Question

The difference between length of a certain brass rod and that of a steel rod is claimed to be constant at all temperatures. Is this possible ?

Answer 1

Yes, it is possible. Let α₁ and α₂ be the coefficients of linear expansion and l₁ and l₂ be the lengths of brass and steel rods respectively. Suppose that the temperature of the rod is increased by ΔT. Them, change in length of brass rod,

Δl₁ = l₁α₁ ΔT

and change in the length of the steel rod,

Δl₂ = l₂α₂ ΔT.

If the difference between the lengths of the two rods is to remain same then

Δl₁ = Δl₂

or, l₁ α₁ ΔT = l₁ α₂ ΔT

or, l₁/l₂ = α₂/α₁

Thus, the lengths of the two rods should be in the inverse ratio of their coefficients of linear expansion.