A brass rod and lead rod each 80 cm long at 0°C are clamped together at one end with their free ends coinciding. The separation of free ends of the rods if the system  is placed in a steam bath is:

$\left({\alpha }_{\text{brass }}=18\times {10}^{-6}/{}^{\circ }\mathrm{C}\text{ and }{\alpha }_{\text{lead }}=28\times {10}^{-6}/{}^{\circ }\mathrm{C}\right)$

The Brass rod and the lead rod will suffer expansion when placed in steam bath.

$\begin{array}{l}\therefore \text{ Length of brass rod at }100°C L_{\text{brass }}^{\text{'}}=L_{\text{brass }}\left(1+{\alpha }_{\text{brass }}\Delta T\right)\\ \\ =80\left[1+18\times {10}^{-6}\times 100\right]\end{array}$

The length of lead rod at ${100}^{\circ }C$

$L_{\text{lead }}^{\text{'}}=L_{\text{lead }}\left(1+{\alpha }_{\text{lead }}\Delta T\right)=80\left[1+28\times {10}^{-6}\times 100\right]$

Separation of free ends of the rods after heating

$\begin{array}{l}=L_{\text{lead }}^{\text{'}}-L_{\text{brass }}^{\text{'}}=80[28-18]\times {10}^{-4}\\ =8\times {10}^{-2} \mathrm{cm}=0.8 \mathrm{mm}\end{array}$