**Thermal expansion**

Most of the material expand when their temperature increases. Then the phenomenon of expansion of material when it is heated is known as thermal expansion.

1. **Linear expansion**– When a rod heated then the temperature of the body increases due to which length of the rod increases , this phenomenon is known as the linear expansion .

Suppose a rod is of length l_{0} at the initial temperature T_{0}, when its temperature is rises by temperatureT , then the length changes by l. Then the change in length is proportional to original length and rise in temperature,

i.e. l α T……………(i)

And l α l_{0} ……………..(ii)

From eq. (i) and (ii)

l α l_{0}T,

Or, l = α l_{0}T , where α is the coefficient of linear expansion its unit is K^{-1} or ( C^{0})^{-1}.

Then the final length l = l_{0}+ l

Or, l = l_{0} + α l_{0}T

L = l_{0} ( 1+ α T)………….(iii)

**Area expansion or superficial expansion** – When a surface heated then the temperature of the body increases due to which area of the rod increases , this phenomenon is known as the Area expansion .

Suppose a rod is of length A_{0} at the initial temperature T_{0}, when its temperature is rises by temperatureT , then the length changes by A. Then the change in area is proportional to original area and rise in temperature,

i.e. A α T……………(i)

And A α l_{0} ……………..(ii)

From eq. (i) and (ii)

A α A_{0}T,

Or, A = β A_{0}T , where β is the coefficient of Superficial expansion its unit is K^{-1} or ( C^{0})^{-1}.

Then the final area A = A_{0}+ A

Or, A = A_{0} + β A_{0}T

A = A_{0} ( 1+ β T)………….(iii)

**Volume expansion-** When a rod heated then the temperature of the body increases due to which volume of the rod increases , this phenomenon is known as the volume expansion .

Suppose a rod is of length V_{0} at the initial temperature T_{0}, when its temperature is rises by temperatureT , then the length changes by V. Then the change in length is proportional to original length and rise in temperature,

i.e. V α T……………(i)

And V α V_{0} ……………..(ii)

From eq. (i) and (ii)

V α V_{0}T,

Or, V = Ÿ V_{0}T , where Ÿ is the coefficient of linear expansion its unit is K^{-1} or ( C^{0})^{-1}.

Then the final length V = V_{0}+ V

Or, V = V_{0} + Ÿ V_{0}T

V = V_{0} ( 1+ Ÿ T)………….(iii)

Relation between linear, area and volume expansion (α,β and Ÿ )

2α=β; and 3α=Ÿ

Or , α = β/2=Ÿ/3 .

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