CarNet, i.e. the CARNOT NETWORK, is the pan-European network on `Thermodynamics and thermoeconomics of energy conversion, transport and accumulation', sponsored by the Commission of European Communities, under the Inco-Copernicus program. An important project is concerned with the publication of a joint multi-author book `Thermodynamics and thermoeconomics of energy conversion and transport' by Springer Verlag New-York.
The 3 rd Chapter is entitled `Thermodynamics of photovoltaics' and is written by A. De Vos. Here follows an abstract:
A solar cell is a thermodynamic engine working between two heat reservoirs,
one at high temperature T1 (= the temperature of the Sun = 5762 K) and one at low temperature T2 (= the temperature of the Earth = 288 K).Its electric current consists of two parts: the light current, strongly dependent on T1, and the dark current, strongly dependent both on T2 and on material constants and technology parameters. The maximum power, we can extract from the cell, is found by searching for the maximum rectangle inscribed in the current-voltage characteristic. This requests the solution of a transcendental equation. The numerical result (for a focused solar spectrum and for a `reasonable choice' of the material constants) is in the range 30 to 40 %. The above procedure stands in strong contrast to the Carnot theory of reversible heat engines. From the first and second law of thermodynamics, we immediately find the Carnot formula: 1 - T2/T1, yielding 95 %. Two questions arise:
(1) Why does photovoltaic theory, in contrast to Carnot theory, need a search for
the maximum rectangle within a characteristic that is dependent on material constants?
(2) Why does photovoltaics yield so much lower efficiencies than the Carnot engine?
The first puzzle is illuminated by application of endoreversible
thermodynamics. Novikov proposed a simple
heat engine model, where an ideal Carnot engine is combined with a linear heat
resistor. This leads to a maximum-power condition
where some intermediate temperature T3 plays the same role as
the voltage V in the solar cell.
By generalizing the Carnot engine by a reversible thermochemical engine and
the finite heat conduction by heat radiation, one can model
a solar cell as an endoreversible engine.
The second puzzle is solved by introducing multi-gap solar cells (or tandem
solar cells), i.e. by applying different materials with different bandgaps.
This leads (in the limit) to an efficiency of 87 %,
rather close to the Carnot limit. The fact we cannot get the Carnot efficiency
itself, is caused by the fact that absorption of radiation without
simultaneous emission of radiation with the same spectrum, is inevitably an
irreversible process.
Endoreversible thermodynamics not only is useful for describing photovoltaics, but also has been successfully applied in numerous other fields, like chemistry, climatology, economics, computing, etc.
This page
http://www.elis.UGent.be/ELISgroups/solar/projects/carnet.html
is maintained by
Alexis De Vos.
Last maintenance on 13 July 99.