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?

Answer 1

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

Step-by-step 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;

`(Q)/(t) = \alpha \epsilon AT^4\\\\P = \alpha \epsilon AT^4\\\\(P_1)/(T_1^4) = (P_2)/(T_2^4)\\\\P_2 = (P_1T_2^4)/(T_1^4) \\\\P_2 = (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.