In order for the overunity LED to break the 2nd law of thermodynamics it has to be coupled to a solar cell collector which will achieve more than 43% efficiency (as the LED is around 230% efficient, and this must be with the spectrum of light emitted by the LED.
However, this is not the only requirement. In order to fall outside the second law in a simple demonstration then the solar cell collector must be at the same temperature as the LED system, which the paper says is at 135 degrees C.
The following graph is extracted from a web article on Solar Cell Efficiency.
Now you have to extrapolate from the figures what you would expect the efficiency to be when the cell is at a temperature of 135 degrees C. My estimate is that the solar cell efficiency is about halved from the figure at 25 degrees C, because the current stays about constant, but the voltage decreases, and I'm assuming the voltage decrease at all currents is identical to the extrapolated reduction in open-circuit voltage (i.e. at zero current on the x axis) as it is easiest to read the voltage figures there. The relative x axis offset of the three lines at varying currents looks pretty constant so this does not seem unreasonable.
Since the solar cell efficiency does not start off at 100%, by the time you have reduced it by 50% then you are almost certain to be under 43% efficiency.
Some caveats and other points to note are:-
1) the reduction in solar cell efficiency is extrapolated based on measurements for sunlight, but the reduction for infra-red at 2.4um will be different.
2) rather than actual efficiency of the infra-red solar cell what you really need is the calculated maximum thermodynamic efficiency. The practical figures are just presented above as a guide to what might happen in theory.
3) the solar cell required to match the LED must peak in sensitivity around 2.4 um (0.5eV?), and operate at 135 degrees C (= 400K, kT = 0.033eV, ratio = 15:1). This is likely to be much less efficient and much more demanding than taking sunlight of 400-600nm (2-3eV) and expecting to operate at 25 degrees C (= 300K, kT = 0.025eV, ratio = 80:1) as the changed ratio of light temperature to kT is clearly stacked against you.
So, taking the solar cell performance into consideration it is unlikely that you can break the 2nd law, even with experimental 230% LED efficiency, and even in theory. It looks like the solar cell collector thermodynamic efficiency is what is going to stop you.
Last edited Fri, 16 Mar 2012, 1:55pm
Assumptions: 1) E=1/2CV2. (Only dummies assume this). (I am one of these dummies).