My Notes A certain lightbulb has a tungsten filament with a resistance of 21.4 Ω when at 20.0°C and 147 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.

Answer: Temperature of hot filament T2 is 1324.3 degree Celsius

Explanation: The formula that relates change in temperature to change in resistance is

R2

= R1*{1 + temp coefficient * (temp2 - temp1) }

R2 is 147ohms, R1 is 21.4ohms, temperature coefficient of tungsten is 0.0045/degree Celsius. Temperature2 is what we are looking for, while temperature1 is 20 degrees Celsius.

We have that after substitution

147 = 21.4*{1+0.0045 (T2 - 20) }

147 = 21.4*{1 + 0.0045T2 - 0.09}

147 = 21.4*{0.91 + 0.0045T2}

Opening the bracket we have that,

147 = 19.47 + 0.0963T2

Collecting like terms we have,

147 - 19.47 = 0.0963T2

127.53 = 0.0963T2

Making T2 subject of formula we have

T2 = 1324.3 degree Celsius