Thermal Expansion of Solids
Definition. Increase in dimensions of a solid on heating, is called thermal expansion of the solid. All dimensions increase in same proportion.
(i) Linear expansion. A rod or wire has length only. When heated, its length increases. Increase in length is called linear expansion.
(ii) Superficial expansion. A sheet has area. When heated, its area increases. Increase in area is called superficial expansion.
(iii) Cubical expansion. A body has volume. When heated, its volume increases. Increase in volume is called cubical expansion.
Coefficient of linear expansion
Coefficient of superficial expansion
Coefficient of cubical expansion
Introduction. Let a body of certain material have volume V0 at 0°C. Let the volume become Vt at t°C.
Then, like linear and superficial expansion, cubical expansion (Vt – V0) depends upon original volume (V0) and rise in temperature (t). It also depends upon the material of the body.
Hence, proceeding as in linear expansion,
Vt-V0 = γ V0 t
where γ is constant of proportionality whose value depends upon the material of the body. It is called coefficient of cubical expansion of the material of the body.
Definition. In Eq. (1),
if V0=1, t=1,
then, cubical expansion, Vt-V0 = γ.
Hence, the coefficient of cubical expansion of the material of the body may be defined as the increase in volume of a body of unit volume for one degree rise in temperature.
From Eq. (1), Vt-V0 = y V0 t
or Vt = V0[1+γ(t2 -t1)] …(2)
From Eq. (2), Vt can be found if V0, γ and t are known.
In general, if a body has volume V1 at t°C and V2 at t2°C we may prove that
V2 = V1[1+γ(t2-t1)]
Equation (3) is possible because γ has Small value and γ2 is negligible.
Relation between α, β and γ by differential method
Question.1. Which part of the bimetallic strips lie outside on heating ?
Answer. The metal which has higher coefficient of linear expansion lies on the outer side.
Question.2. Where bimetallic strips are used ?
Answer. In fire alarm, thermostats, etc.