**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 V_{0} at 0°C. Let the volume become V_{t} at t°C.

Then, like linear and superficial expansion, cubical expansion (V_{t} – V_{0}) depends upon original volume (V_{0}) and rise in temperature (t). It also depends upon the material of the body.

Hence, proceeding as in linear expansion,

V_{t}-V_{0} = γ V_{0} 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 V_{0}=1, t=1,

then, cubical expansion, V_{t}-V_{0} = 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}-V_{0} = y V_{0} t

or V_{t} = V_{0}[1+γ(t_{2} -t_{1})] …(2)

From Eq. (2), Vt can be found if V_{0}, γ and t are known.

In general, if a body has volume V_{1} at t°C and V_{2} at t_{2}°C we may prove that

V_{2} = V_{1}[1+γ(t_{2}-t_{1})]

Equation (3) is possible because γ has Small value and γ^{2} 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.