# Thermal Expansion Revision Notes

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13.2Thermal Expansion

In these revision notes for Thermal Expansion, we cover the following key points:

• What is the phenomenon of thermal expansion (contraction)?
• How does it differ from the other types of matter's volume change?
• How many types of thermal expansion contraction are there?
• What are the factors affecting thermal expansion (contraction)?
• Where is the phenomenon of thermal expansion (contraction) encountered in daily life?
• How is the phenomenon of thermal expansion (contraction) applied in technology?
• What are the main types of thermometers?
• What property of matter do most thermometers use to operate?

## Thermal Expansion Revision Notes

Thermal expansion is the general increase in the volume of a material as its temperature is increased. Also, thermal contraction, is the general decrease in the volume of a material as its temperature is decreased.

Thermal expansion (contraction) has no unit; it is represented through a fractional change in length, area or volume of material in respect to the original dimensions.

All objects expand or contract thermally in all dimensions (in 3 D). However, when one dimension is much greater than the other two (such as a long and thin bars for example), only the dimension corresponding to the greater value (usually the length) is considered. This phenomenon is called linear thermal expansion.

The factors affecting the amount of thermal expansion or contraction of a long bar of original length L0 are:

1. Type of material. Different types of materials experience different amounts of thermal expansion (contraction) for the same conditions. There is a quantity known as the coefficient of linear expansion, α (measured in Kelvin or Celsius degree at power -1), which represents numerically the type of material in the formula of thermal expansion (contraction).
2. Length of material. Longer the material, more it expands for the same conditions. Original length of material is represented in formula by the letter L0.
3. Change in temperature. When the change in any object's temperature is slight, it does not experience any considerable change in length. On the other hand, if there is a considerable change in object's temperature, its dimensions change a lot. For temperatures measured in Celsius scale, we can write Δt = t - t0 for the change in temperature where t is the final and t0 the initial temperature of the object, while for temperatures measured in Kelvin scale we can write ΔT = T - T0 for the same thing.

Putting all together, the equation of linear thermal expansion or contraction therefore is:

∆L = L0 × α × ∆T

The final length of a bar after experiencing thermal expansion or contraction, is

L = L0 × (1 + α × ∆T)

When an object is foil-like, it has two relevant dimensions, length and width. Height is very small to take into consideration. Therefore, another coefficient, known as area thermal expansion coefficient, β is introduced. Mathematically, we ca write β = 2α for the same material, because each dimension experiences the same degree of thermal expansion or contraction.

The formula is similar to that used for linear thermal expansion, i.e.

A = A0 × (1 + β × ∆T)

where A is the final area and A0 is the original area, and ΔT = T - T0 is the change in temperature.

When an object expands or contract due to the change in temperature, it experiences a volume thermal expansion or contraction. Since objects extend in three dimensions in space, they experience a linear expansion or contraction for each dimension. This mean the coefficient of volume expansion or contraction γ is triple the corresponding linear expansion coefficient α, i.e.

γ = 3 × α

In this way, if an object has a volume V0 at temperature T0, its volume V at another temperature T becomes

V = V0 × (1 + γ × ∆T)

Thermal expansion and contraction are encountered very often in daily life, and many engineering applications of this phenomenon are of a very wide range. Some of them include:

1. Railway tracks are placed at a certain distance from each other to avoid issues caused by thermal expansion during hot days in summer.
2. Electricity or telephone cables bend down in summer and strain in winter due to thermal expansion and contraction respectively.
3. Metal rings are heated prior to being fixed to a wooden barrel. The rings contract when they cool down and thus, they hold the barrel tightly as shown in the figure.

A bimetallic strip is a system composed by two different metal strips, which are placed side by side and welded together. The property of different amount of thermal expansion or contraction two metals of a bimetallic strip experience when they are exposed to the same change in temperature, is used to construct thermostats, which are equipment that keep heaters at constant temperature by controlling the current flow in an electric circuit through bimetallic strips.

All thermometers except digital (electronic) thermometers use the property of thermal expansion (contraction) to measure the temperature. There are the following types of thermometers in use:

a) Clinical thermometer. It is used to measure the temperature of human body. A clinical thermometer uses the expanding property of mercury, whose level rises or drops in a narrow column according the body temperature. Therefore, mercury here acts as a capillary liquid.

The range of most clinical thermometers varies from 35°C to 42°C as the body temperature of a healthy person is typically about 37°C.

b) Household (home) thermometer. Since the range of air temperatures are wider than those of the human body this thermometer uses (coloured) alcohol instead of mercury as capillary liquid, because alcohol has a lower freezing point than mercury.

The range of most room thermometers varies from -30°C to + 50°C.

c) Lab thermometer. This kind of thermometer must have a much wider range than room thermometers as it is used in various thermal and chemical processes, which involve many substances that are not commonly used in daily life.

Lab thermometers contain a variety of capillary liquids and ranges but the most typical capillary liquid is alcohol and their range usually varies between -50°C to 250°C.

d) Metallic thermometer. This kind of thermometer is used to measure the temperature of melting metals, so its range must be very wide. Since we cannot use glass as cover or mercury and alcohol as capillary liquids because they cannot resist to such high temperatures, most metallic thermometers constructors use the properties of bimetallic strip to measure the temperatures of very hot objects.

The range of metal thermometers typically varies from -200°C to +1600°C.

e) Digital thermometer. This kind of thermometer uses the digital technology to convert the heat energy into electric energy. There are two main types of digital thermometers: contact thermometers, which are operated in a similar way to clinical ones, and infra-red (contactless) thermometers which are operated remotely, in a similar way to remote controls.

Digital thermometers use the fact that hotter the object, more infrared radiation it emits. This radiation is converted by the thermometer's software into digital values accordingly.

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