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  4. A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is (aCu=1.7 × 10-5 K-1 and .aAl=2.2 × 10-5 K-1)

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Q. A copper rod of $88 \,cm$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is $(a_{C_{u}}=1.7 \times 10^{-5}\,K^{-1}$ and $\left.a_{A_{l}}=2.2 \times 10^{-5} K^{-1}\right)$

NEETNEET 2019Thermal Properties of Matter

Solution:

$\Delta\,l_{1}=\Delta \,l_{2}$
$l_{1} \propto_{1} \Delta \theta=l_{2} \propto_{2} \Delta \,\theta $
$88 \times 1.7 \times 10^{-5}=l_{2} \times 2.2 \times 10^{-5} $
$\Delta I_{2}=88 \times 1.7 / 2.2=68 \,cm$