Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10 –6 °C –1 and 23 × 10 –6 °C –1 respectively.

Question

Philoid · Accepted Answer

Given:
Coefficient of Linear Expansion of iron rod : α_Fe = 12 x 10^-6 °C^-1
Coefficient of Linear Expansion of Aluminium Rod : α _Al = 20 x 10^-6 °C^-1
Formula used:

The formula for Linear Expansion is:

Let, L_Fe and L_Al be the original lengths of the iron and aluminium rods respectively.
Let, L’_Fe and L’_Al be the changed lengths (ΔL) of iron and aluminium rods respectively when temperature is changed by ΔT.
Now ,

Since , the difference in lengths is independent of temperature it shows that their difference is constant. That is, L’_Fe – L’_Al= L_Fe - L_Al

By arranging the terms we get,

Hence, the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature is 23:12.

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10–6 °C–1 and 23 × 10–6 °C–1 respectively.

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10^–6 °C^–1 and 23 × 10^–6 °C^–1 respectively.