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Recycling Heat


Photon Guy

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I believe heat is one of the greatest losses of kinetic energy. For instance, whenever energy is transferred some is lost in the form of heat. Take for instance when you fire a gun, when you pull the trigger it causes a hammer or pin to strike the primer which sets off the propellant. The propellant is the source of the gun's power. When the propellant is set off it burns and expands, releasing kinetic energy which forces the bullet out of the cartridge, down the barrel and out the muzzle. However, at the same time tremendous heat is produced which is why guns get hot when you fire them. Same thing with cars, a car works by the gasoline being ignited in the cylinder which in turn produces kinetic energy that forces up the piston which turns a series of gears which in turn causes the wheels to turn and the car to move forward. However, tremendous heat is being produced with that too which is why car engines get really hot when you run them and need cooling systems to keep from melting. 

Anyway, I was thinking if there was some way to recycle heat back into usable energy. Usually heat is a nuisance but I was thinking if there was a way to make it into something useful. Maybe turn it back into potential energy somehow. 

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23 minutes ago, Photon Guy said:

I believe heat is one of the greatest losses of kinetic energy. For instance, whenever energy is transferred some is lost in the form of heat. Take for instance when you fire a gun, when you pull the trigger it causes a hammer or pin to strike the primer which sets off the propellant. The propellant is the source of the gun's power. When the propellant is set off it burns and expands, releasing kinetic energy which forces the bullet out of the cartridge, down the barrel and out the muzzle. However, at the same time tremendous heat is produced which is why guns get hot when you fire them. Same thing with cars, a car works by the gasoline being ignited in the cylinder which in turn produces kinetic energy that forces up the piston which turns a series of gears which in turn causes the wheels to turn and the car to move forward. However, tremendous heat is being produced with that too which is why car engines get really hot when you run them and need cooling systems to keep from melting. 

Anyway, I was thinking if there was some way to recycle heat back into usable energy. Usually heat is a nuisance but I was thinking if there was a way to make it into something useful. Maybe turn it back into potential energy somehow. 

You can't just recycle it, because of "entropy", but you may be able to get some further use out of it, depending on the circumstances. The basic problem is that heat energy is the kinetic energy of random motion of atoms and molecules. It is thus in a sense "disordered" and cannot be completely re-ordered again. All non-reversible processes lead to an increase in entropy, which means (loosely speaking) a dispersion of energy in a way that cannot be completely recovered. 

However waste heat from many processes can be put to further use. For example waste heat from power stations can heat homes, commercial greenhouses, or swimming pools. And heat pumps can raise the temperature of heat energy from ambient air or the ground to something useful for home heating, although some extra energy has to be put in to do that.

High temperature heat energy has lower entropy than low temperature heat energy, so the higher the temperature the more uses it can be put to. Machines like car engines and power station turbines are "heat engines", which rely on converting high temperature heat energy into mechanical work. However, due to the disordered nature of heat energy, they can't convert 100% of it, so there is always waste heat rejected from any heat engine, usually more than half of it in fact. 

I've tried to explain this in simple words, but really you need to read about the second law of thermodynamics and a bit about the concept of entropy, to see what the limitations are. 

Edited by exchemist
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Optical Rectenna can convert Infrared radiation - radiant heat - directly into electricity but in practice so far the yields are extremely low. Like an antenna does with longer (radio) wavelengths - like the old "crystal radio" that powered itself from the radio waves. Not sure how that works in entropy terms - heat loss in the conversion?

Of all the out there possibilities this would be one I'd like to see get some serious attention because if they can be made to work we could not only make electricity from waste heat but from radiant heat of all kinds, including down-radiation from clouds and atmosphere by night as well as from sunshine by day.

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35 minutes ago, Ken Fabian said:

Optical Rectenna can convert Infrared radiation - radiant heat - directly into electricity but in practice so far the yields are extremely low. Like an antenna does with longer (radio) wavelengths - like the old "crystal radio" that powered itself from the radio waves. Not sure how that works in entropy terms - heat loss in the conversion?

Of all the out there possibilities this would be one I'd like to see get some serious attention because if they can be made to work we could not only make electricity from waste heat but from radiant heat of all kinds, including down-radiation from clouds and atmosphere by night as well as from sunshine by day.

That's intriguing. I suppose that strictly speaking radiation energy is not heat energy. So I don't think (though someone may correct me) that one has to treat energy conversion to electricity by the antenna as a heat engine. 

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26 minutes ago, exchemist said:

That's intriguing. I suppose that strictly speaking radiation energy is not heat energy. So I don't think (though someone may correct me) that one has to treat energy conversion to electricity by the antenna as a heat engine. 

Radiation is heat if it’s coming from a thermal source, e.g. the sun’s blackbody radiation has a fair amount in the visible. Something cooler radiates in the IR

”yields are low” is a key phrase in the above description 

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7 hours ago, Photon Guy said:

Anyway, I was thinking if there was some way to recycle heat back into usable energy. Usually heat is a nuisance but I was thinking if there was a way to make it into something useful. Maybe turn it back into potential energy somehow.

You can recycle all of it back into 'useful energy' in principle if you have a handy heat sink at absolute zero and lots of time to realise near-reversible thermodynamic processes. 

Trouble is the 'ifs'. They tend to cost a lot of capital.

 

 

 

 

 

 

 

 

 

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On 1/9/2024 at 11:37 AM, exchemist said:

You can't just recycle it, because of "entropy", but you may be able to get some further use out of it, depending on the circumstances. The basic problem is that heat energy is the kinetic energy of random motion of atoms and molecules. It is thus in a sense "disordered" and cannot be completely re-ordered again. All non-reversible processes lead to an increase in entropy, which means (loosely speaking) a dispersion of energy in a way that cannot be completely recovered. 

However waste heat from many processes can be put to further use. For example waste heat from power stations can heat homes, commercial greenhouses, or swimming pools. And heat pumps can raise the temperature of heat energy from ambient air or the ground to something useful for home heating, although some extra energy has to be put in to do that.

High temperature heat energy has lower entropy than low temperature heat energy, so the higher the temperature the more uses it can be put to. Machines like car engines and power station turbines are "heat engines", which rely on converting high temperature heat energy into mechanical work. However, due to the disordered nature of heat energy, they can't convert 100% of it, so there is always waste heat rejected from any heat engine, usually more than half of it in fact. 

I've tried to explain this in simple words, but really you need to read about the second law of thermodynamics and a bit about the concept of entropy, to see what the limitations are. 

So it sounds like what you're saying is that chaos cannot lead to order. That's what you seem to be saying to a certain extent when you talk about how heat is disordered and can't be re-ordered. The concept of entropy is associated with disorder, randomness, or uncertainty, in short, its associated with chaos. But chaos can lead to order, sometimes. 

There is the concept that if you have an infinite number of chimpanzees with an infinite number of typewriters there is a chance that one of them might write Shakespeare. If you randomly press keys on a keyboard there is a chance, however slim, that you could write the complete works of William Shakespeare. That would be an example of how chaos, pressing keys at random, can lead to order. 

On 1/9/2024 at 4:57 PM, Ken Fabian said:

Optical Rectenna can convert Infrared radiation - radiant heat - directly into electricity but in practice so far the yields are extremely low. Like an antenna does with longer (radio) wavelengths - like the old "crystal radio" that powered itself from the radio waves. Not sure how that works in entropy terms - heat loss in the conversion?

Of all the out there possibilities this would be one I'd like to see get some serious attention because if they can be made to work we could not only make electricity from waste heat but from radiant heat of all kinds, including down-radiation from clouds and atmosphere by night as well as from sunshine by day.

That would work wonders for electric cars. 

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6 hours ago, Photon Guy said:

So it sounds like what you're saying is that chaos cannot lead to order. That's what you seem to be saying to a certain extent when you talk about how heat is disordered and can't be re-ordered. The concept of entropy is associated with disorder, randomness, or uncertainty, in short, its associated with chaos. But chaos can lead to order, sometimes. 

There is the concept that if you have an infinite number of chimpanzees with an infinite number of typewriters there is a chance that one of them might write Shakespeare. If you randomly press keys on a keyboard there is a chance, however slim, that you could write the complete works of William Shakespeare. That would be an example of how chaos, pressing keys at random, can lead to order. 

That would work wonders for electric cars. 

Actually no, that is not what I am saying. Be careful not to make sweeping simplifications or you will get entirely the wrong idea. But it is interesting you make this mistake, as it is an assertion that one sometimes finds creationists making*, so it may be quite a common misconception.

First, the word "chaos" is not one I used. I spoke of degrees of "disorder", or of "dispersion of energy". I could equally have said "dissipation" or "spreading out" of energy,  it gives the same idea. This does not indicate "chaos" which, to me at least, implies total disarray and absence of any order whatsoever. That's a wrong idea. Entropy is a quantitative concept. It's not all or nothing. There are even entropy tables you can look up, for various chemical substances. 

Second, it is perfectly possible for ordered systems to arise spontaneously, so long as the overall entropy of the process involved increases. When water freezes, the order in the water increases,  because the molecules all line up in particular positions in the ice crystal structure. This is a far more ordered arrangement than the randomly moving and tumbling molecules in the liquid phase. But what happens is that energy is given off (the Latent Heat of Fusion) as the bonds in the crystal form. This energy gets dissipated into the surrounding environment.  Overall, entropy - the degree of dissipation of energy - increases in the course of ice forming, even though the ice itself has lower entropy than the water it formed from.  

 

* Creationists sometimes claim the increasing complexity of life in the course of evolution could not have taken place naturally, because it involves "order" spontaneously arising out of "chaos"  (a word they love because of its association with creation myths). This ignores the obvious fact that organisms continually take in lower entropy energy (e.g. sunlight or complex, ordered molecules like sugars) and give out higher entropy products of respiration (lots of small molecules like water and CO2) and heat.  So overall entropy goes up during all the processes of life, including replication of DNA etc. during reproduction. 

 

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On 1/9/2024 at 10:57 PM, Ken Fabian said:

Optical Rectenna can convert Infrared radiation - radiant heat - directly into electricity but in practice so far the yields are extremely low. Like an antenna does with longer (radio) wavelengths - like the old "crystal radio" that powered itself from the radio waves. Not sure how that works in entropy terms - heat loss in the conversion?

Of all the out there possibilities this would be one I'd like to see get some serious attention because if they can be made to work we could not only make electricity from waste heat but from radiant heat of all kinds, including down-radiation from clouds and atmosphere by night as well as from sunshine by day.

Imagine the current generated is used to charge a battery. Losses are generated by the required electrode overpotentials and internal Ohmic resistance of the cell resulting in radiation of waste heat to the environment.

An overall picture of the thermodynamics can be found here.

Closely related is Thermodynamic bounds on Work Extraction from Photocells and Photosynthesis which connected a lot of loose strings for me at least. Attached. Well worth a read imho.

Photocells and Photosyntesis.pdf

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On 1/10/2024 at 10:06 AM, swansont said:

Radiation is heat if it’s coming from a thermal source, e.g. the sun’s blackbody radiation has a fair amount in the visible. Something cooler radiates in the IR

”yields are low” is a key phrase in the above description 

I would expect waste heat in it's most accessible forms eg warm or hot water, would not radiate IR strongly. Maximising surface area, perhaps like filter cartridges do - folded or coiled sheets - would give better results but more area means more cost too.

The antenna part looks suited to cheap roll to roll "printing" (already tried successfully) but they need very fast response diodes included, of yet unknown suitability for "printing" on thin films. Get fast enough diodes and the potential conversion efficiency is very high, better than photovoltaics and, significantly, able to utilize bands like IR that PV cannot. PV struggles with longer (IR) wavelengths whereas Optical Rectennas should be a bit easier, with slower diodes.

I suppose Optical Rectenna's are more likely to be a rival to photovoltaics for daytime energy before being rival to energy storage - worthwhile but I think PV costs are not the constraining factor anymore. Until or unless it is very cheap to make and use scavenging waste heat may still be out of reach.

19 hours ago, Photon Guy said:

That would work wonders for electric cars. 

Not sure I see much significance for EV's directly. Whilst a high fossil fuels (or nuclear) grid suits overnight charging a high renewables one will likely suit daytime charging better. We are seeing a couple of ways forward eg faster charging is a highly sought option, to be more like fast filling up our tanks from service stations. But other options include abundance of charger fitted parking spaces that suit daytime charging and I expect there will be benefits to electricity grids by having EV's plugged in when not in use.

A parked and plugged in (or for convenience a hands free, perhaps wireless induction connected) EV can be more than just another unresponsive source of demand - just the option to vary charge rates according to overall balance of supply and demand would make them a load leveling option for electricity grid managers. Drive to work, have the charge rate to a set to reach minimum requirement as priority and vary charge rates after that to achieve full charge by a set time, at the grid operator's discretion. Even potentially they can draw on those batteries, (under agreed terms and conditions) as well as have them contribute to household electricity use. I believe there is a trial section of road somewhere in the US with induction charging built into it - ie charge as you drive. Which I think may be more the kind of solution we will need for decarbonising road freight vehicles, that we don't want to have to sit idle for long periods. Railway style overhead (being trialed in Europe) is probably more efficient and cost effective than in-road induction... not electrification everywhere but strategically, so battery electric vehicles charge up on approaches and exits to cities and town and on long, heavily used inclines. Faster charging would also reduce how much of this style of highway electrification is needed too.

I also expect it will be possible to unify electricity accounts so that charging an EV anywhere is billed to a household account - and for solar fitted households to have their contributions to the grid count towards it, wherever the car is used.

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1 hour ago, Ken Fabian said:

I would expect waste heat in it's most accessible forms eg warm or hot water, would not radiate IR strongly. Maximising surface area, perhaps like filter cartridges do - folded or coiled sheets - would give better results but more area means more cost too.

Depends on the temperature difference. Which is why it becomes less efficient with each stage of trying to recover energy.

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6 hours ago, swansont said:

Depends on the temperature difference. Which is why it becomes less efficient with each stage of trying to recover energy.

 

Off the top of my head I don't think that is correct. I think IR intensity of the emitter is purely temperature dependent but is not dependent on a difference in temperature - ie is independent of the temperature of the receiver. Except maybe will be receiving IR or conducted heat back - which, if the receiver is heated by the process would counter intuitively increase the efficiency... ?? Doesn't sound correct, but...

@sethoflagos Any thoughts on this?

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1 hour ago, Ken Fabian said:

 

Off the top of my head I don't think that is correct. I think IR intensity of the emitter is purely temperature dependent but is not dependent on a difference in temperature - ie is independent of the temperature of the receiver. Except maybe will be receiving IR or conducted heat back - which, if the receiver is heated by the process would counter intuitively increase the efficiency... ?? Doesn't sound correct, but...

@sethoflagos Any thoughts on this?

As I understand it, the theorical maximum efficiency from a 2nd Law point of view is 1 minus the temperature ratio of absorber over emitter. 

This yields something like 85% for solar spectrum conversion.

Trying to convert near ambient spectrum IR would yield zilch I suspect as the antenna would be emitting about as much as it absorbed.

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7 hours ago, Ken Fabian said:

Off the top of my head I don't think that is correct. I think IR intensity of the emitter is purely temperature dependent but is not dependent on a difference in temperature - ie is independent of the temperature of the receiver. Except maybe will be receiving IR or conducted heat back - which, if the receiver is heated by the process would counter intuitively increase the efficiency... ?? Doesn't sound correct, but...

Fourth power of the temperature (Stefan-Boltzmann law), but the net power depends on what the reservoir is radiating back at the object. You can’t spontaneously transfer heat to a body at a higher temperature (there has to be work done), per the second law

If you have an object at room temperature, it will not transfer heat to the room (regardless of the actual temperature of the room) because there must be a difference in temperature to transfer heat. True for radiation, conduction and convection.

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I admit I am still unclear on this.

Won't the receiver in this case only gain heat from what is not converted to electricity and will radiate back less than reaches it? Seems to me the rate of absorption by the antennae is independent of temperature of the antennae.

A cooling emitter - radiating away some of it's energy, yes - but a cooling receiver too (?), diverting what reaches it to electricity instead of raising it's temperature (and radiating it back). Again, adding to efficiency??

I recall one of the suggested possible uses for Optical Rectenna is surface coatings on walls for cooling rooms, an alternative to A/C - "waste" heat turned to electricity as a bonus.

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The bottom line here is Kirchoff's Law of Thermal Radiation which is often expressed as:

Quote

For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

If this were not true then there could be spontaneous nett heat flow from a cool body to a hotter one which simply doesn't happen.

However, the proviso 'in thermal equilibrium' is key since 'arbitrary bodies' can have widely different emissivities at different wavelengths corresponding to different equilibrium temperatures. This is where the misunderstandings arise.

Taking an arbitrary example quote from https://en.wikipedia.org/wiki/Emissivity

Quote

Solar water heating system based on evacuated glass tube collectors. Sunlight is absorbed inside each tube by a selective surface. The surface absorbs sunlight nearly completely, but has a low thermal emissivity so that it loses very little heat. Ordinary black surfaces also absorb sunlight efficiently, but they emit thermal radiation copiously.

Here the absorptivity is with reference to thermal equilibrium radiation at the surface temperature of the sun, whereas the emissivity is with reference to local thermal equilibrium in the vicinity of the collectors. The collectors are NOT in thermal equilibrium with the surface of the sun. Without the temperature difference, there would be no loophole to exploit.

10 hours ago, Ken Fabian said:

Won't the receiver in this case only gain heat from what is not converted to electricity and will radiate back less than reaches it? Seems to me the rate of absorption by the antennae is independent of temperature of the antennae.

Okay so far. But note that emission by the antennae is NOT independent of the temperature of the antennae,

10 hours ago, Ken Fabian said:

A cooling emitter - radiating away some of it's energy, yes - but a cooling receiver too (?), diverting what reaches it to electricity instead of raising it's temperature (and radiating it back). Again, adding to efficiency??

The receiver does not reradiate incident solar radiation because it is not at the same equilibrium temperature. Therefore there is an asymmetry between absorption and emission that can be exploited. 

10 hours ago, Ken Fabian said:

I recall one of the suggested possible uses for Optical Rectenna is surface coatings on walls for cooling rooms, an alternative to A/C - "waste" heat turned to electricity as a bonus.

But refer to the relevant paragraph in https://en.wikipedia.org/wiki/Optical_rectenna

Quote

In an interview on National Public Radio's Talk of the Nation, Dr. Novack claimed that optical rectennas could one day be used to power cars, charge cell phones, and even cool homes. Novack claimed the last of these will work by both absorbing the infrared heat available in the room and producing electricity which could be used to further cool the room. (Other scientists have disputed this, saying it would violate the second law of thermodynamics.[16][17])

The proposal neglects to consider the equivalence of absorptivity and emissivity at thermal equilibrium. So it falls foul of Kirchoff's Law, and by logical extension, the 2nd Law of Thermodynamics. 

Edited by sethoflagos
typo
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Thanks Sethoflagos. I admit I still can't say I understand.

14 hours ago, sethoflagos said:

Okay so far. But note that emission by the antennae is NOT independent of the temperature of the antennae,

Seems to me the materials of an antennae will get warmed by what the antenna doesn't turn into electricity - but a warmer antenna should work at similar efficiency as a cold one, it not being a thermal phenomena; unlike an ordinary material less energy/heat is added to the material of an IR antenna than the total energy received and absorbed by it. I still think diverting it away as electricity diverts energy away from the combined emitter + receiver and should result in loss of energy within them, ie cooling.

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The detailed mechanics of aerial design are way beyond my pay grade, but you seem to be making two distinctions here that I would be wary of:

5 hours ago, Ken Fabian said:

... it not being a thermal phenomena

Until it is. Can you say this when the received phonons are indistinguishable from the sea of thermal phonons flooding the lattice of the receiving aerial? 

5 hours ago, Ken Fabian said:

... ie cooling

Cooling is thermodynamically difficult. I'd be reluctant to use the word in place of "not getting quite as warm as you might otherwise expect".

Revisiting Kirchoff's Law briefly, there are some useful bits of information to be had from Electromagnetic Reciprocity.

This caught my eye:

Quote

Forms of the reciprocity theorems are used in many electromagnetic applications, such as analyzing electrical networks and antenna systems.[1] For example, reciprocity implies that antennas work equally well as transmitters or receivers, and specifically that an antenna's radiation and receiving patterns are identical.

 

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@sethoflagos

I understand that antennae work as transmitters and receivers (but little real understanding of how they work). I am simply looking at energy flows. Antennae do turn EMR - if only narrow bands of it - into electricity and that energy is not being absorbed into the substance of the receiver. Simply, the energy that is diverted away isn't turned into heat in the receiver. In an otherwise closed system it has a leak; there will be loss of energy, ie cooling.

Are you (or Kirchoff) saying an antenna won't work if the substance of an antenna radiates within the band it is tuned to - that IR emissions (specifically) are too close in wavelength to the receiver and prevent it working?

This may indeed be the case - ie there isn't any flow of energy away as electricity in a rectenna tuned to the bands that materials radiate heat because it doesn't work. But at shorter or longer wavelengths - outside the IR - they will? Yet my understanding is optical rectennae have been shown to work - albeit at very low conversion efficiencies; at just what wavelengths, at what temperatures and under what conditions I don't know.

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4 hours ago, Ken Fabian said:

Simply, the energy that is diverted away isn't turned into heat in the receiver. In an otherwise closed system it has a leak; there will be loss of energy, ie cooling.

You're effectively claiming the ability to extract useful work from a system at thermal equilibrium.

Not sure there's anywhere to go from here.

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14 hours ago, Ken Fabian said:

I understand that antennae work as transmitters and receivers (but little real understanding of how they work). I am simply looking at energy flows. Antennae do turn EMR - if only narrow bands of it - into electricity and that energy is not being absorbed into the substance of the receiver.  

This is not owing to heat transfer - the radiation isn't thermal. It's doing work. 

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4 hours ago, swansont said:

This is not owing to heat transfer - the radiation isn't thermal. It's doing work. 

I'm getting a picture here of transmitted photons perturbing the EM field of an antenna aligned with the source somewhat analogously to a steady trade wind generating oceanic waves. And just as the energy of oceanic waves  can be harvested by an appropriate machine, the waves in the field of the antenna induce an alternating pd across the terminals of the antenna which can in turn be harvested.

Is this analogy a useful one?

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On 1/17/2024 at 3:01 PM, sethoflagos said:

You're effectively claiming the ability to extract useful work from a system at thermal equilibrium.

Not sure there's anywhere to go from here.

I don't know why Dr Novack thinks it but I think it because I think the photons interacting with an antenna don't add (all of) their energy as heat to the antenna, some energy making electrical potential. Some gets converted to electrical energy and carried away. It may initially be at thermal equilibrium but it isn't a closed system. Note, I don't think this as a certainty - I don't know enough.

But if the antenna can't absorb IR because the temperature of the antenna makes it radiate IR - not the antenna transmitting IR because that takes electricity from somewhere else, but the materials radiating it in the normal way things that are warm radiate - then, yes, it is at thermal equilibrium and an IR rectenna cannot work.

I had thought that interaction between EMR and an antenna was independent of antenna temperature but that was most likely ignorance - most working antenna aren't tuned to the band the antenna normally radiates in.

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9 hours ago, Ken Fabian said:

I don't know why Dr Novack thinks it but I think it because I think the photons interacting with an antenna don't add (all of) their energy as heat to the antenna, some energy making electrical potential. Some gets converted to electrical energy and carried away. It may initially be at thermal equilibrium but it isn't a closed system. Note, I don't think this as a certainty - I don't know enough.

But if the antenna can't absorb IR because the temperature of the antenna makes it radiate IR - not the antenna transmitting IR because that takes electricity from somewhere else, but the materials radiating it in the normal way things that are warm radiate - then, yes, it is at thermal equilibrium and an IR rectenna cannot work.

I had thought that interaction between EMR and an antenna was independent of antenna temperature but that was most likely ignorance - most working antenna aren't tuned to the band the antenna normally radiates in.

We're pretty much aligned here, and I too am pushing the limits of my understanding of EM field behaviour.

I was hoping that @swansont or someone else with expertise in this field would have picked up on my previous post and confirmed or otherwise the mental picture I have of this. But in the absence of such... 

I think it reasonable to picture the thermal energy of a metallic antenna as being largely contained in the motion of a 'gas' of the unbound electrons. If you can persuade a significant excess of these to move in a coordinated way in a particular direction then that yields an electrical current distinct from the thermal motion. However, I suspect that this requires the incoming radiation to be both directional and/or phase-coordinated. Thermal radiation from the sun satisfies the directionality requirement and I presume the higher frequency part of the spectrum may have sufficient 'kick' to push a few electrons across the junction gap of a diode which might explain the measurable current reported in that scenario. But ambient thermal radiation is omnidirectional and the individual photons are much weaker. Trying to extract energy from this scenario just sounds a little too Maxwell's Demonish for comfort.  May be this picture is all wrong, but it at least tends towards consistency with the Kirchoff's Law/2nd Law objections I raised earlier.  

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