The Carnot theorem has been used to derive the Clapeyron-Clausius equation. This topic has been discussed pedagogically on page 27 in the article "The friction and pressure of skating" published in the magazine Quantum (July/August 1994):
https://static.nsta.org/pdfs/QuantumV4N6.pdf
It will be beneficial for both students and teachers of physics to have knowledge of other applications of the Carnot theorem.