Question

A brass rod of length $40cm$ is joined to a copper rod of length $50cm$. The two rods are of the same thickness and at initial temperature of ${40}^{\circ }C$. What is the change in length of the combine rod, when the same is heated to ${280}^{\circ }C$. Coefficients of linear expansion of brass and copper are $1.9\times {10}^{-5}{}^{\circ }{C}^{-1}$ and $1.7\times {10}^{-5}{}^{\circ }{C}^{-1}$ respectively.

Answer 1

We know that change in length $\Delta L=L\alpha \Delta T$

For brass :

$\Delta T=280-40=240$, L=40m, $\alpha =1.9\times {10}^{-5}{}^o{C}^{-1}$

$\Delta L_{brass}=40\times 1.9\times {10}^{-5}\times 240=0.1824cm$

For copper :

$\Delta T=280-40=240$, L=50m, $\alpha =1.7\times {10}^{-5}{}^o{C}^{-1}$

$\Delta L_{copper}=50\times 1.7\times {10}^{-5}\times 240=0.204cm$

Change in length of combined rod $\Delta L=\Delta L_{copper}+\Delta L_{brass}$

$\Delta L=0.1824+0.204=.3864cm$