Physics
Cambridge IGCSE

TOPIC 2: THERMAL PHYSICS

# 2.2a Thermal Expansion

We learned in section 2.1a how the particles in a solid are held in place by strong forces, and they vibrate. What happens if you heat the substance, giving more energy to the particles?

Figure 1. Heating a metal rod

The answer is that the particles vibrate faster as shown in figure 1 above. The hotter the substance, the more kinetic energy the particles have, and the faster the vibrations. However this additional energy usually means that the particles take up more space as shown here in figure 2:

Fig 2 . Thermal Expansion - particle view
Kayau, CC BY 3.0

Here, the particles can be seen to be further apart as they vibrate faster and take up more space - the substance has expanded as it is heated.

Nearly all solids, liquids and gases expand (increase volume) as they are heated.

They also contract (decrease in volume) when they are cooled again.

A thermometer uses this expansion to push a thin column of liquid up the tube as it gets hotter, and gives us a measure of temperature based on the expansion of the liquid.

Note that this expansion and contraction happens in all states of matter, but during a change of state such as melting or boiling, the arrangement of particles changes completely. Melting and boiling usually results in expansion, but not always! For example, ice is less dense than water. As ice melts, the volume actually decreases and becomes more dense. This is why ice cubes float on water, and this is one example that does NOT follow the general rule of expansion and contraction.

Thermal expansion has many implications and uses, and a few of the common examples are given below:

### 1. Bridges

A road bridge is often made of steel, concrete and many other solid substances that would all expand on a hot day. To allow for this, bridges have an 'expansion gap' which lets the main section of the bridge expand and contract without cracking the bridge surface, which would be very dangerous to traffic.

Next time you go over a bridge have a look for these plates across the road. The movement is often small unless there is a really big temperature change in one day, but engineers around the world have to account for high summer temperatures and sometimes very cold conditions in winter.

Figure 3. Bridge thermal expansion plate

### 2. Railway lines

Just as bridges need to allow for expansion, so do railway lines. In figure 4, the engineers have not left enough room for expansion. On a really hot day, the rails have expanded and pushed each other out of place, making it extremely dangerous for the train.

All railway lines need to be checked thoroughly that sufficient gaps have been left for all weather and temperature conditions in the region.

Figure 4. Warped Railway lines
( U.S. Geological Survey)

### 3. Electricity Cables

Electricity cables are a common sight around the world, carrying electricity to homes and industry. Have you noticed that they always hang down, and are not tightly fastened? Why is this?

The answer is to allow for contraction on cold days. If the cables were fastened tightly on a hot day, then as the temperatures drop and the cables contract, they could snap! This would be extremely dangerous for anyone below. The slightly loose fit allows for expansion and contraction as needed for the region.

Figure 5. Electricity cables on pylons
Albrecht Fietz Pixabay

### 3. Bimetallic strips

A bimetallic strip is made of 2 different metals joined together. In the example shown here, the top metal expands considerably when heated as shown in diagrams (1) and (2). The bottom metal does not expand in comparison. If these metals are joined together, then as the top metal segment expands, it bends the strip over (3). The bigger the temperature rise, the larger the downwards bend (4).

Bimetallic strips can be used as switches, to turn circuits on/off depending on the temperature. They are used in simple temperature controls for heating a house.

Figure 6. Bimetallic Strips

### Expansion of solids, liquids and gases compared

All of the examples above are about the expansion of solids. Liquids also expand when heated in the same way. The expansion rate varies from material to material, but is a small fraction of the total volume of the solid or liquid. This is because the forces between atoms / molecules in solids and liquids prevents the spacing between these particles increasing significantly,

However in gases, the force between particles is negilgible. A temperature increase makes the particles move much faster the volume will increase dramatically, assuming the pressure in the gas stays the same. In fact, a doubling in the kelvin temperature should lead to a doubling in the volume (if the mass and pressure of the gas is constant. The volume is proportional to the kelvin temperature, leading to very high rates of expansion in gases.

Questions:

1. The metal lid on a jar of tomato sauce is very tight and difficult to open.

A student suggests pouring really hot water on to the lid to make it easier to open. Explain if this suggestion is valid.

By pouring hot water on the lid, the metal will expand. This will reduce the force holding it in place (reduce the friction/increase the gap between the jar and lid), and mean it will open with less force required. Therefore this is a good suggestion.

2. A large cube of aluminium is being investigated.

• a). Describe the two measurements required to find the density of the cube.
• b). Explain how the density might change if the cube is heated heated.

a) The density ρ can be calculated from the formula ρ = m /V. The mass m can be measured using an electronic balance. The volume V can be found by finding the length L of one side using a ruler , and then using V = L3. Then calculate m/V to find the density.

b) If the cube is heated, the mass would remain the same. However the cube would expand, increasing the volume. This means that as m is constant and V increases, then as ρ = m /V, the density would decrease.

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