I was struck that I don’t really know how (internally, electronically) a 60 watt lightbulb differs from a 100 watt lightbulb. Do they just have more filiment? Why wouldn’t they burn out faster if they were burning hotter.
My first thought is that a 100W bulb would have to have a shorter coil to give less resistance and pass more current giving more power. But that would also cause it to burn hotter, probably not good.
A better way would be to have a longer filament but make it thicker (less resistance again), the filament could then be at the same temperature as the 60W bulb there would simply be more of it.
The 60 watt lightbulb has greater resistance to current flow, therefore it draws less current for the same voltage and consumes less power. The diameter and length of filament wire are calibrated to get the correct current flow and give a similar temperature range even for bulbs rated at different power. You are correct that just making a filament run at a much higher temperature would cause it to burn out faster but temperature has a direct impact on the color of the light produced. One can demonstrate this pretty easily with a digital camera that has manual control of white balance. A 100 watt bulb may produce more light than a 60 watt bulb but it will have similar color. If you take a 100 watt bulb and reduce the voltage with a dimmer so it only consumes 60 watts it will look very different than a normal 60 watt bulb because the color will be shifted farther to the red end of the spectrum.
Either way will work equally well. a 100 W bulb does burn hotter than a 60 W bulb – that’s why it’s brighter. In practice, both of those configurations are used, and various combinations of shorter/longer and thicker/thinner filaments can be found.
I can make a good guess at this. Higher wattage bulbs probably have thicker filaments. This would carry more current, which accounts for the higher power use. It would also have more surface area, so it would provide more light.
That said, I must confess that I’ve never directly compared the filaments in different-wattage bulbs, and I am not a lightbulb designer.
The length of the filament.
The diameter of the wire.
The geometry of the coil (this wire is wound like a little spring).
The geometry of the coil that that is wound into, if they do that.
The resistance of the filament is equal to some constant times its length times its absolute temperature divided by the square of its wire diameter.
The temperature varies approximately as the fourth root of the amount of power leaving the space around the filament. Incandescent bulbs operate with filament temperatures in the 2000 K to 3000 K range.
Coil geometry lets the temperature get higher with a lower power output.
Life varies as a very steep function of inverse temperature.
The ability to render greens and especially blues gets better throughout the increasing temperature range of incandescent bulbs, but by around 5000 or 10000 K increasing the temperature stops increasing the blues.