# Cooler objects able to increase the temperature of warmer objects?

• B
Not sure this should go here (you guys need a thermodynamics section). But there is quite the debate going on about cooler objects being able to increase the temperature of warmer objects here:
https://wattsupwiththat.com/2017/11/24/can-a-cold-object-warm-a-hot-object/comment-page-1

They are claiming that the IR from the colder object is absorbed by molecules of the warmer object, thereby thermalizing the molecules more, increasing the temp of the warmer object.

Thanks.

Ugur

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Dale
Mentor
A cold object cannot warm a warm object without work being done.

A cold object cannot warm a warm object without work being done.
Yes I know that. The point in that debate is IR from the cooler object must be being absorbed by the warmer object. The question is, what happens to the IR photons from the cooler object when they come in contact with the atoms in the hotter object?

A cold object cannot warm a warm object without work being done.
Of course it can. The temperatur of an object in thermal equilibrium can be increased by any additional heat source, including colder objects.

Of course it can. The temperatur of an object in thermal equilibrium can be increased by any additional heat source, including colder objects.
[sigh]

No it cant. Entropy forbids a colder object from giving energy to a hotter object. Why is this such an issue? This is basic thermodynamics.

anorlunda
Staff Emeritus
Heat flows from warm to cold. The warm object will send more IR to the cold one than it receives.

Delta2 and davenn
Heat flows from warm to cold. The warm object will send more IR to the cold one than it receives.
These are the arguments I've been dealing with.

Warm to cold is a NET flow of energy.
Cold IR photons get absorbed by the warmer atoms which get "thermalized".

So what happens to the warmer atoms when they encounter IR photons from a colder object? I say nothing happens. If anything, the atom immediately re-emits that energy.

anorlunda
Staff Emeritus
Your over thinking it. Thermodynamics is the study of averages of many particles. You can not apply it one photon at a time.

Just believe what @Dale said.

Ugur and davenn
russ_watters
Mentor
Not sure this should go here (you guys need a thermodynamics section). But there is quite the debate going on about cooler objects being able to increase the temperature of warmer objects here:
https://wattsupwiththat.com/2017/11/24/can-a-cold-object-warm-a-hot-object/comment-page-1

They are claiming that the IR from the colder object is absorbed by molecules of the warmer object, thereby thermalizing the molecules more, increasing the temp of the warmer object.
The article doesn't say that (and "thermalizing" isn't a word). It says a warm object will be kept warmer by exchanging radiation with a cold object that is blocking an even colder object than if the cold object weren't there....which is kinda a "duh".

Here's the point of the article:
Can a cold object leave a warm object warmer than it would be without the cold object?

While the answer is generally no, it can do so in the special case when the cold object is hiding an even colder object from view.

Tom.G, DrewD and Lord Jestocost
Dale
Mentor
Of course it can. The temperatur of an object in thermal equilibrium can be increased by any additional heat source, including colder objects.
Do you have a reference for this?

Your over thinking it. Thermodynamics is the study of averages of many particles. You can not apply it one photon at a time.

Just believe what @Dale said.
The article doesn't say that (and "thermalizing" isn't a word). It says a warm object will be kept warmer by exchanging radiation with a cold object that is blocking an even colder object than if the cold object weren't there....which is kinda a "duh".

Here's the point of the article:
Thermalizing is the term Willis used. I know it's not a word. And if you read through the comments, Willis et al state categorically that the colder objects emitting IR which when interacting with a warmer object, will increase the energy of that warmer object, and hence it's temperature.

It is clear reading the comments that people do not understand the difference between energy, heat and temperature. One person even objected to the official definition of heat!!!

russ_watters
Mentor
Thermalizing is the term Willis used.
No, he doesn't, unless he's posting under an alias in the comments section -- it looks to me like you are reading through comments to the article (and "thermalz..." is used there several times). Please quote exactly what you are referring to.
No, that isn't how this works. In general, you need to quote exactly what you are referencing, but for this case, we're not going to argue by proxy with the comments section to an article. That's a waste of our time.
..Willis et al state categorically that the colder objects emitting IR which when interacting with a warmer object, will increase the energy of that warmer object, and hence it's temperature.
You're skipping part of the article's claim, per my previous post.
It is clear reading the comments that people do not understand the difference between energy, heat and temperature. One person even objected to the official definition of heat!!!
I really don't care -- is that what this is about? A proxy argument with the people commenting on that article? We don't do that here. We'll help you understand what the author is saying, but that's it. If you have a question of your own, ask it yourself.

davenn
Dale
Mentor
Warm to cold is a NET flow of energy.
This is correct, and it doesn’t matter if the mechanism of heat transfer is through thermal radiation or through thermal conduction. In both cases on a microscopic level there is energy going both ways and on a statistical level the energy goes from hot to cold.

So what happens to the warmer atoms when they encounter IR photons from a colder object? I say nothing happens.
They can be absorbed, reflected, scattered, or transmitted, based on the spectral characteristics of the object. IR photons are not particularly different from other photons.

the colder objects emitting IR which when interacting with a warmer object, will increase the energy of that warmer object, and hence it's temperature.
Of course that's what happens. Just let’s do the math for a simple example: A spherical black body with the radius ##r## (e.g. Earth), heated by a heat source with the power ##P## (e.g. absorbed light from the Sun). In the dynamic equilibrium the body will emit as much energy as it absorbs from the heat source. Assuming a homogeneous temperature distribution this results in the equilibrium temperature

$T_{eq}^4 = \frac{P}{{4 \cdot \pi \cdot \sigma \cdot r^2 }}$

according to the Stefan–Boltzmann law. That’s the warm object.

Now let’s see what happens if we add another black body as additional heat source – let’s say a spherical shell (e.g. the atmosphere) with the temperature ##T_{add}## around the first body. This shell will also emit heat radiation. If this radiation hits the first body, it will be absorbed, resulting in the additional heat

$P_{add} = 4 \cdot \pi \cdot r^2 \cdot \sigma \cdot T_{add}^4$

and therefore in the new equilibrium temperature

$\frac{P}{{4 \cdot \pi \cdot \sigma \cdot r^2 }} + T_{add}^4 > T_{eq}^4$

no matter if ##T_{add}## is above, equal or below ##T_{eq}##.

Claiming that this is not possible is a usual argumentation in climate change denial. I can’t believe that something like this is supported in this forum!

mfb
Mentor
To thermalize is a word.

There are two different things discussed here, and the lack of separation between them leads to the confusion.

* If you look at an existing system and add a new object to it, that can increase the temperature of an existing object, even if the new object is colder than the existing object.
* The net power flow between these objects (any pair of objects in fact) will be from hot to cold.

Both statements are true, and they don't contradict each other.

As an example, the presence of Mars increases the temperature of Earth a tiny bit, as some light from it reaches Earth. The heat Earth emits is independent of the existence of Mars, but the heat it gets is increased from Mars.

Dale
Mentor
heated by a heat source with the power P
It is this power source that warms the object, not the colder object. This is work, as I mentioned above.

Assuming a homogeneous temperature distribution this results in the equilibrium temperature

T4eq=P4⋅π⋅σ⋅r2Teq4=P4⋅π⋅σ⋅r2T_{eq}^4 = \frac{P}{{4 \cdot \pi \cdot \sigma \cdot r^2 }}

according to the Stefan–Boltzmann law.
Here you areassuming a cold reservoir at 0 K.

and therefore in the new equilibrium temperature

Yes, if you have two different systems, one with a cold reservoir at 0 K and the other with a cold reservoir at a higher temperature then the equilibrium temperature will be higher for the system with the warmer cold reservoir. This is not an example of a cold reservoir increasing the temperature of a hot reservoir without work. Without P the temperature will drop to the temperature of the cold reservoir, not increase.

Claiming that this is not possible is a usual argumentation in climate change denial.
I stay out of climate change arguments. What I said is correct, regardless of what other groups of people may misuse the concepts. Please do not attempt any “guilt by association” here.

It is this power source that warms the object, not the colder object.
No, the object is warmed by the power source and by the colder object. Claiming that the colder object doesn't warm the warmer object is simply wrong. Any heat source contributes to the warming regardless of its temperature.

This is work, as I mentioned above.
The absorbed sunlight provides heat only. Tere is no work involved.

Without P the temperature will drop to the temperature of the cold reservoir, not increase.
That doesn't justify your general claim that "A cold object cannot warm a warm object without work being done."

What I said is correct
It would be correct if you would say that a cold object cannot warm a warm object without work being done if no additional heat sources and no heat sinks are involved. But you didn't do that.

mfb
Mentor
Claiming that the colder object doesn't warm the warmer object is simply wrong.
It depends on your perspective. You can also say it cools, but it cools less than whatever else it blocks e.g. an even colder object).

russ_watters
Objects radiate energy to the surroundings and absorb energy from the surroundings. Because of temperature differences the hot object will be a net radiator and cool down and the cold object a net absorber and heat up.

Delta2
It depends on your perspective. You can also say it cools, but it cools less than whatever else it blocks e.g. an even colder object).
Yes, I could say that, but we are talking about warming and not about cooling and it is no matter of perspective that any heat source contributes to the warming.

Dale
Mentor
The absorbed sunlight provides heat only. Tere is no work involved.
Then you are introducing an extra thermal reservoir and it doesn’t simply provide a power P but has some temperature dependent heat transfer. You are talking about something substantially different than what I was talking about.

Even in your scenario I would not say that the >0 K cold reservoir increased the temperature of the system. I would just say that it kept it from cooling as much as a 0 K cold reservoir would. I wouldn’t say that failure to decrease the temperature as much as a 0 K reservoir is the same increasing temperature. After all, I say that my clothing keeps me warm, not that my clothing warms me.

As long as we are considering alternative configurations, if you have the hot-reservoir/system/cold-reservoir configuration and you remove the cold reservoir then the system temperature goes up and if you remove the hot reservoir then the system temperature goes down. So I think that the “consider alternative configurations” approach is inconclusive.

It would be correct if you would say that a cold object cannot warm a warm object without work being done if no additional heat sources and no heat sinks are involved. But you didn't do that.
I do apologize for failing to specify the scenario I had in mind completely.

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Then you are introducing an extra thermal reservoir and it doesn’t simply provide a power P but has some temperature dependent heat transfer.
That is completely irrelevant. It doesn't matter where the heat comes from. Absorbed sunlight, thermal radiation from the atmosphere or geothermal energy contribute in the same way to the heat balance. It doesn't matter if there is an external thermal reservoirs or a temperature dependent heat transfer. The temperatures of the heat sources just determines their individual power and the sum of the power received by an object (no matter how that happens in detail) and it's own emission profile determines it's equilibrium temperature.

You are talking about something substantially different than what I was talking about.
I'm talking about the topic of this thread which was clearly given by the OP and the provided link.

Even in your scenario I would not say that the >0 K cold reservoir increased the temperature of the system.
The colder body is no "cold reservoir" (this term makes no sense because there is no such thing like "cold" in physics) but a heat source. It emits thermal radiation which is partially absorbed by warm body, increasing its equilibrium temperature (see my calculation above).

I would just say that it kept it from cooling as much as a 0 K cold reservoir would.
That depends on your definition of "cooling". If you man the release of heat than you are wrong because

1. The emission of thermal radiation of the warm object is independent from its environment. It only depends on the shape and temperature of the warm object itself according to the Stefan-Boltzmann law and therefore cannot be altered by external objects or the 2.7 K background.

2. The heat release will not be reduced but increased if the temperature rises.

If you mean net heat release (including incoming heat) than you are partially right. The warm body will absorb more heat due to the additional thermal radiation of the cold body. But in the steady state the net heat flow is (of course) always zero - with or without the cold body.

If you mean temperature decay, than you are partially right. If the warm body starts above its equilibrium temperature, the resulting temperature decay will be reduced and stopped at a higher equilibrium temperature. But the temperature can also be increased (see my calculation above). That can’t be explained with the ability to keep the temperature from decreasing.

jerromyjon
Dale
Mentor
That is completely irrelevant. It doesn't matter where the heat comes from.
Sure it does. If the system is the same temperature as the hot reservoir then P=0. So if P is not work then it cannot be independent of the system’s temperature.

The colder body is no "cold reservoir" (this term makes no sense because there is no such thing like "cold" in physics) but a heat source.
The term “cold reservoir” is pretty standard in thermodynamics. Particularly for heat engines. It is the heat sink not a heat source. I can provide references for this usage, if you like.

That depends on your definition of "cooling". If you man the release of heat than you are wrong because
Yes, by the word “cooling” I mean heat leaving the system. And by “warming” I mean heat entering the system.

1. The emission of thermal radiation of the warm object is independent from its environment. It only depends on the shape and temperature of the warm object itself according to the Stefan-Boltzmann law and therefore cannot be altered by external objects or the 2.7 K background.
You seem to be confusing energy flow and heat. Energy flows both ways, but heat only goes from hot to cold by definition. Suppose the system gives 7 W of radiation to the hot reservoir and recieves 10 W from it, then the heat is 3 W. Neither the 10 W nor the 7 W is heat. The Stefan Boltzmann law describes power, not heat.

A cold reservoir cannot be a heat source, by definition.

2. The heat release will not be reduced but increased if the temperature rises.
Interestingly, this is wrong if P is a thermal source instead of work. If P is work then the equilibrium heat release is constant, but if P is thermal then the equilibrium heat release decreases as the system temperature rises. In neither case is the heat flow increased.

Frankly, I think that we mostly agree on the physics, but we seem to disagree pretty strongly on the terminology. I can provide references to support my terminology if you wish, but you have not provided any references to support yours, despite my request.

But the temperature can also be increased (see my calculation above). That can’t be explained with the ability to keep the temperature from decreasing.
Sure it can. If I have a bathtub with a faucet and a drain I can easily describe the action of closing the drain as keeping the water level from decreasing. The water level may raise without me needing to claim that the drain is filling the tub. The faucet only fills and the drain only empties.

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DrStupid and davenn
The arguments provided by Anthony Watts and others arises out of not understanding how the laws of thermodynamics we're developed and the systems that they describe. Thermodynamic principles define the average property of mass quantities of materials, such as steam. It is an excellent example of how being self taught often fails. They are only as good as their teachers. The laws of thermodynamics do not apply to electromagnetic energy or individual quantum particles

bob012345
Gold Member
This paper may relate to the question at hand. It refers to a different but I think equivalent situation. Here is the reference;

Found Phys
DOI 10.1007/s10701-014-9781-5

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