplied by a temperature, for example, the evaporator temperature.

It may be more productive to multiply the specific heat by the temperature lift, the temperature difference between evaporator and condenser. In this way, the operating conditions have a more direct bearing on the figure of merit, l/(c_p * ΔT).

This figure accounts only for the effect of the working fluid itself; it does not include any consideration of the performance of components, such as heat exchangers, compressors, and others. For refrigerants typically used in vapor compression systems, the figure of merit is in the range of 3 to 4.

It appears that this definition of the figure of merit is applicable for a wider range of working fluids than originally anticipated. Consider magneto-caloric cooling; as long as the working fluid has a latent heat, the figure of merit applies in the same above-indicated form. For fluids without latent heat, the nominator can be replaced with a term of specific heat multiplied by the temperature difference that is available for cooling. The figure of merit then conveys the same information. The same holds for thermo-elastic cooling. Because of the relatively small or nonexistent latent heat, the figure of merit for these solid-state working fluids is in the range of 1.0 and degrades quickly with increasing temperature lift. This indicates that the net cooling effect is smaller than in vapor compression systems and that internal heat exchange that pre-heats/pre-cools the working fluid as it cycles through the system is so much more important.

Interestingly, thermoelectric cooling, albeit a solid-state process, does not have a working fluid cycling through various thermodynamics states, as is the case in the above-discussed systems, and a different figure of merit is in use.

It will be an interesting and rewarding research endeavor that will develop a figure of merit that is applicable to all cooling processes, including thermoelectric systems, gas cycles, and any others that are not considered here.

Fellow ASHRAE Member

Minta Martin Professor of Engineering