- 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
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
where αA 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=αVVΔT ----(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
when temperature increase by a amount ΔT then each linear dimension changes and then new volume is
if ΔT is small the higher order can be neglected.Thus we find
Comparing this with equation (5) we find
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