Question

The length of a brass rod at $0^{\circ }C$ is 10m. Find its length at ${100}^{\circ }C$ if $\alpha$ of brass is $18\times {10}^{-6}{}^{\circ }{C}^{-1}$.

Answer 1

The equation for linear expansion is given as:
$\Delta L=\alpha L_1\Delta T$
Where $\alpha$ is the coefficient of linear expansion $=18\times {10}^{-6}{}^{\circ }{C}^{-1}$
$L_1$ is initial length = 10 m
$\Delta L$ is the change in length
& $\Delta T$ is the change in temperature $={100}^{\circ }$ C or 100k
Therefore, $L_2=\Delta L+L_1$
$=L_1(1+\alpha \Delta T)$
On putting the values,
$L_2=10.018$ m