Question

The base of an iron saucepan has a diameter of $20cm$ at ${15}^{\circ }C$. What will be the increase in the area of the base of the scaucepan when it is filled with boiling water? Given coefficient of linear expansion of iron $=2\times {10}^{-6}pe{r}^{\circ }C$

Answer 1

Linear expansion coefficient $\alpha =2\times {10}^{-6}$

Area expansion coefficient $\beta =2\alpha =4\times {10}^{-6}$

Area of saucepan is $A=\pi R^2=\pi {10}^2=314c{m}^2$

Temperature of boiling water is ${100}^{o}C$.

$\Delta T=100-20={80}^{o}C$

$\Delta A=A\beta \Delta T=314\times 4\times {10}^{-6}\times 80$

$\Delta A=0.1c{m}^2$