A method to calculate the thermal efficiency of any closed-loop curve

A core problem in thermodynamics is calculating the efficiency of an engine cycle. Given a curve in a pressure-volume graph, and some information about the system, it should be possible to calculate its efficiency. In practice, however, this can only be done easily with certain specific curves.

Könye and Cserti developed a generalized method to easily calculate the thermal efficiency for any closed-loop system. They demonstrated their method on several unconventional curves and discussed the implications.

“If anybody gives you a curve in the p-V diagram, you can get a result for the thermal efficiency,” said author Viktor Könye. “We show that it also works for different kinds of gasses.”

The pair of researchers first developed their method to calculate the efficiency of a circle-shaped curve. This nontrivial problem was solved by parameterizing the circle and expressing the exchanged heat as an integral over this parameter. Könye and Cserti realized this method could be used to solve any cycle.

One interesting consequence they found is that this calculation only requires the thermodynamic curve, the equation of state, and the heat capacity of the system. This same method can also be used to calculate the entropy of the system and the amount of work done.

The researchers hope this method could make it easier for scientists and engineers to work with unconventional engine designs. They also believe this method would make a great teaching tool.

“This is good fun because the students can devise some new cycles and they are able to calculate the efficiency,” said author Jozsef Cserti. “And in the meantime, they learn the whole subject.”

Source: “General formalism for calculating the thermal efficiency of thermodynamic cycles defined in a p-V diagram,” by Viktor Könye and József Cserti, American Journal of Physics (2022). The article can be accessed at https://doi.org/10.1119/5.0064010 .