Pressure Inside a Light Bulb

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 $frac61000 atm$, 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 not be generalized to any given bulb you are looking at.

1. where can I find a WHITE light bulb at Salford- Manchester?

Try in the massive lighting shop on corner of Deansgate and Trinity Way, opposite side of MEN Arena, and at bottom end of Bury New Road. They have everything!

2. Does it save more electricity to wait for an incandescent bulb to burn out before replacing it with an led bulb?

There an immediate savings of electricity as soon as you change the bulb.Whether you save enough to pay for the bulb in a reasonable amount of time should be the real question.I have in the past calculated that a 100W light bulb that you used to be able to buy for about 50 cents would use $20 worth of electricity over its rated life. Clearly its a clean choice to replace it with a 18W equivalent LED bulb costing about $8 today as soon as possible IF YOU USE IT A LOT. If you have a box of saved incandescents throw them away and do not donate them to the local thrift shop... you will cost some unsuspecting poor person $20 for each one.But if you have a attic light you use four times a year for 10 minutes. . do not bother. Wo not be economical for the price of the LED compared to the total electricity used

3. how did edison actually invent the light bulb, what did he do to make it work?

He did not invent the light bulb. Joseph Swan did. Edison's company, Edison Electric Light Company bought the invention from Swan

4. Can you put a ceiling fan bulb in a three way lamp?

Yes if it fits the socket it will work . The switch reduces the resistance to the bulb that gives a different brightness .The only way it wont work is if it is an energy saving bulb that looks like a fluorescent bulb but is coiled like a spring