A Few More General Topics Thermodynamic Efficiency

A system receives energy and entropy from a pump and emits energy and entropy into surroundings at steady rates E, S, E, S, It also emits heat and performs work at steady rates Q, W. 

We first check that this formula for a thermodynamically maximal temperature yields the Carnot efficiency. As heat transfer is included explicitly in the formulae, we simply remove the sink (E = S =0) and associate a temperature T E E /S with ss PP P 

Next we take black-body radiation to be the pump, and regard black-body radiation as emitted, Then we may put 

Both limits are shared by the Carnot efficiency, but (between these limits) the new efficiency lies lower. It is still unrealistically high, however, 

A further reduction may be achieved by assuming radiation to pass in sequence through n ideal solar cells of decreasing band gaps so that longer wavelengths are absorbed later. At the same time each cell emits radiation to keep in a steady state and this is absorbed by the two neighbouring cells. This radiation becomes important as n - , since for many cells the photons 

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