Efficiency of thermoelectric material and Carnot Is Carnot efficiency also relevant for "open systems"?
Example - If we take a thermoelectric material with the hot side connected to a stable heat source and the cold side to an infinite heat sink (say the earth), this is not a closed system.
Is Carnot efficiency still relevant? I thought It's basically relevant only for closed system but somehow the Carnot efficiency always pops back.
Why?
 A: A closed system in thermodynamics is one that does not exchange mass with its surroundings. If the thermoelectric material is the system and the surroundings are the heat source and heat sink, the thermoelectric material is a closed system since it does not exchange mass with its surroundings.
The efficiency $\eta$ of the thermoelectric device equals the energy provided to the electrical load divided by the heat absorbed at the hot junction. Since thermoelectric devices are heat engines, their maximum efficiency $\eta$ is theoretically limited to the Carnot efficiency of
$$\eta=\frac{T_{H}-T_{C}}{T_H}$$
For thermoelectric devices the actual maximum efficiency is a function is a fraction of the Carnot efficiency based on the devices "figure of merit". See devices efficiencies in the following: https://en.wikipedia.org/wiki/Thermoelectric_materials
Hope this helps.
A: The Carnot efficiency arises because entropy can't be destroyed and because work carries no entropy—but heat transfer does carry entropy. Thus, if we wish to extract work from a heat source (termed the hot reservoir), we have to dump the associated entropy somewhere, and we achieve this by heating something else (termed the cold reservoir). The energy we spend to do this reduces our efficiency below 100% even with the gentlest operation and the highest-quality engineering.
There's nothing incompatible with an open system here, and if our system is our heat engine, then we require an open system for these energy and entropy transfers from and to the hot and cold reservoir, respectively. Is this what you're asking about?
