An iron rod and a copper rod lie side by side. An the temperature is changed, the difference in the length of the rods remains constant at a value of 10 cm. Find the lengths at `0^o C`. Coefficients of linear expansion of iron and copper are `1.1 xx 10^(-5) C^(-1) and 1.7 xx 10^(-5) C^(-1)` respectively.

Explanation

Since copper expands more than iron the length of the iron rod must be great than that of the copper rod. Let their length be `l_1` and `l_2`. The `l_1-l_2=10cm`. Since the difference is always same at all temperatures, their increase in length must be the same whatever the rise in temperature.
`:. Deltal=l_1alpha_(Fe)DeltaT=l_2alpha_(Cu)DeltaT`
or `(l_1)/(l_2)=(alpha_(Cu))/(alpha_(Fe))=(17)/(11)`
Also `l_1-l_2=10cm`
Soving for `l_1` and `l_2`
`l_1=28.3cm` `l_2=18.3cm`