Photon upconversion and second law of thermodynamics

[Papatom]

Wiki states: Photon upconversion (UC) is a process in which the sequential absorption of two or more photons leads to the emission of light at shorter wavelength than the excitation wavelength. https://en.wikipedia.org/wiki/Photon_upconversion

Is it possible to have the emitted light with the shorter wave light make electricity with a solar panel? If so then is the useless infrared light converted into useful electricity. This is in contrast with the second law. Where is my mistake?

 

[jfizzix]

The second law of thermodynamics does not prohibit harvesting useful work from infrared radiation. Nor does it prohibit photon up-conversion.
The reverse process is also possible, too, and more likely for a closed system in equilibrium.

Even though most solar panels don't convert much infrared light into electricity, solar power plants that use big reflectors to heat up water boilers do.

 

[Papatom]

More specific:

In a closed system with all temperatures in equilibrium at 300 K is it possible to upconvert IR photons to photons that at the end can charge a battery? This is in contradiction with the second law. Where is my mistake?

 

[jartsa]

A piece of matter must emit and absorb equally any frequency that we choose consider. It's a law.

That law applies to all pieces of matter. An up-converter is a piece of matter. And so is a solar panel.
I mean this law:
https://en.wikipedia.org/wiki/Kirchhoff's_law_(thermodynamics)

The law applies to any kind of object, red, green, opaque, translucent, multicolored, it just has to be in equilibrium.

 

[HAYAO]

Is it possible to have the emitted light with the shorter wave light make electricity with a solar panel? If so then is the useless infrared light converted into useful electricity. This is in contrast with the second law. Where is my mistake?

From the context of your post, I am assuming that you do not have good idea of absorption/emission of light and/or conversion of light into some other form of energy.

If you are talking about crystalline Si solar panel, photons of UV region does not yield high conversion efficiency although it is not zero. Look at the figure below. You can see that the solar spectrum ranges from UV to near-IR region. The crystalline Si solar cells do not efficiently convert all of the region into electricity (green region). Around 1000 nm is the wavelength in which crystalline Si solar cells convert photons into electricity the most efficiently.

1) So what do you mean by "shorter wave light make electricity"? Which region in the spectrum are you specifically talking about?
2) Your second question also does not make sense. What do you mean by "if so"? What you said in the second question does not reflect anything about the first question.
3) Your third question once again does not make any sense. What does your first and second question have to do with second law of thermodynamics?
4) The answer to your fourth question "where is my mistake", is probably scattered everywhere. We need to tackle them one by one.

In a closed system with all temperatures in equilibrium at 300 K is it possible to upconvert IR photons to photons that at the end can charge a battery? This is in contradiction with the second law. Where is my mistake?

It does not matter if it is 300 K or 0 K. For example, if you have a material that can convert two or more IR photons to shorter wavelength photon, then it can be done regardless of temperature. For example, if you have Er(III) and Yb(III) and you excite Yb(III) ion with 980 nm laser, then you can produce 650 nm and/or 540 nm (or even higher depending on the material and the laser). This also does not violate any law.

 

[Andy Resnick]

Wiki states: Photon upconversion (UC) is a process in which the sequential absorption of two or more photons leads to the emission of light at shorter wavelength than the excitation wavelength. https://en.wikipedia.org/wiki/Photon_upconversion

One aspect of your post that hasn't been addressed is the mis-statement of "sequential" absorption: it's not sequential, it's *simultaneous*, and the process is modeled using virtual states. The energy density of sunlight is generally not large enough to provide simultaneous absorption of two photons. Typical two-photon systems require energy densities on the order of GW/cm^2 in order to have an appreciate probability of two-photon absorption.

 

[HAYAO]

One aspect of your post that hasn't been addressed is the mis-statement of "sequential" absorption: it's not sequential, it's *simultaneous*, and the process is modeled using virtual states. The energy density of sunlight is generally not large enough to provide simultaneous absorption of two photons. Typical two-photon systems require energy densities on the order of GW/cm^2 in order to have an appreciate probability of two-photon absorption.

With all due respect, this is not exactly true. Upconversion in broader term does include two-photon absorption, but should most of the time refer to sequential absorption (excited state absorption), energy transfer upconversion, and photon-avalanche.

I believe the OP is referring to upconversion in the more narrower term: systems like rare-earth doped material and triplet-triplet annihilation. Rare-earth, due to its very small absorption cross-section cannot upconvert sunlight, but triplet-triplet annihilation can.

 

[jartsa]

A piece of matter must emit and absorb equally any frequency that we choose consider. It's a law.

That law applies to all pieces of matter. An up-converter is a piece of matter. And so is a solar panel.
I mean this law:
https://en.wikipedia.org/wiki/Kirchhoff's_law_(thermodynamics)

The law applies to any kind of object, red, green, opaque, translucent, multicolored, it just has to be in equilibrium.

As an exercise let's say we have a converter that converts 1000 nm photons to 500 nm photons. So this device can convert radiation from a warm sauna stove to small amount of light. But not radiation from the walls of a warm sauna, that would be against the second law.

A solar panel is quite clearly a heat engine, it makes electricity from heat. Is an up-converter a heat engine too? Yes it is, it makes light from heat.

So these devices are heat engines that behave like heat engines.

I leave as an exercise to anyone interested to find out what radiations the aforementioned up-converter in the uniformly warm sauna absorbs and emits.

 

[slow]

In thermodynamics, the infinitesimal entropic change is expressed in the following way.
$$\displaystyle dS=\dfrac{dQ}{T}$$
The heat is energy. Heat transfer is a variation in the energy of the system. The equation indicates that without variation of the energy of the system the entropy does not change.

The definition of entropy is applicable to radiation, taking into account that energy does not occur in the form of heat. It is presented in electromagnetic form. But the same thing happens. Without variation of the energy of the system the entropy does not change. And the parametric conversion modifies the frequency without altering the total energy of the radiation involved. Frequency changes and entropy does not. The entropy of radiation is a subject that Planck has deepened when he dedicated himself to the black body, although the subject was raised from before.