Theory:

Cubical expansions:
When we heat a solid, if there is an increase in the volume of the body, this is called Cubical expansion. It is also known as Volumetric expansion.

The amount by which the volume of a material increases when the temperature is raised to one degree is called the coefficient of volumetric expansion.

The coefficient of volumetric expansion can be represented by the symbol γ (gamma).

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Volume expansion

Consider a material with the volume of V1 at t1o \(c\) and the material is heated upto t2o \(c\). Now, the volume of the material is V2.

Let γ be the coefficient of cubical expansion.

We know that,

The change in volume \(ΔV\) is proportional to original volume V1, rise in temperature \(ΔT\), and material type.

ΔV=V2V1andΔT=t2t1ΔVV1ΔTΔV=γV1ΔT

Rearranging the above equation,

γ=V2V1V1t2t1Where,V1andV2arethevolumesofthematerialbeforeandafterheatingrespectively.t1andt2arethetemperaturesofthematerialbeforeandafterheatingrespectively.γisthevolumetriccoefficientofexpansion.

Relation between α,βandγ: 

6α=4β=2γ