Question

Two rods of brass and iron are fixed to a short cross bar. If the iron is 1m long, what must be the length of the brass rod that the distance AB between the free ends of the rods remain constant at all temperature? ( take αfe= 0.000012k, αbrass=0.000019k)

Answer 1

The lengths must be the same:

$$L_{fe}=L_{brass},\\ L_{0 fe}(1+\alpha_{fe}\Delta T)=L_{0 br}(1+\alpha_{br}\Delta T),\\ 1(1+0.000012·\Delta T)=L_{0 br}(1+0.000019\Delta T).$$

This is the relation.