Volumetric Expansion

Created: Monday, 29 August 2011 10:42 | Published: Monday, 29 August 2011 10:42 | Written by Super User | Print | Email

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 ^ΔT. Experiments will then show that its increase in volume (^ΔV) will be directly proportional to its initial volume (V1) and the rise in temperature (^ΔT).

^ΔV V1---------(1)

^ΔV T---------(2)

combining (1) and (2)

^ΔV V1 ^ΔT

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 + ^ΔV

Which makes the value of ΔV

V2 = V1 + βV1^ΔT

V2 = V1( 1+ β^ΔT)

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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