The filament temperature of a light bulb is 1500 K when the bulb delivers 60 W of power. If its emissivity remains constant, what power is d

Question

The filament temperature of a light bulb is 1500 K when the bulb delivers 60 W of power. If its emissivity remains constant, what power is delivered when the filament temperature is 2000 K?

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Eirian 1 day 2021-07-21T22:24:42+00:00 1 Answers 0 views 0

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    2021-07-21T22:26:32+00:00

    Answer:

    The power delivered when the filament temperature is 2000 K is  189.63 W.

    Explanation:

    Given;

    initial temperature of the light bulb, T₁ = 1500 K

    initial power delivered, P₁ = 60 W

    Final temperature, T₂ = 2000 K

    Final power delivered, P₂ = ?

    Apply Stefan-Boltzmann law of radiation;

    \frac{Q}{t} = \alpha \epsilon AT^4\\\\P =  \alpha \epsilon AT^4\\\\\frac{P_1}{T_1^4} = \frac{P_2}{T_2^4}\\\\P_2 = \frac{P_1T_2^4}{T_1^4} \\\\P_2 = \frac{60*(2000)^4}{(1500)^4}\\\\ P_2 = 189.63 \ W

    Therefore, the power delivered when the filament temperature is 2000 K is  189.63 W.

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