Find the ratio of the lengths of an iron rod and an aluminum rod for which the difference in the lengths in independent of temperature. Coefficients of linear expansion of iron and aluminum are `12 xx10^(-6)C^(-1)` and `23 xx 10^(-6)C^(-1)`respectively.

Explanation

Iron Rod= `L_Fe alpha_Fe=12 xx 10^-6/^0C`
`aluminium rod = L_Al alpha_Al= 23 xx 10^-6/^0C`
Since the difference in length is
independent of temperature the difference
always remains constant.
`L'_Fe= L_Fe(1+alpha_Fe xx DeltaT) ...........(1)`
`L'_Al= L_Al(1+alpha_Al xx DeltaT ..........(2)`
`L_Fe-L'Al= L_Fe-L_Al+L_Fe xx alpha_Fe DeltaT- L_Al xx alpha_Al xx Delta T`
Given
`L'_Fe -L'_Al= L_Fe- L_Al`
Hence `L_Fe alpha_Fe=L_Al alpha_AL`
`L_Fe/L_AL=23/12 Ans`.