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 o

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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.

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Helga 4 years 2021-08-31T08:03:09+00:00 1 Answers 6 views 0

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  1. Euphemia
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    2021-08-31T08:04:29+00:00
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    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

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