# Volumetric Expansion

Volume expansion works almost exactly like linear expansion. If an object or substance of initial volume Vi undergoes a change in temperature ΔT, then its volume will change by an amount

**ΔV = βViΔT**

## What is volumetric expansion?

"

**Volumetric expansion**" or "**cubical expansion**" is the increase in the volume of a body when it is heated.Consider a metallic body of volume =

**V1**. Let its temperature be raised by**. Experiments will then show that its increase in volume (**^{Δ}T**) will be directly proportional to its initial volume (**^{Δ}V**V1**) and the rise in temperature (**).**^{Δ}T

^{Δ}V V1---------(1)

^{Δ}V T---------(2)combining (1) and (2)

^{Δ}V V1^{Δ}TOR

**ΔV = βV1ΔT**

**Where β is a constant known as the material’s "coefficient of volumetric expansion"**

## Expression for Final Volume

We know that

**Final volume = Initial volume + increase in volume**

**V2 = V1 +**

^{Δ}VWhich makes the value of ΔV

**V2 = V1 + βV1**

^{Δ}T**V2 = V1( 1+ β**

^{Δ}T)## Coefficient of Volumetric Expansion

A material’s coefficient of volumetric expansion (

**β**) is defined as its increase in volume per unit original volume per Kelvin rise in temperature.**Unit:1K OR K**

^{-1 }**β= 3α**

For example, the value of a for a solid object does not depend on whether we are talking about its length or width. Such an object is called an isotropic solid. In this case, the volume expansion coefficient b is simply given by

β= 3α. (Isotropic solid)

Unless stated otherwise, we shall assume that any solid material that we are working with can be treated as an isotropic solid.

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