Question

A brass rod of length $30cm$ is joined to a copper rod of length $60cm$. The two rods are of the same thickness and at initial temperature of ${20}^{\circ }C$. What is the change in length of the combined rod, when the same is heated to ${160}^{\circ }C$. 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

Expansion in rod $\delta l=l\alpha \Delta T$

Here $\Delta T=160-20=140$

Expansion in brass $\Delta l_{brass}=l_{brass}{\alpha }_{brass}\Delta T$

$\Delta l_{brass}=30\times 1.9\times {10}^{-5}\times 140=0.0798cm$

Expansion in copper $\Delta l_{cu}=l_{cu}{\alpha }_{cu}\Delta T$

$\Delta l_{cu}=60\times 1.7\times {10}^{-5}\times 140=0.1482cm$

Total expansion $\Delta L=\Delta L_{brass}+\Delta L_{cu}=0.0798+0.1482=.22cm$