Thermal Expansion of Solids
Physics Lab Manual NCERT 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.