Suppose a rod of length l1 at temperature T1 is heated to temperature T2 such that ΔT = T2 – T1 is very small. Let l2 be the length of the rod at temperature T2 .
Experimentally, it is found that the increase in the ength of the rod (linear expension), l2 – l1 , is proportional to l and ΔT. Therefore, (l2 – l1 ) α, l1 ΔT
∴ l2 – l1 = λl1 ΔT, where X is the constant of proportionality, called the coefficient of linear expansion of the solid.
λ = \(\cfrac{l_2-l_1}{l_1ΔT}\) It is expressed in per °C.
We have l2 – l1 + λΔT = l1(1 + λΔT).
