Linear Thermal Expansion

Most solids expand when heated because rising temperature increases the average separation between vibrating atoms in the lattice. For a rod the change in length is $\Delta L=L_0\alpha \Delta T$, where $L_0$ is the original length, $\alpha$ the coefficient of linear expansion and $\Delta T$ the temperature rise. The temperature increases from $20^{\circ }\text{C}$ to $60^{\circ }\text{C}$, so $\Delta T=40^{\circ }\text{C}$. Substituting $L_0=50\text{m}$, $\alpha =1.2\times 10^{-5}{/}^{\circ }\text{C}$ and $\Delta T=40$ gives $\Delta L=50\times 1.2\times 10^{-5}\times 40=2.4\times 10^{-2}\text{m}=24\text{mm}$. The value 12 mm uses only half the temperature change. The value 36 mm overstates $\Delta T$ as 60. The value 48 mm doubles the correct expansion. This is the standard NCERT relation for linear thermal expansion and explains why expansion gaps are left between rail segments. As a check, a 24 mm expansion over 50 m is a tiny relative change of about $5\times 10^{-4}$, which is the small magnitude expected for solid expansion over a modest temperature rise.