Thermal Expansion

- Increase in dimension of body due to increase in temperature is call thermal expansion
- Most of the solid material expand when heated

-Consider a rod of length L then for small change in temperature ΔT,the fractional change in length ΔL/L is directly propertional to ΔT
ΔL/L=αΔT --(2)
or ΔL=αLΔT --(3)
- constant α characterizes the thermal expansion properties of a particulaqr material and it is known as coefficient of linear expansion.
- for materials having no prefential direction,every linear dimension changes according to equation (3) and L could equally well represent the thickness of the rod,side lenght of the square sheet etc
-Normally metals expand more and have high value of α
- Agian consider the intial surface area A of any surface .Now when the temperature of the body is increases by ΔT ,the increase in surface area is given by
ΔA=α_AAΔT ----(4)
where α_A is the coefficient of area expansion
-Similary we can define coefficient of volume expansion as fractional change in volume ΔV/V of a substance for a temperature change ΔT

as ΔV=α_VVΔT ----(5)
- K^-1 is the unit of these coefficents expansions
- These three coefficent are not strictly constant for a substance and these value is depends on temperature range in which they are measured.

Relation between volume and linear coefficient of expansion for solid materail: Consider a solid parallopide with dimension L₁,L₂ and L₃
then volume is
V= L₁L₂L₃
when temperature increase by a amount ΔT then each linear dimension changes and then new volume is
V+ΔV=L₁L₂L₃(1+α_L )
V+ΔV=V(1+α_LΔT)³
V+ΔV=V(1+3α_LΔT+3α_L²ΔT²+α_L³ΔT³)
if ΔT is small the higher order can be neglected.Thus we find
V+ΔV=V(1+3α_LΔT)
ΔV=3α_LVΔT
Comparing this with equation (5) we find
α_V=3α_L