Thermal Expansion of Solids

Thermal Expansion of Solids

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

THERMAL EXPANSION
Definition. Increase in dimensions of a solid on heating, is called thermal expansion of the solid. All dimensions increase in same proportion.
Types
(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 V_t at t°C.
Then, like linear and superficial expansion, cubical expansion (V_t – 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,
V_t-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, V_t-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), V_t-V₀ = y V₀ t
or V_t = 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

VIVA VOCE

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.

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