Most things expand when they get hotter.
The increase in length is given by the original length, Lo, multiplied by a constant, a, and the temperature change, DT.
The new length is the original length plus the extension.
Alpha - the coefficient of linear expansion - is a small positive number for most materials, almost constant over a 100° temperature range.
Negative expansion
A few metal alloys, ceramics and glass with the addition of a few % of boric oxide (B2O3), rubber, nylon, [and water between 0 and 3.98°C], have negative coefficients of thermal expansion. They get smaller when heated.
Zero expansion
Zerodur® is a carefully chosen combination of glass with a positive expansion coefficient and a form of quartz with a negative expansion coefficient. The mixture has a near zero coefficient of thermal expansion. Due to very little transmission near the blue end of the visible spectrum Zerodur® looks yellow to brown and is rarely used for lenses or prisms, but it makes an ideal backing for large astronomical telescope mirrors etc.
 Zerodur® mirror blank |
Railway lines must be laid in sections with gaps to allow for thermal expansion.
Bridges must have expansion plates built in to the carriage way.
1 Bimetallic strips act as thermal switches in many applications. [For example: flashing light bulbs and automatic kettles.]
2 The metal rims of wagon wheels were fitted by heating the metal. Modern shafts are fitted the same way.
3 Nuts on metal bolts can be loosened by heating just the nut.
4 Mercury in glass thermometers work because of the different thermal expansion of glass and mercury.
Since the coefficient of linear expansion is small....
The coefficient of area expansion is very nearly equal to 2a.
For the same reason ...
... and the coefficient of volume expansion is very nearly equal to 3a.
Examples:
1 An alcohol in glass thermometer indicates temperature because of the different expansion coefficients of alcohol and glass
The temperature scale is not linear because the linear coefficient of volume expansion (3a) is the increase in volume per unit volume. As the volume increases, the alcohol rises a little more in the capillary for each degree temperature rise.
2 The forces involved in the confined expansion of solids and liquids are enormous. A 19th century school teacher's trick was called a bar-breaker. A hot cast iron bar was fixed at both ends in a heavy framer. It broke as it contracted as it cooled. The same effect is seen when a glass soda bottle is broken in a freezer.
3 Ryne Larsen informs us that the Thai ten baht coin can be taken apart without damaging the central disc by repeatedly clamping the coin edge-on in a vice to stretch the outer alloy ring. He also reports that the similar Canadian coin can be dismantled by freezing and hammering out the central disc.
 |
It is suggested that freezing two-part coins in liquid nitrogen, may, because of different expansion coefficients, allow the separation with less effort.
4 Polystyrene is mostly air trapped in an open lattice. Air pressure reduces the volume of a polystyrene ball placed in liquid nitrogen. The effect is not typical thermal contraction.
The ball is still soft when cold. With some effort a 5 cm diameter ball may be squeezed into a coke bottle. The ball expands to its original condition as it returns to room temperature.