# The expansion of solids and liquids

When a substance is heated the molecules within it gain energy. If you look at a graph showing the potential energy of two adjacent molecules you will notice that as energy is gained the separation of the molecules increases. The material therefore expands on heating.

This expansion must be allowed for in the construction of buildings and bridges where large steel girders are used and where very great stresses develop.

It has been found experimentally that the change in dimension depends on:
(a) the original dimension of the specimen, the change in temperature, and
(b) the material of which the specimen is made.

For a change in length this can be expressed as:

Change in length = a x original length x temperature change

where a is the linear expansivity of the material, defined as the fractional change in length for a unit rise in temperature or:

a = [L – Lo]/Loq

where Lo is the original length L the final length and q the change in temperature The units for a are K-1 or oC-1.

The linear expansivtttes for a number of solid materials are given in the following table

 Material Linear expansivity (x106/K-1 Aluminium 23 Brick 9 Copper 17 Diamond very nearly zero Invar 0.9 Iron 12 Quartz 0.4 Rubber 220 Zinc 31

Example problems
Calculate the increase in length of a 20 m steel girder in a building when the temperature changes from 0oC to 30oC. Change in length = Loa(q2a1) = 20x1.2x10-5x30 = 7.2 mm

Student investigation
Suspend a metre length of resistance wire between two supports and hang a weight from the centre as shown in Figure 1. Record the position of the weight and then pass a current through the wire so that the wire heats up and expands. Record the new position of the weight and hence find the extension of the wire. Measure the current passing through the wire and the potential difference between its ends.

Using the known value of the expansivity of the material of the wire, estimate the mean temperature of the wire.

Repeat for various power inputs, and plot a graph of temperature against power.

### Other expansivities

It can be shown that the superficial (or area) expansivity is about twice that of the linear expansivity and that the cubical (or volume) expansivity is roughly three times the linear expansivity.

### Applications and effects of solid expansion

The effects of solid expansion are used in the bimetallic thermostat and the hot-wire ammeter, and must be allowed for in the design of a parallel-plate condenser, the compensated pendulum and telephone wires. Special low-expansion glass is used in precision optical devices such as telescope mirrors.

### Expansion of liquids

When considering the increase in the volume of a liquid with temperature we must use its cubical expansivity. Allowance should also be made for the expansion of the container, although this may be ignored except in accurate work, since the expansivities of liquids are usually greater than those of solids - for example, the expansivity of ethanol is some 100 times that of iron!
The cubical expansivity of some common liquids is shown in the following table.

 Liquid Cubical expansivity (x104/K-1) Ethyl alcohol 10.8 Mercury 1.82 Olive oil 7.0 Paraffin oil 900 Turpentine 9.7 Water 2.1

The strange behaviour of water around 4 oC is covered the 14-16 section of the site.

© Keith Gibbs 2010