It is known that nowadays most light bulbs are filled with gas in order to minimise the evaporation rate of tungsten. Is e.g. argon put into the bulb with reduced pressure, so that the glass doesn't explode while heating the wire?
Answer
A great link that details some experiments that looked for the answer to this is Experiment Tests Pressure in light bulbs. But first we need to cover some basis of the gas law to do comparisons. Firstly, most the time a bulb is off, it is near room temperature and most of the time it is on it is at a high temperature but the quantity of gas in the bulb remains the same. Engineering-wise, it is most desirable to have the pressure close to atmosphere when on, because at that time the glass will be hot and more prone to failure. Denoting these states as on and off, I will write the gas law for the case.
$$PV=nRT$$ $$\frac{ P_{on} }{ T_{on} } = \frac{ P_{off} }{ T_{off} }$$
The link I am referencing does an experiment where the bulb is submerged in water and the pressure boundary is broken. Since the bulb has a lower pressure than atmosphere water rushes in, this water mass can be measured and used to find the pressure before it was broken. This state I will denote as test and it is compared to the off state as a constant temperature process.
$$P_{off} V_{off} = P_{test} V_{test}$$
From this experiment they found two 25 W incandescent lamps to have a pressure of about $\frac{6}{1000} atm$, which is consistent with the low pressure inert atmosphere most people expect. For higher wattage lamps, they found the pressure to be close, but slightly lower, than atmospheric pressure. Temperature of the filament, when on, is in the neighborhood of 2700-2900 K, but this is not the temperature of the gas. Any reasonable assumptions will put the $P_{on}$ value for the low pressure bulbs at much smaller than atmosphere. For the higher power, higher pressure bulbs, I will address it more specifically using the surface temperature numbers from this source with clearly no credibility.
$$T_{off} \approx 298 K$$ 40 W $$P_{off} \approx 0.914 atm$$ $$T_{on} \approx 395 K$$ $$P_{on} = \frac{ T_{on} P_{off} }{ T_{off} } = 1.21 atm$$ 60 W $$P_{off} \approx 0.768 atm$$ $$T_{on} \approx 400 K$$ $$P_{on} = \frac{ T_{on} P_{off} }{ T_{off} } = 1.03 atm$$
To conclude, there are two types of constructions of incandescent light bulbs discussed here, one entailing a low vacuum and one that objectively reaches near atmospheric pressure in the on state. There is likely significant variation in products you can buy, and sample numbers given here can't be generalized to any given bulb you're looking at.
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