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