 ## Thermal expansion

When heat is applied to most materials expansion occurs in all directions.  Conversely if heat energy is removed contraction occurs in all directions.  The affects of expansion and contraction depend on the change in temperature of the material.
Practical applications where expansion and contraction of solid materials must be allowed for include:-

• overhead electrical transmission lines
• railway lines
• bridges

Fitting a metal collar to a shaft or a Steel tyre to a wheel, is often achieved by first heating them so that they expand, fitting them into position and then cooling them so that contraction holds them firmly in place.  This is known as shrink fitting.  Hot rivets and bimetallic strips are further practical examples of thermal expansion.

Water
Water is a liquid which at a low temperature displays an unusual affect.  If cooled contraction occurs until about 4° C, when the volume is at a minimum.  Further cooling towards 0° C results in expansion, when the ice is formed considerable expansion occurs, which often causes frozen water pipes to burst.

Temperature coefficients
The change in a property of a material is not always proportional to the change in temperature, but we can describe those that approximate to, in a similar way.  The variation in each property is described as a temperature coefficient, defined as a fractional change in the property per degree rise in temperature.  The temperature coefficient of resistance would be an example.

Linear expansion
The amount by which unit length of a material expands when the temperature is increased by 1°is known as the coefficient of linear expansion.
The coefficient of linear expansion α is the fractional change in length per degree rise in temperature.

α = expansion
original length x temperature rise
or
α = l₂ – l₁
l₁ ΔT
(expansion = l₁α ΔT)

From the definition we can estimate the new length of the material l₂ at a temperature T₂ from the equation;

New length = original length + expansion

l₂ = l₁ + l₁ α(ΔT) or l₂ = l₁ [(1 + α(ΔT)]

The amounts of expansion for most solid materials are known and can be found in tables of coefficients of linear expansion.

An example being iron at 12 x 10¯⁶ m K¯¹

Example problem
The length of an iron steam pipe is 20.0m at a temperature of 18°C. Determine the length of the pipe under working conditions when the temperature is 300°C.

l₂ = l₁ [(1 + α(ΔT)]    ->   l₂ = 20[(1 + (12 x 10¯⁶)(300-18)

l₂ = 20(1.003384)   ->   l₂ = 20.06768m

Thermal expansion coefficients table

 Material Linear coefficient α at 20°C (10¯⁶/°C) Aluminium 22.2 Brass 18.7 Carbon steel 10.8 Copper 17 Concrete 12 Diamond 1 Glass 8.5 Gold 14 Iron(pure) 12 Lead 29 Magnesium 26 Mercury 61 Molybdenum 4.8 Nickel 13 PVC 52 Silver 18 Stainless steel 17.3 Steel 11 – 13 Tungsten 4.5 Water 69

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