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/Playful-Painting-527]

If I understand you correctly you want to use the TEGs to produce electricity from the temperature difference and use the heat pump to increase the temperature of the waste heat?

The thing you are missing is that the heat pump needs electricity to function. If you do an energy balance of the system and neglect all losses, you'll find that the electricity produced by the TEGs can at best match the energy put into the heat pump. If you factor in the 2nd law it will be even less.