Why and how exactly does the quantity of energy radiated per second increase with the temperature of the radiating object?

Question

I read in my textbook that the quantity of energy (in the form of electromagnetic waves) radiated per second increases with the temperature of the radiating object. However, I can see two ways of interpreting this and am not sure which is correct.

Would it be true to say that an object that was a good absorber and emitter of radiation would always be absorbing and emitting as much EM radiation per second as was possible with the level of available EM radiation lying around in its environment? So, for example, in a really cold, low-energy environment, it might only be absorbing 20 joules worth of EM radiation per second, and also (of course) only emitting 20 joules of EM radiation per second. But in a much warmer, high-energy environment, it might be absorbing and emitting, say, 1000j EM radiation per second, just because there would be more EM radiation available for it to channel in the second environment. If the above is true, then is this the reason that objects with a higher temperature would radiate more EM radiation per second (since good absorbers and emitters would only have a higher temperature if they were already in a higher energy environment)?

Or, alternatively, is this phrase actually just trying to say that the higher temperature a good absorber and emitter is compared to its environment, then the more energy that object will radiate per second? If so, is this because the object would originally be emitting much more energy than it was absorbing, and then as it got closer and closer to being at thermal equilibrium with its environment (and so had a lower and lower temperature), the rate of emission would decrease until it was equal to the rate of absorption?

Which is the correct interpretation, or, if neither is correct, then what is the explanation behind this phrase, please? Thanks so much.

Answer 1

Certainly an object that is in thermal equilibrium with its environment will always be absorbing and emitting radiation at the same rate. This applies to both good and bad absorbers/emitters because thermal equilibrium means the temperature of the object is not changing.

However, while admittedly not knowing exactly the context of the statement in your book, usually it is meant that if you change the temperature of a body, its rate of emitting radiation changes.

So as you heat up your stove, the heating element will begin to emit more radiation as its temperature is elevated to that of the surroundings. You also may see color changes (the element may turn red) as the quality of the radiation changes too. This also doesn't depend on being a good or bad emitter. All objects, when heated, radiate more energy, or when cooled, radiate less energy.

The Stefan-Boltzmann law shows that the radiated power depends upon the temperature to the fourth power.