Light bulbs, Wattage meaning? Light bulbs, Wattage meaning?
Two incandescent bulbs (120 V, 25 Watt) and (120 V, 500 Watt) connected to the same batteries.
Which one shines brighter? And why?
 A: The bulb rated 500 W is doing more work per unit time, which implies that it is either emitting more light or just using up the energy to generate more heat. If both the bulbs have the same efficiency then it follows that the higher wattage bulb shines brighter.
A: What is the point of batteries? Obviously higher W will drain them faster. 
If question is wattage -> luminocity function then I think that there will be two components. One is that every watt is converted into a lumen (683 lm/W, to be exact according to Wikipedia). It is like $E=mc^2$: more mass = more energy. They are equivalent. So more power <=> more light. 500 is 20 times more than 25, which translates into 20x brighter. 
Another component is that 683 lm/W coefficient is not constant because 500W emits light at higher temperature. This results in the brightness(power) function being a bit square rather than purely linear. So, you get more visible photons per watt, provided more watts. So 500W must give more light than 20x25W bulbs. According to Wikipedia, overall luminous efficiency of 25W is 1% whereas 500W gives 3% of light. Totally, consuming 20 times more energy, 500W will shine 60 times brighter. 
To achieve this, as I have said, higher temperature is needed. Higher temperature increases luminous efficacy but tungsten filament is evaporated, deposits on the bulb, the bulb becomes intransparent and luminous efficacy drops. To prevent this, halogen is injected into more powerful lamps (and therefore more efficient lamps) http://en.wikipedia.org/wiki/Halogen_lamp 
Yet, it seems that incandescent are still way less efficient than the others and might be useful only when you use them very shortly because they are cheap but not efficient. If you need a constant light source, take a more expensive but much more effective fluorescent or LED. (NB! Treat and reclaim the fluorescent with great care as they contain mercury - it is dangerous for the nature)
