# What kind of engine is a photovoltaic solar cell?

I have read several times here (on PSE) and there (in Google) that photovoltaic solar cells aren't heat engines. I.e. they are not working via a heat transfer between 2 reservoirs, and so they are not limited by Carnot efficiency. Ok, very good, but then what kind of engines are they?

And why can I find highly cited papers A thermodynamic cycle for the solar cell claiming that they are heat engines? That's utterly confusing!

So, in the end, can a solar panel work if the luminous source comes from a colder object than the solar cell itself? I guess the answer is yes because the solar cell isn't a heat engine, but I am not sure at all because some sources claim that they are heat engines...

I would tend to think that the temperature of the luminous source is irrelevant for the solar cell operation. For the solar cell only get to know about the incident light, which may give almost no information on the temperature of the light source. Indeed, not all luminous source follow a blackbody spectrum, in fact none or close to none do.

• According to de Vos, Landsberg, etc. "Entropy fluxes, endoreversibility, and solar energy conversion", J. Appl. Phys. 74 (6), 15 September 1993, a solar cell can be modeled as as an endoreversible engine (heat conductive envelope + Carnot cycle reversible engine inside) – hyportnex Aug 19 at 11:29
• @hyportnex Are you sure? This answer physics.stackexchange.com/questions/175692/… claims that it's a hybrid photovoltaic-thermal device that can be modeled as an endoreversible engine, not a photovoltaic solar cell. Is he wrong? (note that his answer is based off de Vos paper) – thermomagnetic condensed boson Aug 19 at 16:17
• – hyportnex Aug 19 at 20:23
• @thermomagneticcondensedboson I was the author of that other answer. The photovoltaic-thermal device is a the general solution. If the temperature difference is zero it reduces to the photovoltaic limit. So yes hyportnex is correct. – boyfarrell Aug 20 at 15:34
• Normally efficiency limits are calculated with solar illumination. It’s true monochromatic efficiencies of solar cells can be very high, there are plenty of power-over-fibre products that use this fact! Lasers are not a thermal source of radiation; virtually no entropy associated with beam. – boyfarrell Aug 21 at 13:40

In response to light a solar cell generates an electrochemical potential which provides the thermodynamic driving force for extraction of work. This is the fundamental operation of a solar cell and is independent of the nature of the incident light — be it from the sun, a LED or a laser — because information regarding the initial photon distribution is rapidly lost as the electronic system thermalise to a new equilibrium state. This process is called thermalisation.

The instant after absorption, the electronic distribution directly matches the spectral distribution; this is non-thermal as it cannot be described by a temperature. Rapidly a thermal distribution forms with temperature hotter than the material. Eventually, this excess energy is dissipated an a fully thermalised distribution with a non-zero electrochemical potential is formed.

In thermodynamics we need to define the boundary of our “system”. For energy conversion we must include the incident light source too. This is because different light sources will have different spectral distributions and hence bring with them different amounts of heat and entropy. In general the more entropy associated with the incident light, the more inefficient the energy conversion process.

Solar cells can have very highly monochromatic efficiencies for this reason.

So what type of engine is a solar cell. It’s unique, is neither a pure heat engine nor a pure chemical engine. In the endoreversible scheme it looks like this,

The input is a hot body with temperature $$T_1$$ and zero chemical potential, where $$T_1>T_2$$, that emits light which generates a chemical potential in the solar cells $$\mu_3$$ that drives an engine. There is no temperature gradient across the engine. But there is a temperature gradient across the full system.

So I can understand why people refer to them as heat engines, but I also understand that’s a bit misleading because it only tells half the picture.

So what about if a solar cell is illuminated by a laser, then there is no temperature gradient!?

Laser light is described by a temperature and a chemical potential. The seminal paper on this is P Wurfel, The Chemical Potential of Radiation in which thermodynamics of thermal, luminescent and laser light are discussed.

A suitable endoreversible model of this case would be to replace the hot body in the diagram with an emitter described by $$T_3$$, which could be greater or less than $$T_2$$, and a chemical potential $$\mu_2$$. Provided that there is net positive energy current exchanged between the laser and the solar cell, work can be extracted.

In the limiting case of no temperature gradients in the system, provided that $$\mu_2 > \mu_1$$, work can be extracted because of the positive gradient in chemical potential.

However, this is no longer a solar cell! Although power-over-fibre products benefit from the high efficiency of solar cells when illuminated by monochromatic light. From the endoreversible model we can see why; the entropy of the incident light is very low, allowing the engine to operate more efficiently.

This paper is also relevant, A De Vos, Is a solar cell an endoreversible engine?

• Does this mean that if $T_1$ were to be lesser than $T_2$ then no positive work could be done by the photovoltaic cell? I.e. a laser kept at say 10°C cannot be absorbed and converted to any useful work by a photovoltaic cell at 20°C? That seems very strange to me, in that I see no way for the photovoltaic cell to get to know the temperature of the laser, where the light was emitted. – thermomagnetic condensed boson Aug 22 at 12:20
• You are not thinking about laser light in the correct way. Thermodynamically laser light is described by a temperature and a chemical potential of the photons. In this case it is not necessary to have a positive temperature gradient because energy conversion can occur by the gradient in chemical potential. Read this highly cited Paper from Peter Wurfel, The Chemical Potential of Photons, there is a section on laser light math.unife.it/astro-fisica/insegnamenti/ottica-applicata/… – boyfarrell Aug 22 at 13:36
• I would appreciate if you could include this information in your answer, I would accept it. – thermomagnetic condensed boson Aug 22 at 19:06
• Thanks for the good questions! If you found the answer useful please mark as accepted. – boyfarrell Aug 22 at 20:32
• When you say that this isn't a solar cell, it is still a photovoltaic cell, right? (Your answer satisfies me, I've accepted it and upvoted it). – thermomagnetic condensed boson Aug 22 at 20:56