A certain lightbulb has a tungsten filament with a resistance of 21.7 Ω when at 20.0°C and 146 Ω when hot. Assume the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here. Find the temperature of the hot filament.

1321.57 °C

Explanation:

Using,

R = R'[1+α(T-T')] Equation 1

Where R = final resistance of the tungsten filament, R' = Initial resistance of the tungsten filament, T = Final Temperature, T' = Initial temperature, α = Temperature coefficient of tungsten filament.

Make T the subject of the equation,

T = [(R-R')/R'α]+T' Equation 2

Given: R = 146 Ω, T' = 21.7 Ω, T = 20 °C,

Constant: α =  0.004403/°C

Substitute into equation 2

T = [(146-21.7)/(21.7×0.004403)]+20

T = (124.3/0.0955)+20

T = 1321.57 °C

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