A copper rod and a steel rod are to have lengths LC and LS, such that the difference between their lengths is the same at all ambient temperatures. If the coefficients of linear expansion of copper and steels are αC and αS respectively. The lengths are related to the coefficient of linear expansion as :

1
\(\rm \frac{L_C}{L_S}=\frac{\alpha_S}{\alpha_C}\)
2
LC - LS = αC - αS 
3
\(\rm \frac{L_C}{L_S}=(\frac{\alpha_C}{\alpha_S})^{1/2}\)
4
\(\rm \frac{L_C}{L_S}=\frac{\alpha_C}{\alpha_S}\)
5
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