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A thin aluminium plate has an area 286 c...

A thin aluminium plate has an area 286 `cm^2` at `20^@ `C. Find its area when it is heated to `180^@ `C.
` ( beta ` for aluminimum `=4.9 xx 10^(-5) //""^(@)C )`

Text Solution

Verified by Experts

Given
`T_1 =20^@ C`
` T_2 = 180^@ C`
`A_1 = 286 cm^2`
` beta =4.9 xx 10^(-5) //^@ C`
we have
` beta = (A_2 -A_1)/( A_1 (T_2 -T_1))`
` therefore A_2 =A_1 [1 + beta (T_2 -T_1 )]`
`= 286 [1 + 4.9 xx 10^(-5) (180-20)]`
` = 286[ 1+4.9 xx 10^(-5) xx 160]`
` = 286 [ 1+784 .0 xx 10^(-5)]`
` = 286 [ 1 + 0.00784 ]`
`= 286 [ 1.00784 ]`
` therefore A_2 = 288.24 cm^2`
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