Question

Explain with the help of a formula the volumetric expansion coefficient of a solid.

Answer 1

Suppose a solid with volume V₁ at temperature T₁ is heated to temperature T₂ such that T₁ = T₂ – T₁ is very small.
Let V₂ be the volume of the solid at temperature T₂. Experimentally, it is found that the increase
in the volume of the solid (volumetric expansion), V₂ – V₁, is proportional to V₁ and ΔT. Therefore, (V₂ – V₁)α V₁ΔT.
∴ V₂ – V₁ = βV₁ΔT, where β is the constant of proportionality, called the volumetric expansion coefficient of the solid.
β = V2−V1 / V1ΔT It is expressed in per °C.
We have V₂ = V₁ + βV₁ ΔT = V₁ (1 + βΔT).
is the increase in the volume of a solid per unit original volume per unit rise in its temperature.