Question

Coefficient of cubical expansion of solid, liquid and gas

Answer 1

The coefficient of cubical expansion is generally defined as

The increment in volume of a unit volume of solid, liquid, or gas for a rise of temperature of 1° at constant pressure. Also known as coefficient of expansion; coefficient of thermal expansion; coefficient of volumetric expansion; expansion coefficient; expansivity.

Let V1 be the initial volume at temperature T1 (in ∘C, or in K)

V2 is the volume at temperature T2 , with T2>T1

Then the coefficient of cubical expansion β can be expressed as:

β=ΔVV1ΔT

The coefficient of cubical expansion represents the ratio of the increase in volume per original volume for every degree increase in temperature:

β=V2−V1V1(T2−T1)

or also:

V2=V1(1+β(T2−T1))

It can be shown that (for isotropic materials) the coefficient of cubical expansion is equal to three times the coefficient of linear expansion α :

β=3α

Answer 2

Coefficient of cubical expansion is the fraction of volume increased when a body is heated. Its the property of the material and Aluminium has the highest coefficient of expansion among the metals.

α=ΔVVΔT

Unit of α is /oC.

In Engineering its usually represented as α

An interesting fact is that Invar (An alloy of Fe and Ni —FeNi36) show approximately zero coefficient of expansion. The name came from “Invariable”.

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