An incandescent light bulb produces light using a thin tungsten filament (wire) heated to about 3000 K

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An incandescent light bulb produces light using a thin tungsten filament (wire) heated to about 3000 K by an electric current that passes through it. A typical filament has a diameter of 10 µm and a length of 2.0 cm. 

(a) What is the rate at which heat energy is emitted by the filament? 

(b) When the current through the filament is turned off, the filament cools as heat is radiated away. Estimate how long it takes the filament to cool 100 K to a final temperature of 2900 K.

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