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# Thermal expansion

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 l0 at the initial temperature T0, 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 l0 ……………..(ii)

From eq. (i) and (ii)

l α l0T,

Or, l = α l0T , where α is the coefficient of linear expansion its unit is K-1 or  ( C0)-1.

Then the final length l = l0+ l

Or, l = l0 + α l0T

L = l0 ( 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 A0 at the initial temperature T0, 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 l0 ……………..(ii)

From eq. (i) and (ii)

A α A0T,

Or, A = β A0T , where β is the coefficient of Superficial expansion its unit is K-1 or  ( C0)-1.

Then the final area A = A0+ A

Or, A = A0 + β A0T

A = A0 ( 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 V0 at the initial temperature T0, 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 V0 ……………..(ii)

From eq. (i) and (ii)

V α V0T,

Or, V = Ÿ V0T , where Ÿ is the coefficient of linear expansion its unit is K-1 or  ( C0)-1.

Then the final length V = V0+ V

Or, V = V0 + Ÿ V0T

V = V0 ( 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 .