Carnot Heat Engines

Nicolas Léonard Sadi Carnot was a young French mechanical engineer. You’ll remember Archimedes asserted, ‘Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.' I like to think Carnot would instead have declared, ‘Give me two bodies of differential heat and I’ll mathematically demonstrate how much work may be accomplished.' He sought answer to 2 questions:

Is the work available from a heat source potentially unbounded?”

"Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?

After deliberation, at age twenty-seven, Carnot published Reflections on the Motive Power of Fire, the first successful theory about the maximum hypothetical efficiency of generic heat engines. Carnot's work attracted little attention during his truncated lifetime [died of a combination of scarlatina and cholera]. It was modernized by Émile Clapeyron in 1834 and later enhanced even further by Rudolf Clausius and Lord Kelvin, ultimately becoming formalized as the now familiar second law of thermodynamics and the concept of entropy.

He defined W or work as weight lifted through a certain distance, as he visualized a bucket of sorts lifting water out of a flooded mine, one of the fundamental engineering challenges of the day. Critically, Carnot's conceptualization was that the idealized reservoirs were isothermic + boundless, the whole apparatus was frictionless, and insulation of components was so perfect such that there was no leaking of heat by conduction.

Thus his theorem was simply that no heat engine operating between any two bodies of heat can be more efficient than a Carnot engine operating between the same 2 storage pools.
The vapor compression cycle is the basis all refrigerators and heat pumps. But the engineering challenge is that even the best designed systems only achieve about 60% of the ideal Carnot efficiency. And they are fairly mature technologies. And they also pose release risk of synthetic heat-trapping refrigerant during manufacture, use and decommissioning. Which is obviously terrible for the atmosphere.
So our challenge is to develop thermoelectric material technology that cools with field effect, such as electrocaloric or magnetocaloric cooling. Also under investigation are mechanocaloric material technology such as barocaloric, elastocaloric, + twistocaloric cooling.
Finally, the human lip is very sensitive to temperature. Lest you think this is only for lascivious purposes, a more common and prosaic reason is that the safe temperature range of food we eat is important to our survival. So, do try this at home: Take a common rubber band, suddenly + alarmingly stretch it out, then touch it to your lips. Warmer of course. Then relax it + touch it to your lips again. That's the surprise. And like a lot of good science, this was a phenomenon discovered in the nineteenth century, 1805 to be exact. You may have a twistocaloric refrigerator in your future, based on this seemingly inexplicable experience.