We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length would change in such a way that difference between their lengths remain constant. If αiron = 1.2 × 10-5/K and αbrass = 1.8 × 10-5/K, what should we take as length of each strip?
Change in length of iron rod
$\Delta L=\alpha_{\text {iron }} L_{\text {iron }} \Delta T$
Change in length of brass rod
$\Delta L=\alpha_{\text {brass }} L_{\text {brass }} \Delta T$
Change in both the rods are equal, so
$\alpha_{b r a s s} L_{b r a s s} \Delta T=\alpha_{b r a s s} L_{b r a s s} \Delta T$
Substituting the values we get, Lbrass = 20 cm.