First slide

Thermal expansion

Question

A copper rod of length 88 cm and an aluminium rod of unknown length have same increase in length at same increase in temperature. The length of aluminium rod is
$\large ({\alpha _{Cu}} = 1.7 \times {10^{ - 5}}{K^{ - 1}}\,and\,{\alpha _{Al}} = 2.2 \times {10^{ - 5}}{K^{ - 1}})$

Moderate

A

88 cm
B

68 cm
C

6.8 cm
D

113.9 cm

Solution

Increase in length is given by $\large {l}'-l= l\alpha .\Delta\theta$
$\large \therefore l_{cu}.\alpha_{cu}.\Delta \theta=l_{al}.\alpha_{al}.\Delta\theta$
$\large \alpha_{cu}L_{cu}=\alpha_{Al}L_{Al}$
$\large 1.7\times 10^{-5}\times 88cm=2.2\times 10^{-5}\times L_{Al}$
$\large L_{Al}=\frac {1.7\times 88}{2.2}=68cm$

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