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A solid sphere of copper weighs 1kg, Fin...

A solid sphere of copper weighs 1kg, Find the increase in its surface area when its temperature rises from `15^(@)C" to "500^(@)C`. Relative density of copper at `0^(@)C` is 8.39. `alpha=16.07xx10^(-6)//""^(0)C`

Text Solution

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`r_(0)=[1000/(4"/"3pi)]^(1//3)=2.99cm," "r_(15)" at "15^(@)C`
`r_(15)=r_(0)(1+alphaDeltatheta)=2.99(1+16.07xx10^(-6)xx15)=2.991cm`
`therefore` Area at `15^(@)C=A_(15)=4pir_(15)^(2)=112.4cm^(2)`.
At `500^(@)` the radius is `r_(500)=2.99(1+alphaxx500)=3.014`
`A_(500)=4pir_(500)^(2)=114.2cm^(2)`
Hence increase in surface area
`DeltaA=A_(500)-A_(15)=114.2-112.4=1.8cm^(2)`
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