Thermal expansion

A2

As materials get hotter the particles oscillate (vibrate) more, so the average distance between them increases. This means that the material expands.

University

In 2D, the expansion is linear, and is given by the equation:

scan0001

ΔL is the change in length, L0 is the original length, ΔT is the change in temperature, in Kelvin, K, and α is the coefficient of linear expansion, in K-1 (or the inverse of whichever temperature unit is used).

In 3D, the expansion is given by the equation:

scan0002

ΔV is the change in length, V0 is the original length, ΔT is the change in temperature, in Kelvin, K, and β is the coefficient of volume expansion, in K-1 (or the inverse of whichever temperature unit is used).

We can work out how β is related to α using:

scan0003

for a cube.

We can also use the chain rule, which says:

scan0004

So we get:

scan0005

because:

scan0006

We know dL already from the equation for linear expansion, so we substitute it in, and equate what we get with the equation we already have for volume expansion:

scan0007

This means:

scan0008

Thermal stress is created when a material is held in position.

scan0009

where F is force and A is area. For more about this, visit stress and strain.

Young’s modulus gives us:

scan0010

For gases expanding freely:

scan90004

(since W = pV, substitute p using the ideal gas equation)

Back to Contents: Physics: Thermodynamics

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s