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.

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

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