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Question

A brass rod and a steel rod are both measured at 0oC and their lengths found to be 120 cm and 120.2 cm respectively. At what temperature are their lengths equal?
(αbrass=12×106oC1,αsteel=17×106oC1)

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Solution

Let temperature at which the lengths of brass rod (lb) and a steel rod (ls) are equal
lb=ls
l0(1+αbΔθ)=l10(1+αsΔθ)
120(1+12×106×θ)=120.2(1+17×106×θ)
120+120×12×106×θ=120.2+120.2×17×106θ
solving we get,
θ=57.415oC

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