Absorption of radiation from a 'cooler' source

[Arfur Bryant]

This post specifically queries the absorption, by matter, of (thermal) radiation which has been emitted from a source of a cooler temperature than the receiving matter.

As I understand it, when matter 'receives' radiation, that radiation is either a) absorbed, b) reflected (or absorbed and instantly re-emitted) or c) transmitted.

When radiation from a warmer source is absorbed, the molecules of the matter gain an increase in energy which is manifested as an increase in temperature. In this sense, the radiation is absorbed 'for energy gain'.

My questions are:

What happens when radiation from a cooler body meets the receiving matter?
And,
Can receiving matter gain (thermal) energy from any 'absorption' from a cooler source? (Or is it 'transparent' due to the wavelength of the 'cooler' radiation?

 

[ZapperZ]

This post specifically queries the absorption, by matter, of (thermal) radiation which has been emitted from a source of a cooler temperature than the receiving matter.

As I understand it, when matter 'receives' radiation, that radiation is either a) absorbed, b) reflected (or absorbed and instantly re-emitted) or c) transmitted.

When radiation from a warmer source is absorbed, the molecules of the matter gain an increase in energy which is manifested as an increase in temperature. In this sense, the radiation is absorbed 'for energy gain'.

My questions are:

What happens when radiation from a cooler body meets the receiving matter?
And,
Can receiving matter gain (thermal) energy from any 'absorption' from a cooler source? (Or is it 'transparent' due to the wavelength of the 'cooler' radiation?

I am not exactly sure what the issue is here.

Once a body has emitted a radiation, it really doesn't care what other body absorbs it. That other body can be cooler, warmer, or at the same temperature as the original body. The same can be said about the receiving body. It doesn't really care about what body emitted that radiation. All it sees is some radiation coming its way.

For example, the Earth also gives out its own radiation. Some of it reaches the sun, and the sun can certain absorbs that radiation.

I think you may be confusing this with heat flow and the Zeroth Law of Thermo.

Zz.

 

[Arfur Bryant]

Zz,

OK, I'll try to clarify 'the issue'. It's not about what a body 'cares'. It's not actually about the emitter, but about the 'receiver'. It's about whether or not the receiving body gains energy by absorbing the radiation from a cooler source. Or, if you like, does the warmer receiving body gain any heat by absorbing the cooler radiation? To use your analogy, does the Sun become hotter because it absorbs the Earth's radiation? If the answer to that is 'yes', then by what mechanism (on a molecular level) does the sun become hotter?

You could say I'm confusing this with heat flow, but my question is more precise. I know the heat flow will be from hot to cold. Most textbooks will talk about Prevost's theory but science has moved on since the late eighteenth century and my question is specifically how can the cooler (lower energy) radiation add to the energy level of the warmer body?

I hope this clarifies. Thanks for your time.

AB

 

[Jano L.]

Sun receives part of the EM radiation due to the Earth. This radiation wiggles the charged particles in the Sun and gives them some energy. This is most probably entirely negligible for the total energy balance, as the Sun itself is much hotter and much bigger than the Earth, and is losing incredibly more energy by radiating its own radiation, part of which falls on the Earth.

 

[Arfur Bryant]

Jano L.

How exactly does the radiation 'wiggle' the charged particle if the charged particle is at a higher energy level then the radiation (photon)?

I appreciate the difference in scale of this (Zz's) analogy. But the scale is irrelevant to my question. My original question was not about the Sun. It was simply about whether or not radiation from a cooler source can add to the energy level of a warmer body.

It would seem to me that the 'cooler' radiation simply either passes through the warmer body (transmitted), or it is 'reflected' (absorbed and instantly emitted for no energy gain. But that is my interpretation and I would like something more definite please.

AB

 

[ZapperZ]

What is "add to the energy level"? The fact that it can absorb the energy means that the body's energy content has increased, even temporarily. If not, then we have a violation of energy conservation.

Do you feel your body's energy level increasing right this very second?

Zz.

 

[Jano L.]

It was simply about whether or not radiation from a cooler source can add to the energy level of a warmer body.

Yes, the radiation, no matter which source it is from, can do microscopic work on the particles of any other body. Take two hot bodies with no internal energy production, e.g. not Sun, but, say, hot and cold metal block of the same dimensions and composition. Since the hotter body H radiates to colder body C more energy than C radiates to H (intensity of radiation depends on the temperature), the net effect of the mutual irradiation is that the energy of the colder body increases, and the energy of the hotter body decreases, possibly to the point they acquire same temperatures.

 

[Dale]

Or, if you like, does the warmer receiving body gain any heat by absorbing the cooler radiation?

Yes. Consider two scenarios
1) a warm blackbody in the absence of any other object, simply radiating into empty space.
2) a warm blackbody in the presence of a cooler blackbody, both radiating to empty space and to each other.

The warm body in 1) will cool off faster than the warm body in 2). The warm body in 1) emits the same amount of blackbody radiation as in 2), but in 2) it also receives blackbody radiation from the cooler body.

 

[Arfur Bryant]

Zz: ["What is "add to the energy level"? The fact that it can absorb the energy means that the body's energy content has increased, even temporarily. If not, then we have a violation of energy conservation."]

In this context "add to the energy level" means become warmer. There is no suggestion of a violation of energy conservation as the radiation - if not absorbed - is not destroyed. Radiation does not 'have' to be absorbed, it can be reflected (or absorbed and instantly emitted, if you prefer) or transmitted.

How does a cooler body get warmer? It absorbs thermal energy (in the form of photons) which is of a suitable frequency so as to elevate the electron orbit to a higher level. Do you agree? So, how does a photon from a 'cooler' source raise the electron level of the receptor in the case when the wavelength of the photon may not be at the correct level to do so?

AB

 

[Arfur Bryant]

Yes, the radiation, no matter which source it is from, can do microscopic work on the particles of any other body. Take two hot bodies with no internal energy production, e.g. not Sun, but, say, hot and cold metal block of the same dimensions and composition. Since the hotter body H radiates to colder body C more energy than C radiates to H (intensity of radiation depends on the temperature), the net effect of the mutual irradiation is that the energy of the colder body increases, and the energy of the hotter body decreases, possibly to the point they acquire same temperatures.

Jano,

Can you provide supporting evidence for your first sentence?

In your example of the two blocks - you are not addressing my point. I am not asking whether block H can heat block C; I know it can. My question is can block C heat block H? Your first sentence and you other answers indicate you think it can. I don't, as I think that would invalidate the 2nd Law of Thermodynamics.

Hence my original question: Can emitted radiation from a cooler source ever warm a hotter body?

 

[Arfur Bryant]

Yes. Consider two scenarios
1) a warm blackbody in the absence of any other object, simply radiating into empty space.
2) a warm blackbody in the presence of a cooler blackbody, both radiating to empty space and to each other.

The warm body in 1) will cool off faster than the warm body in 2). The warm body in 1) emits the same amount of blackbody radiation as in 2), but in 2) it also receives blackbody radiation from the cooler body.

DaleSpam,

A blackbody is an idealised concept. I am talking about the real world. Yes, a blackbody can absorb all radiation but this has no relevance to my question.

But let's pretend you were <not> talking about blackbodies. Now...

In your situation 2), you state that the warm body would cool slower due to the absorption of radiation from the cooler body. This is exactly what my original question asked. If the warmer body absorbs that radiation for energy gain, how can this happen when the frequency of the receiving radiation cannot elevate the electron orbit?

Further, if what you say is true, what would happen if more cooler bodies were added, surrounding the warmer body? Would the warmer body cool even slower until - eventually - the number of cooler surrounding bodies is such that the warmer body is absorbing so much energy it starts to warm up! At this point you have engineered a situation whereby adding more cooler objects to a system actually increases the temperature of the warmer body!

This cannot be correct.

AB

 

[Nugatory]

Hence my original question: Can emitted radiation from a cooler source ever warm a hotter body?

If by "warm" you mean "increase the temperature of" and they're both reasonable black-bodies so we're talking thermal radiation, no.

Although thermal radiation from the cooler body will transfer energy to the warmer one, more energy will be transferred by thermal radiation in the other direction so net the warmer object will cool while the cooler one warms.

If the cooler body happens to be a very powerful gamma emitter so that its radiation output is not thermal, then it could heat its surroundings.

 

[Nugatory]

If the warmer body absorbs that radiation for energy gain, how can this happen when the frequency of the receiving radiation cannot elevate the electron orbit?

Pushing a bound electron up to a higher energy level is only one of many ways that incoming radiation can transfer energy to a material.

 

[256bits]

DaleSpam,

A blackbody is an idealised concept. I am talking about the real world. Yes, a blackbody can absorb all radiation but this has no relevance to my question.

But let's pretend you were <not> talking about blackbodies. Now...

In your situation 2), you state that the warm body would cool slower due to the absorption of radiation from the cooler body. This is exactly what my original question asked. If the warmer body absorbs that radiation for energy gain, how can this happen when the frequency of the receiving radiation cannot elevate the electron orbit?

Further, if what you say is true, what would happen if more cooler bodies were added, surrounding the warmer body? Would the warmer body cool even slower until - eventually - the number of cooler surrounding bodies is such that the warmer body is absorbing so much energy it starts to warm up! At this point you have engineered a situation whereby adding more cooler objects to a system actually increases the temperature of the warmer body!

This cannot be correct.

AB

Not sure what you are getting at.
A blackbody is an idealized concept, that is true but idealization aids in the analysis of a concept.

Real bodies can be idealized as what is called a grey body, where emmisivity < 1.
Then you can also deal with absorption, transmission and reflectivity.

Even if the hotter body does not absorb or transmit the radiation from the cooler body, then it must reflect. If some of the reflected radiation is sent back to the cooler body, from the perspective of the cooler body it is the same thing as if the hotter body had emmited the radiation. The cooler body has no way to know otherwise, and the hotter body will appear to have increased its radiation output, in other words, hotter.

 

[Arfur Bryant]

Pushing a bound electron up to a higher energy level is only one of many ways that incoming radiation can transfer energy to a material.

Thanks for your comment.

So does this mean you assert that a cooler object can make a warmer object even warmer?

AB

 

[Arfur Bryant]

Not sure what you are getting at.
A blackbody is an idealized concept, that is true but idealization aids in the analysis of a concept.

Real bodies can be idealized as what is called a grey body, where emmisivity < 1.
Then you can also deal with absorption, transmission and reflectivity.

Even if the hotter body does not absorb or transmit the radiation from the cooler body, then it must reflect. If some of the reflected radiation is sent back to the cooler body, from the perspective of the cooler body it is the same thing as if the hotter body had emmited the radiation. The cooler body has no way to know otherwise, and the hotter body will appear to have increased its radiation output, in other words, hotter.

256bits,

I'm sorry you're not sure what I'm getting at. I don't think I'm getting at anything. I'm just asking a simple question: Does thermal radiation from a cooler source ever make a warmer source even warmer? There is no agenda. It is just that specific question.

You say: ["If some of the reflected radiation is sent back to the cooler body, from the perspective of the cooler body it is the same thing as if the hotter body had emmited the radiation. The cooler body has no way to know otherwise, and the hotter body will appear to have increased its radiation output, in other words, hotter."]

I disagree. Any reflected radiation will be at the same wavelength as the original radiation emitted by the cooler object. It will therefore not be the same thing as the warmer body radiating. It will not add to the cooler body's energy. Only 'warmer' radiation can do that. (By warmer I mean radiation from a warmer source.)

Perhaps you could consider my example above where additional cooler bodies are added to the system?

AB

 

[Arfur Bryant]

Thanks for your comment.

So does this mean you assert that a cooler object can make a warmer object even warmer?

AB

Nugatory,

That question did not come across as I intended. I meant no criticism, I am just curious what other mechanisms there may be.

Regards,

AB

 

[Jano L.]

Jano,
Can you provide supporting evidence for your first sentence?

This is just something that comes naturally from the EM theory and is part of the theory of heat radiation. EM radiation goes to all directions and acts on all matter that it encounters.

My question is can block C heat block H? Your first sentence and you other answers indicate you think it can. I don't, as I think that would invalidate the 2nd Law of Thermodynamics.

In non-relativistic theory (most of daily cases) it can heat it in the sense that the radiation of the cold body deposits some energy in the hot body. It cannot heat it in the sense that the temperature of the hot body would become even greater, since that would most probably lead to violation of 2nd law.

According to the relativity theory though, in strong gravitational field, thermodynamic equilibrium is no longer consistent with equal temperatures; instead, regions closer to heavy body tend to higher temperatures than the places higher above it. Take two heights, $0,h$; in equilibrium, the temperatures will obey

$$
\frac{T(h)}{T(0)} = e^{-\frac{|\Delta \phi|}{c^2}}
$$
where $\Delta\phi$ is a difference of gravitational potentials at those two heights.

If the distribution of temperature in the radial direction is not equilibrium but still the upper regions have lower temperature, then the radiation from these regions, although they have $lower$ temperature than the bottom parts, will heat the bottom parts even in the sense that the temperature of the hotter regions will becomes even hotter (to get closer to the above equilibrium condition).

 

[256bits]

256bits,

I disagree. Any reflected radiation will be at the same wavelength as the original radiation emitted by the cooler object. It will therefore not be the same thing as the warmer body radiating. It will not add to the cooler body's energy. Only 'warmer' radiation can do that. (By warmer I mean radiation from a warmer source.)

AB

Look up radiosity.

 

[ZapperZ]

Thanks for your comment.

So does this mean you assert that a cooler object can make a warmer object even warmer?

AB

No one can answer that based on the premise you gave. This is because it depends on the rate of energy loss of the body versus the rate of energy absorption. If an object absorbs more than it emits, then of course that body will increase in temperature. It doesn't matter where that energy comes from, be it from a cooler or warmer object.

The problem I see with this thread is that you have a particular scenario in mind, but you are giving an incomplete picture. I've shown one particular example where what you are asking can't be answered because of an incomplete description of the scenario (rate of energy radiated by the body doing the absorbing).

So let's get this point across as accurately and clearly as possible: THE SUN DOES ABSORBS THE RADIATION ENERGY FROM THE EARTH, EVEN WHEN IT IS AT A HIGHER TEMPERATURE THAN THE EARTH

Is that clear enough?

Now, what happens after that is more complicated because the sun also radiates, at the same time, its own energy! If the sun is a blackbody and does not radiate anything away, then yes, it will continue to increase in temperature simply because it is absorbing more energy than it emits! Notice that this has nothing to do with where that energy came from.

I'm not sure how to make this any clearer than that.

Zz.

 

[Nugatory]

So does this mean you assert that a cooler object can make a warmer object even warmer?

I think/hope that I answered that in my other post: https://www.physicsforums.com/showthread.php?t=734589#post4640694, number 12 in those thread.

 

[FactChecker]

You may have to look to quantum theory here. No matter what energy state an electron / atom is in, a quantum of energy may knock it into a higher energy state. The probabilities may be small.

 

[UltrafastPED]

What happens when radiation from a cooler body meets the receiving matter?
And,
Can receiving matter gain (thermal) energy from any 'absorption' from a cooler source? (Or is it 'transparent' due to the wavelength of the 'cooler' radiation?

The hotter body will be emitting thermal radiation at a higher rate than it is absorbing it; thus it will not grow warmer.


Note: the absorbed energy ultimately goes into the motion of the atoms of the body; this means that the energy absorbed is being transformed into phonons (quantized sound) internally.

 

[Arfur Bryant]

Thank you UltrafastPED and Factchecker. I will look into that.

AB

 

[Arfur Bryant]

No one can answer that based on the premise you gave. This is because it depends on the rate of energy loss of the body versus the rate of energy absorption. If an object absorbs more than it emits, then of course that body will increase in temperature. It doesn't matter where that energy comes from, be it from a cooler or warmer object.

The problem I see with this thread is that you have a particular scenario in mind, but you are giving an incomplete picture. I've shown one particular example where what you are asking can't be answered because of an incomplete description of the scenario (rate of energy radiated by the body doing the absorbing).

So let's get this point across as accurately and clearly as possible: THE SUN DOES ABSORBS THE RADIATION ENERGY FROM THE EARTH, EVEN WHEN IT IS AT A HIGHER TEMPERATURE THAN THE EARTH

Is that clear enough?

Now, what happens after that is more complicated because the sun also radiates, at the same time, its own energy! If the sun is a blackbody and does not radiate anything away, then yes, it will continue to increase in temperature simply because it is absorbing more energy than it emits! Notice that this has nothing to do with where that energy came from.

I'm not sure how to make this any clearer than that.

Zz.

It is clear apart from what you mean by 'absorbs'. Do you mean that it gains energy from this absorption?

As you seem keen on a scenario, I will try to give one as specifically as I can...

In a spacious closed room there is an electric (filament) fire. It is switched on and the electricity supply is constant. The room establishes equilibrium. Now, a wooden chair (at room temperature) is placed a few feet in front of the fire. The chair heats up because it absorbs thermal radiation from the fire. In heating up, it then emits radiation back to the fire (and other directions). This radiation is still from a cooler source (longer wavelength) than the fire. Does the fire (filament) heat up because it absorbs this 'cooler' radiation from the chair? If so, does the addition of more chairs incrementally heat the fire further?

How's that?

AB

 

[Arfur Bryant]

Look up radiosity.

Did that. Not sure that it addresses the difference in wavelength though...

AB

 

[Arfur Bryant]

You may have to look to quantum theory here. No matter what energy state an electron / atom is in, a quantum of energy may knock it into a higher energy state. The probabilities may be small.

Factchecker,

Can I have your opinion on this statement? (From hyper-physics)

["In the interaction of radiation with matter, if there is no pair of energy states such that the photon energy can elevate the system from the lower to the upper state, then the matter will be transparent to that radiation."]

AB

 

[Dale]

DaleSpam,

A blackbody is an idealised concept. I am talking about the real world. Yes, a blackbody can absorb all radiation but this has no relevance to my question.

There are lots of things that are reasonable approximations to blackbodies. In any case, going to a greybody complicates the analysis, but doesn't change the conclusion. All you have to do is do the analysis at each frequency, factor in the emissivities of the two bodies at that frequency, and integrate over the frequencies. The end result is the same.

But let's pretend you were <not> talking about blackbodies. Now...

In your situation 2), you state that the warm body would cool slower due to the absorption of radiation from the cooler body. This is exactly what my original question asked. If the warmer body absorbs that radiation for energy gain, how can this happen when the frequency of the receiving radiation cannot elevate the electron orbit?

Not all thermal absorption is due to elevating atomic orbits.

For example, in a star the most common interaction will probably be inelastic scattering off a free charge carrier. In other cases an absorbed photon will increase molecular energy by bending or rotating or some other degree of freedom. Or in a solid a photon can be absorbed to produce several phonons in the lattice. Or a photon can produce standing waves inside a cavity. Etc.

It is a mistake to think of a photon's interaction with matter so narrowly. The point is that if a greybody is emitting at a given wavelength then it can also absorb at that same wavelength.

Further, if what you say is true, what would happen if more cooler bodies were added, surrounding the warmer body? Would the warmer body cool even slower until - eventually - the number of cooler surrounding bodies is such that the warmer body is absorbing so much energy it starts to warm up!

The rate at which it cools down would indeed decrease, but it would never start to warm up. Once the warm body is completely enclosed by cooler bodies (they cover 4π steradians) then the addition of more cooler bodies makes no further difference.

At this point you have engineered a situation whereby adding more cooler objects to a system actually increases the temperature of the warmer body!

This cannot be correct.

I agree.

 

[AlephZero]

Does the fire (filament) heat up because it absorbs this 'cooler' radiation from the chair?

You need to take everything in your scenario into account here. If the fire is in a closed room (whatever the size of the room) it will be absorbing the heat radiated back from the walls of the room. Adding a chair into the scenario is just a detail.

Suppose the electrical power into the fire is a constant 1000W.

If the fire was in outer space (and ignoring the existence of the rest of the universe) it would reach a constant temperature where it radiated 1000W, the same as the electrical power.

If it was in a room where its surroundings radiatie say 10W of heat back to the fire, it will be at a slightly higher constant temperature where it radiates 1010W. The net amount of heat entering the room is still 1000W.

Of course there must be some way for the net 1000W of heat to get out of the "closed" room (e.g. conduction through the walls and convection into the air outside), otherwise the fire and the room will never reach a constant temperature. They will both increase in temperature "for ever" (at least, until something melted or caught fire), because of the 1000W of electrical heat input.

 

[Arfur Bryant]

Dalespam,

Thank you for that reply.

AB

 

[Arfur Bryant]

You need to take everything in your scenario into account here. If the fire is in a closed room (whatever the size of the room) it will be absorbing the heat radiated back from the walls of the room. Adding a chair into the scenario is just a detail.

Suppose the electrical power into the fire is a constant 1000W.

If the fire was in outer space (and ignoring the existence of the rest of the universe) it would reach a constant temperature where it radiated 1000W, the same as the electrical power.

If it was in a room where its surroundings radiatie say 10W of heat back to the fire, it will be at a slightly higher constant temperature where it radiates 1010W. The net amount of heat entering the room is still 1000W.

Of course there must be some way for the net 1000W of heat to get out of the "closed" room (e.g. conduction through the walls and convection into the air outside), otherwise the fire and the room will never reach a constant temperature. They will both increase in temperature "for ever" (at least, until something melted or caught fire), because of the 1000W of electrical heat input.

AlephZero,

I understand what you are saying. However, are you really sure that the filament of the fire gets hotter? That was my question. Because, if it does, then it appears to me that the 2nd Law of Thermodynamics has been broken. Remember that the only thermal energy in the room comes from the filament. If it truly absorbs the 10W from the walls, then the filament has heated itself. How can something heat itself?

The chair is not to be dismissed. Adding the chair provides an example of a cooler body in addition to the walls which had been at equilibrium with the fire (as I stated). My question addresses whether the 'backradiation' from the chair can heat the filament. Do you agree with this?

However, thank you for a comprehensive reply.

AB

 

[AlephZero]

Remember that the only thermal energy in the room comes from the filament

No. You are adding 400 joules of energy per second to the filament of the heater, from whatever is generating the electricity supply (plus whatever is radiated from the rest of the room and its contents)

The equilibrium temperature of the filament is whatever it needs to be, so that it loses the same amount of heat as it absorbs.

 

[Dale]

The back radiation doesn't heat the filament, it just makes it cool more slowly. The 1000 W of external power is what heats the filament. Because the filament cools more slowly, the filament must burn hotter to radiate the 1000 W.

The second law is not violated, no net energy is spontaneously going "uphill".

 

[Arfur Bryant]

No. You are adding 400 joules of energy per second to the filament of the heater, from whatever is generating the electricity supply (plus whatever is radiated from the rest of the room and its contents)

The equilibrium temperature of the filament is whatever it needs to be, so that it loses the same amount of heat as it absorbs.

AlephZero,

First of all, thank you. I am getting closer to understanding this subject.

To be pedantic, I still say the only 'thermal' energy is from the filament. The electrical source is not thermal energy.

As for the equilibrium temperature, this goes back to my first post. Is the backradiation from the wall absorbed by the filament for net gain? If yes, you are correct. If no, the filament does not burn hotter. Would that be fair?

So, to make sure I understand, if you have two light bulbs with identical filament and identical electrical supply, but one bulb surface is frosted, according to you the frosted bulb filament would burn hotter, yes?

 

[Arfur Bryant]

The back radiation doesn't heat the filament, it just makes it cool more slowly. The 1000 W of external power is what heats the filament. Because the filament cools more slowly, the filament must burn hotter to radiate the 1000 W.

The second law is not violated, no net energy is spontaneously going "uphill".

DaleSpam,

Thank you for helping me to understand.

However, if the filament burns hotter because it is cooling more slowly (your last sentence), then surely the backradiation has - in fact - heated the filament. Yes?