When the tungsten filament in a 75 W, 120 V light bulb reaches 2040 degree C, 75

Question

When the tungsten filament in a 75 W, 120 V light bulb reaches 2040 degree C, 75 W of electric power is used to produce light and heat. (a) Find the current through the filament under these conditions, which are established very shortly after the light is turned on. (b) Find the filament current when the light is first turned on, assuming an initial filament temperature of 20 degree C Find the power used when the light is first turned on, assuming an Initial filament temperature of 20 degree C. (c) Estimate the time needed to heat the filament to 2040 degree C. The filament has a mass of 0.043 g and a specific heat of 0.032 cal/g-C degree. ___________

Explanation / Answer

Initial temperature = 20o C, final temperature = 2040o C

power = 75 W

For most incandescent bulbs 90 % of power is used as heat.

If 90 % of 75 W is used as heat, Thermal power

= 67.5W

Heat energy required to raise the temperature = m S (t2 - t1) = 0.043 * 0.032 * 2020 = 2.78 cal = 11.6 J

heat energy = Thermal power x time

so time needed to heat the filament = heat energy / power =11.6 / 67.5 = 0.171 s

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