Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He says that a Carnot's machine doesn´t have to be always made with a gas.
Take a paramagnetic lump of matter. That is one whose magnetization increases with the applied magnetic field. Do the following.
Reduce the applied field while maintaining thermal contact with a bath at temperature $T_2$. The little magnetic dipoles get less lined up; heat enters the system.
Thermally isolate the system and reduce the applied field some more. The sample cools, reaching some lower temperature $T_1$.
Increase the applied field while maintaining thermal contact with a bath at temperature $T_1$. The little magnetic dipoles line up; heat leaves the system.
Thermally isolate the system and increase the applied field some more. The sample gets hotter, eventually reaching temperature $T_2$.
The main point is that, whatever the system you have, you need two isothermal stages and two adiabatic stages, all of them reversible, to make a Carnot cycle. (And don't listen to whoever said the Carnot cycle is an idealization. Just about everything we ever do in theoretical work in science involves some sort of idealization, so there is no need to stress this fact for the Carnot cycle, except perhaps to mention that a close approximation to reversibility is hard to achieve.)
A carnot engine is essentially any device that produces work from temperature differences in a reversible way. Ideal gas expansion is an obvious mechanism to accomplish this. A similar example are fluids that undergo a phase change from liquid to gas in the engine, like refrigerants. The principle is the same.
For something involving electrical energy, there are thermoelectric effects that can generate a voltage from a temperature difference and vice versa. For idealized lossless components, this is a carnot engine.
Another idealized example is a photon gas. Blackbody cavities when heated up produce photons that exert a pressure when they reflect off of a surface. This is again similar to how an ideal gas might be used in a carnot engine.
A more inventive example is a blackbody cavity that produces photons, and these photons being absorbed by something like a photodiode or antenna, which uses the electrical signal to do work. In reverse, it uses an electrical signal to generate photons which get absorbed by the cavity, producing a temperature difference. What's not obvious is that the antenna or photodiode part of the system needs to be at a lower temperature relative to the cavity to receive energy, otherwise it generates its own thermal signal of equal energy back.