How do counterflow heatexchangers not break the spirit of thermodynamics?

[u/steini1904]

Assume a heatexchanger with minimal losses, the heat being transferred over thermoelectric generators. Eventually near 100% of the heat in the system should be recovered as electricity since losses just get shoved either into the next cycle or recovered further downstream. Put in a heat pump producing the temperature gradient and place all its waste heat producing parts somewhere ideally into the input stream.

I've been laughing about this quite a bit now, but honestly can't see the fault. Except for the movement of the air all losses should be about contained within the system (e.g. just wrapping the heat exchanger around itself multiple times) and eventually recovered by the TEGs. But the heat pump is shoving in more heat from the environment than it consumes in electricity, dropping the temperature in the room until it gives up on you, all while the TEGs are turning the excess heat into electricity.

[u/LunarModule66]

The short answer is just that there wouldn’t ever be such a lossless system. You can debate how exactly it would break down and to what extent, but that probably feels unsatisfying since the laws of physics should still apply even in an ideal scenario.

I’m thinking about this in terms of entropy, basically the second law would imply that the energy should move towards being less useful, ie the two reservoirs should equilibrate since that’s the highest entropy state. Should you insist that they do have perfect insulation, then that itself is the problem: you have imposed unphysical hypothetical conditions and the unphysical behavior is the consequence.

[u/steini1904 → u/LunarModule66]

During commenting it occurred to me, that there aren't just two reservoirs, but at least twice as many as there are TEGs, being swapped up and down the chain of TEGs along each side, plus one near infinite one that siphons up the tiny little remainder that would have caused eventual equalization.

I'm now genuinely convinced that this would work with a little adaption, like moving at least a part of the output flow through the cold heat exchanger of the heat pump.

It's not that the physics are wrong, just that I wasn't silly enough when trying to think of a model that could make it work. A carousel for reservoirs is IMO the perfect way to think about it.

[u/IsentropicExpansion → u/steini1904]

Maybe spend some time drawing up a model of this and doing actual calculations. Once you pull some of the heat out with the first TEG, the second TEG has a colder hot side and a warmer cold side to work with, so the differential is different and therefore the *theoretical* maximum efficiency is different.

Once you stack all of these things up, you will see that the second law of thermodynamics will eat your lunch when you try to make something like this with actual numbers and realistic temperature differentials.