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If:

  1. Temperature is a measure of the average (kinetic) energy of the particles which make up some material
  2. Power is measure of energy transferred per second (J/s)
  3. The temperature of the filament in a light bulb is proportional to it's brightness

Then:

Why doesn't a light bulb get brighter over time irrespective of power?

For example, 100 joules delivered in 5 hours v.s. 100 joules delivered in 10 hours is still 100 joules being delivered to the filament, raising it's temperature to the same amount despite 100J/hr being the lower amount of power?

Is because the temperature is also lost to the filament's surroundings at the same time or something?

Say, if the heat was unable to leave the filament for some reason, would you end up with two light bulbs with the same brightness at the end of the 10 hours?

Any help would be much appreciated.

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Your car engine can produce something near constant power for a long period of time. If you hold the gas pedal down, why doesn't the car keep going faster and faster? Because energy loss from the system increases as the speed goes up. At some speed the power lost to drag is equal to the power input from the engine.

The same concept applies to the light bulb. The electrical energy delivered to the filament heat it up. But as the temperature increases, the more radiation that the filament emits. At some temperature, the radiative power equals the electrical power and the temperature stops changing.

Say, if the heat was unable to leave the filament for some reason

Remember that it's not just heat. It's any form of radiation. The purpose of the filament is to emit light, so you know some energy is leaving. The more you prevent it from leaving, the hotter it gets inside, but the power has to balance. Bulbs are also made to operate at a particular temperature. If you raise it too much, the filament will lose strength and fail (and then the energy input stops).

Taken to an extreme, see the xkcd what if... archive.

re you saying that the light bulb isn't going be brighter at a lower power because energy is being radiated away at the same time?

All bodies with a temperature radiate. The hotter the body, the more radiation per area is radiated. If the total power output equals total power input, then the temperature will be maintained.

Like say if you ran a light bulb at 100J/hr for one hour and then 50J/hr for two hours, by the end of the two hours the second bulb wouldn't get as bright as the first after one hour, because more energy overall would have radiated away?

The filament of a light bulb has very little mass. This allows it to move to thermal equilibrium with its environment in a very short period of time (think a second or so). In other words it is effectively true that 100% of the power delivered to the filament over a few seconds is radiated away. If you control the circuit to deliver less power, the bulb will cool.

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  • $\begingroup$ While the light bulb part of the answer is a nice one, the car analogy is inaccurate. The reason , car wheels do not go faster at constant power, is because the speed of the car wheels depends on the rpm of the engine. For a given constant power, and the same gear, a car wheel can only spin at a constant rpm, irrespective of how much drag there is. If you increase the drag, the engine power and rpm itself goes down, rather than engine power staying same and some engine power being lost to drag. $\endgroup$
    – silverrahul
    Commented Aug 2, 2021 at 11:56
  • $\begingroup$ I disagree, but I think it's a minor point for this answer. "same gear" isn't a useful constraint here. If you say the power goes down, then that can't be the reason wheels don't go faster at constant power. Let's just assume constant power (which is approximately true given a sufficiently-ranged transmission). $\endgroup$
    – BowlOfRed
    Commented Aug 2, 2021 at 17:17
  • $\begingroup$ " I think it's a minor point for this answer " I know. Which is why i said, the major part of your answer i.e. the explanation about the bulb is perfect. " "same gear" isn't a useful constraint here. " Same gear IS a necessary constraint here. When you insert a bulb into a socket, there isnt anything analogous to gears. So, to keep things similar in car example, you HAVE to assume a constant gear throughout, otherwise the comparison doesn't hold. $\endgroup$
    – silverrahul
    Commented Aug 2, 2021 at 17:57
  • $\begingroup$ Most people with ICE cars have working transmissions, and they expect a particular response from the car when the pedal is mashed. (And I suggest that response is not so very far from "constant power"). I don't see why I should be assuming a single gear is used. $\endgroup$
    – BowlOfRed
    Commented Aug 2, 2021 at 18:10
  • $\begingroup$ " I don't see why I should be assuming a single gear is used " You should not assume single gear if you want it to be true to real life cars. That is the point. That is exactly why the car analogy does not work for bulbs. In cars, multiple gears are used. For car to be an analogy for bulbs, it would have to have a single gear which is not true of real life cars. Hence, it is not good analogy $\endgroup$
    – silverrahul
    Commented Aug 2, 2021 at 21:22

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