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A copper rod of 88 cm and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is: ($\alpha_{Cu}=1.7\times10^{-5}\ K^{-1}$ and $\alpha_{Al}=2.2\times10^{-5}\ K^{-1}$)
Detailed Solution
The difference in lengths is independent of temperature, so the increases in length must be equal:
$\alpha_{Cu}L_{Cu}=\alpha_{Al}L_{Al}$
$1.7\times10^{-5}\times88=2.2\times10^{-5}\times L_{Al}$
$L_{Al}=\frac{1.7\times88}{2.2}=68\ cm$