An iron rod and another of brass, both at 27∘C differ in length by 10−3m. The coefficient of linear expansion for iron is 1.1×10−5/∘C and for brass is 1.9×10−5/∘C. The temperature at which both these rods will have the same length is
0°C
The given data is normally insufficient to determine the result. Either the length of one of the rods at 0∘C must be known or one has to assume that both the rods had the same length at 0∘C which is not possible if they have the same length again at another temperature. Suppose the two rods had the same length L at 0∘C. Then by the given problem,
L[1+1.9×10−5×27]−L[1+1.1×10−5×27] = 10−3
L×0.8×27×10−5 = 10−3
Or L = 10−30.8×27×10−5m = 4.63m
Hence 0∘C is a possible choice and the rods had equal length of 4.63m at 0∘C