When the tungsten filament in a 60 W, 120 V light bulb reaches 1990° C, 60 W of

Question

When the tungsten filament in a 60 W, 120 V light bulb reaches 1990° C, 60 W of electric power is used to produce light and heat. The initial temperature is 20 degrees celsius. (c) Estimate the time needed to heat the filament to 1990° C. The filament has a mass of 0.041 g and a specific heat of 0.032 cal/g-C°.

I only need help with part C but all of the questions are as follows: (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° C. Find the power used when the light is first turned on, assuming an initial filament temperature of 20° C (c) Estimate the time needed to heat the filament to 1990° C. The filament has a mass of 0.041 g and a specific heat of 0.032 cal/g-C°.

**I've tried 0.044 s, 0.44 s, 0.18 s, and 0.018, 1.81 secs among other answers and they were all wrong. I could really use some help with this (detailed explanation please)!

Explanation / Answer

Mass m= 0.041 g
Specific heat, s = 0.032 cal/g deg C
Initial temperature = 20 deg C
Final Temperature = 1990 deg C
Change in temperature = 1970 deg C.
So required energy = ms delta T = 0.041*0.032*1970 cal = 2.58 cal = 10.81 J
This will be supplied by the bulb in time t then,
60*t = 10.81
t = 0.18 sec.

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