LINEAR EXPANSION

For small changes in temperature, the increase in length, Δ l, of a body is directly proportional to its original length, l, and increase in its temperature, ΔT.

 Δ l ∞ l

  And

 Δ l ∞ ΔT

Δ l = α l ΔT, where α is a constant called co-efficient of linear expansion. Its value depends on the material of the body and its temperature. For small changes of temperature, its variation with temperature is negligible.

α = Δ l / l ΔT            the unit of α is (°C)^{- 1} or K ^{- 1}.

Some solids expand uniformly in all directions. Such substances are called isotropic substances. For isotropic solids, increase in area, ΔA = 2 α A ΔT and increase in volume, ΔV = 3 α V ΔT. Increase in volume is more in liquids than in solids and is maximum in gases. Change in volume of water with temperature is anomalous. Water contracts when its temperature is reduced up to 4° C, but when its temperature is decreased from 4° C to 0° C, it expands. As a result, the density of water is maximum at 4° C. The anomalous expansion of water has a favorable effect for animals living in water. As the density of water is maximum at 4° C, even in severe winter when the water on the surface of the lake freezes, water at its bottom remain at 4° C, which allow marine animals to remain alive and move near the bottom.