## The Attempt at a Solution

No .

The number of photons should decrease . As the rate of heat transfer decreases with time , the net electromagnetic radiation from the hot body to the surroundings decrease .

Heat radiations are composed of photons . Hence their number should decrease as time progresses .

Is the reasoning correct ?

I would request the experts to give their opinion .

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BvU
Homework Helper
One can also read the question as:

Is the number of photons increasing compared to before, when the hot body was not present in the room ?

Assuming the question is considering time after the hot body is placed , do you think my reasoning is correct ?

BvU
Homework Helper

Could you explain why my assumption that time after the hot body is placed is incorrect .

Don't you think wording of the question should have been " Has the number of photons increased ? " if the question wanted to compare the number before and after the hot body is placed ?

hilbert2
Gold Member
If the emission rate of thermal radiation would depend linearly on the temperature, the number of photons would stay at same value when the hot object approaches thermal equilibrium with the room. However, the emitted radiation power is not a linear function of temperature.
What kind of function is it and what can you deduce from it?

hilbert2
Gold Member
If the emission rate of thermal radiation would depend linearly on the temperature, the number of photons would stay at same value when the hot object approaches thermal equilibrium with the room.

Sorry, this was a bit hasty conclusion I made and doesn't take into account the heat capacities and surface properties in the room

But still, the idea of the problem is to find a physical law that shows that the emission rate of photons drops much faster than linearly when temperature is decreased.

the problem is to find a physical law that shows that the emission rate of photons drops much faster than linearly when temperature is decreased.

Don't you think we just need to consider whether the rate of heat transfer decreases or not ?

As the temperature of hot body decreases , rate of heat transfer decreases . As a consequence , the photons comprising the heat radiations should decrease with time .

Please have a relook at the OP and let me know what is wrong with my reasoning .

hilbert2
Gold Member
As the temperature of hot body decreases , rate of heat transfer decreases.

Yes, but the surroundings in the room will also heat up because of the object and start emitting more radiation. Also, there is radiation even in thermal equilibrium where the temperature is same everywhere. You need to show that having one very hot object in a room will produce more radiation than having the whole room at a slightly elevated temperature.

Homework Helper
Gold Member
It's a rather poorly worded question, because the blackbody radiation emission of the warmer object is instantaneous and the electromagnetic radiation from it will then decrease as it subsequently cools unless it is continually supplied with a source of power. The question is too vague to be able to give it a very good answer.

hilbert2
hilbert2
Gold Member
It's a rather poorly worded question, because the blackbody emission of the warmer object is instantaneous and the electromagnetic radiation from it will then decrease as it subsequently cools unless it is continually supplied with a source of power. The question is too vague to be able to give it a very good answer.

Yes, the problem may also be about resolving a misunderstanding that some students may have, that the photons emitted by the object will "accumulate" and the number of them is a time integral of the emissive power.

Yes, but the surroundings in the room will also heat up because of the object and start emitting more radiation. Also, there is radiation even in thermal equilibrium where the temperature is same everywhere. You need to show that having one very hot object in a room will produce more radiation than having the whole room at a slightly elevated temperature.

What is your interpretation of the problem statement ?

Are you comparing

1) the time before and after the hot body is placed .

OR

2) the time after the hot body is placed till thermal equilibrium is achieved .

and the electromagnetic radiation from it will then decrease as it subsequently cools

So let it be

If the body cools , the rate of heat transfer will decrease and subsequently the number of photons . No ?

hilbert2
Gold Member
The number of photons will be at the maximum value practically immediately when the object is placed. There would be no reason to compare to the situation before the hot object is in the room. The instantaneous rate of change (time derivative) of the number of photons is probably what is meant here, and we have to show that it is negative at any time.

Jahnavi
Homework Helper
Gold Member
So let it be

If the body cools , the rate of heat transfer will decrease and subsequently the number of photons . No ?
That is correct. The problem is that because the question is so vague, they might tell you that is not the right answer. They might tell you the warm object increased the number of photons from what the room previously had.

There would be no reason to compare to the situation before the hot object is in the room.

Exactly

I asked this because of BvU's objection to my interpretation in post#2 and post#4 .

haruspex
Homework Helper
Gold Member
There would be no reason to compare to the situation before the hot object is in the room.
I agree. It asks whether the number is increasing, not whether it increases. That makes it a question about the ongoing state.

As to the point of the question, not all photons carry the same energy, and as the object cools the room warms. For both reasons, I don't think it is sufficient to argue that the rate of transfer of heat reduces.
Even at equilibrium, photons are being transferred.

Edit: i suspect the question setter intended the room to be taken as constant temperature. If the room plus object form an isolated system and the object has the greater thermal capacity then it may well be that the number of photons will increase over time.

Last edited:
Edit: i suspect the question setter intended the room to be taken as constant temperature

I think the same .

If the room plus object form an isolated system and the object has the greater thermal capacity then it may well be that the number of photons will increase over time.

Why ?

Irrespective of the heat capacity of the hot object , it will start cooling down till it's temperature becomes equal to the room temperature .

Rate of Heat transfer is proportional to the temperature difference (fourth power) . It will be maximum initially and gradually decreases. Same with photons .

haruspex