Question

A circular sheet of copper of radius $35cm$ is at ${20}^{\circ }C$. On heating its area increases by $14.5c{m}^2$. If coefficient of linear expansion of copper is $1.7\times {10}^{-5}{}^{\circ }{C}^{-1}$, find the temperature to which the sheet was heated.

Answer 1

Initial area $A=\pi (35{)}^2=3846.5c{m}^2$

Change in area on heating $\Delta A=14.5c{m}^2$

$\alpha =1.7\times {10}^{-5}$

We know that area expansion coefficient is twice of linear expansion coefficient.

So $\beta =2\alpha =2\times 1.7\times {10}^{-5}=3.4\times {10}^{-5}$

So $\Delta A=A\beta \Delta t$

$14.5=3846.5\times 3.4\times {10}^{-5}\times \Delta T$

$\Delta T={110.8}^{o}C$