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The length of a metal rod at 27^@ C is 4...

The length of a metal rod at `27^@ C` is 4 cm. The length increases to 4.02 cm when the metal rod is heated upto `387^@ C`. Determine the coefficient of linear expansion of the metal rod.

Text Solution

Verified by Experts

Given
` T_1 =27^@ C `
` T_2 = 387^@ C `
` l_1 =4 cm = 4 xx 10^(-2) m`
` l_2 =4.02 cm = 4.02 xx 10^(-2) m`
we have
` alpha = (l_2 -l_1)/(l_1 (T_2 -T_1))`
` = ((4.02 -4.0 ) xx 10^(-2))/(4 xx 10^(-2) (387 -27 ))`
` = ( 0.02 xx 10^(-2))/(4 xx 10^(-2) xx 360 )`
`=1.39 xx 10^(-5) //""^(@ )C `
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