__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:

*ΔL* is the change in length, *L*_{0} 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:

*ΔV* is the change in length, *V*_{0} 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:

for a cube.

We can also use the chain rule, which says:

So we get:

because:

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:

This means:

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

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

Young’s modulus gives us:

For gases expanding freely:

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

Back to Contents: Physics: Thermodynamics

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