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An aluminium rod of length 50cm is heate...

An aluminium rod of length 50cm is heated so that its temperature increases from `20^(0)`C. to `80^(0)`C. If the linear coefficient of expansion of aluminium is `24 xx 10^(-6)//^(0)` C find the increase in the le,igth of the aluminium rod.

Text Solution

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`l_(1) = 50 " cm, " t_(1) = 80^(0)C,`
`t_(2) = 20^(0)C, alpha = 24 xx 10^(-6) //^(0) C `
Coefficent of linear expansion, `alpha = (l_(2) - l_(1))/(l_(2) (t_(2) -t_(1)))`
The increase in length of the rod,
`(l_(2) - l_(1)) = alpha l_(1) (t_(2) - t_(1))`
= `24 xx 10^(-6) xx 50 xx (80 - 20) = 7.2 xx 10^(-2) ` cm.
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