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Coefficient of thermal expansion of a wi...

Coefficient of thermal expansion of a wire varies with temperature T as `alpha = 1.6 xx 10^(-6) T`, where T is temperature in degree Celsius. If the length of wire is 10 m at` 0^@C`, what is the change in length of wire (in mm), when its temperature is raised to `25^@C`?

Text Solution

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The correct Answer is:
5
`dl = l_0 alpha d T`
`int_0^(Delta l) dl = l_0 alpha_0 int_0^25 TdT`
`Delta l = l_0 alpha_0 xx 625/2 " " = 10 xx 1.6 xx 10^(-6) xx 625/2 = 5 xx 1000 xx 10^(-6) = 5 mm`.
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