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The length of a zinc rod, when heated fr...

The length of a zinc rod, when heated from `20^(@)C " to " 80^(@)C`, increase by 0.6 cm. If the coefficient of linear expansion of zinc is `27 times 10^(-6@)C^(-1)`, what is the initial length of the rod?

Text Solution

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`alpha=(l_(2)-l_(1))/(l_(1)(t_(2)_t_(1))) or , l_(1)=(l_(2)-l_(1))/(alpha(t_(2)-t_(1)))`
Given, `alpha=27 times 10^(-6@)C^(-1), t_(1)=20^(@)C, t_(2)=80^(@)C, l_(2)-l_(1)=0.6 cm`
`therefore " " l_(1)=(0.6)/(27 times 10^(-6) times (80-20))`
`" "=(0.6)/(27 times 10^(-6) times 60)`
`" "=370.37 cm.`
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