A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at `27.0^(@)C`. What is the change in the diameter of the hole when the sheet is heated to `227^(@)C` ? Coefficient of linear expansion of copper `=1.70xx10^(-5)K^(-1)`.

Explanation

But area of hole is `A_(1)` at temperature
`T_(1)=27+273=300K`
`:.A_(1)=(pid_(1)^(2))/(4)=(pixx(4.24)^(2))/(4)`
`:.A_(1)=4.4944pi" cm"^(2)`
Area of hole becomes `A_(2)` at temperature `T_(2)=227+273=500K`.
`:.A_(2)=A_(1)(1+beta Delta T)`
`(pid_(2)^(2))/(4)=4.4944pi[1+2alpha(T_(2)-T_(1))]" where "beta=2alpha`
`:.d_(2)^(2)=4xx4.4944[1+2xx1.7xx10^(-5)xx(500-300)]`
`:.d_(2)^(2)=4xx4.944[1+2xx1.7xx10^(-5)xx200]`
`:.d_(2)^(2)=4xx4.944[1+0.0068]`
`:.d_(2)^(2)=4xx4.944xx1.0068`
`d_(2)^(2)=18.0998~~18`
`:.d_(2)=sqrt(18.1)=4.2544" cm"`
`:.` Change in diameter of hole `Deltad=d_(2)-d_(1)`
`=4.2544-4.2400`
`=0.0144" cm"`
`=1.44xx10^(-2)" cm"`