THERMAL EXPANSION AND CONTRACTION

Suppose that we have a sample of solid material that expands when the temperature rises. This is the usual case, but some solids expand more per degree Celsius than others. The extent to which the height, width, or depth of a solid (its linear dimension) changes per degree Celsius is known as the thermal coefficient of linear expansion.
For most materials, within a reasonable range of temperatures, the coefficient of linear expansion is constant. This means that if the temperature changes by 2°C, the linear dimension will change twice as much as it would if the temperature variation were only 1°C. However, there are limits to this, of course. If you heat a metal up to a high enough temperature, it will become soft and ultimately will melt or even burn or vaporize. If you cool the mercury in a thermometer down enough, it will freeze. Then the simple length-versus-temperature rule no longer applies.
In general, if s is the difference in linear dimension (in meters) produced by a temperature change of T (in degrees Celsius) for an object whose linear dimension (in meters) is d, then the thermal coefficient of linear expansion, symbolized by the lowercase Greek letter alpha (α), is given by this equation:
α = s/(dT)
When the linear dimension increases, consider s to be positive; when it decreases, consider s to be negative. Rising temperatures produce positive values of T; falling temperatures produce negative values of T.
The coefficient of linear expansion is defined in meters per meter per degree Celsius. The meters cancel out in this expression of units, so the technical quantity is per degree Celsius, symbolized /°C.

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