# The Application of Linear Expansion in Engineering

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Railroads and bridges may need expansion joints. Metal hot water heating pipes shouldn't be used in long, linear lengths. Scanning electronic microscopes need to detect minute changes in temperature to change their position relative to their focus point. Liquid thermometers use mercury or alcohol, so they flow in only one direction as the liquid expands due to temperature changes. Each of these examples demonstrates how materials expand in length under heat.

#### TL;DR (Too Long; Didn't Read)

The linear expansion of a solid under a change in temperature can be measured using Δℓ/ℓ = αΔT and has applications in the ways solids expand and contract in everyday life. The strain that the object undergoes has implications in engineering when fitting objects among each other.

## Application of Expansion in Physics

When solid material expands in response to an increase in temperature (thermal expansion), it can increase in length in a process known as linear expansion.

For a solid of length ℓ, you can measure the difference in length Δℓ due to a change in temperature ΔT to determine α, the coefficient of thermal expansion for the solid according to the equation:

\frac{\Delta l}{l}=\alpha \Delta T

for an example application of expansion and contraction.

This equation, however, assumes the change in pressure is negligible for a small fractional change in length. This ratio of Δℓ/ℓ is also known as material strain, denoted as ϵthermal. Strain, a material's response to stress, can cause it to deform.

You can use the Engineering Toolbox's Coefficients of Linear Expansion to determine the expansion rate of a material in proportion to the amount of that material. It can tell you how much a material expands based on how much of that material you have, as well as how much of a change in temperature you apply for an application of expansion in physics.

## Applications of Thermal Expansion of Solids in Daily Life

If you want to open a tight jar, you can run it under hot water to expand the lid slightly and make it easier to open. This is because, when substances, like solids, liquids or gases, are heated, their average ​molecular kinetic energy rises​. The average energy of the atoms vibrating within the material increases. This increases the separation between atoms and molecules that makes the material expand.

While this can cause phase changes such as ice melting to water, the thermal expansion is generally a more direct result of the increase in temperature. You use the linear coefficient of thermal expansion to describe this.

## Thermal Expansion from Thermodynamics

The materials may expand or contract in response to these chemical changes bringing a large-scale change in size from these small-scale chemical and thermodynamic processes in much the same way bridges and buildings may expand under extreme heat. In engineering, you can measure the change in the length of a solid substance due to thermal expansion.

Anisotropic material​s, ones that vary in their substance between different directions, may have different linear expansion coefficients depending on the direction. In these cases, you may use tensors to describe the thermal expansion as a tensor, a matrix that describes the thermal expansion coefficient in each direction: x, y and z.

## Tensors in Expansion

Polycrystalline​ materials that make up glass with near-zero microscopic thermal expansion coefficients are very useful for refractories such as furnaces and incinerators. Tensors can describe these coefficients by accounting for different directions of linear expansion in these anisotropic materials.

Cordierite, a silicate materiel that has one positive thermal expansion coefficient and one negative one means its tensor describes a volume change of essentially zero. That makes it an ideal substance for refractories.

## Application of Expansion and Contraction

A Norwegian archaeologist theorized that Vikings used the thermal expansion of ​cordierite​ to help them navigate the seas centuries ago. In Iceland, with large, transparent single crystals of cordierite, they used sunstones made of cordierite that could polarize the light in a certain direction only in a certain orientations of the crystal to let them navigate on cloudy, overcast days. As the crystals would expand in length even with a low coefficient of thermal expansion, they showed a bright color.

Engineers must consider how objects expand and contract when designing structures such as buildings and bridges. When measuring distances for land surveys or designing molds and containers for hot materials, they must account how much the earth or a glass may expand in response to the changes in temperature they experience.

Thermostats​ rely on bimetallic strips of two different thin strips of metals placed one on the other, so one expands much more significantly than the other due to changes in temperature. This causes the strip to bend, and, when it does, it closes the loop of an electric circuit.

This causes the air conditioner to start, and, by changing the thermostat's values, the distance between the strip to close the circuit changes. When the external temperature reaches its desired value, the metal contracts to open the circuit and stop the air conditioner. This is one of many example uses of expansion and contraction.

## Pre-Heating Temperatures of Expansion

When pre-heating metal components between 150°C and 300°C, they expand, so they can be inserted into another compartment, a process known as induction shrink fitting. The methods of UltraFlex Power Technologies have involved induction shrink fitting Teflon insulation onto a wire by heating a stainless steel pipe to 350°C using an induction coil.

Thermal expansion can be used to measure saturation of solids among the gases and liquids it absorbs over time. You can set up an experiment to measure the length of a dried block before and after letting it absorb water over time. The change in length can give the thermal coefficient of expansion. This holds practical use in determining how buildings expand over time when exposed to air.

## Thermal Expansion Variation Among Materials

The linear thermal expansion coefficients vary as an inverse of the melting point of that substance. Materials with higher melting points have lower linear thermal expansion coefficients. The numbers range from about 400 K for sulfur up to about 3,700 for tungsten.

The coefficient of thermal expansion also varies by the temperature of the material itself (particularly whether the glass transition temperature has been crossed), the structure and shape of the material, any additives involved in the experiment and potential cross-linking among the polymers of the substance.

Amorphous polymers​, ones without crystalline structures, tend to have lower thermal expansion coefficients than semicrystalline ones. Among glass, sodium calcium silicon oxide glass or soda-lime silicate glass, has a fairly low coefficient of 9 where has borosilicate glass, used to make glass objects is 4.5.

## Thermal Expansion by State of Matter

Thermal expansion varies between solids, liquids and gases. Solids generally keep their shape unless they're constrained by a container. They expand as their area changes with respect to their original area in a process called areal expansion or superficial expansion, as well as their volume changing with respect to original volume through volumetric expansion. These different dimensions let you measure expansion of solids in many forms.

Liquid expansion is much more likely to take the form of the container, so you can use the volumetric expansion to explain this. The linear coefficient of thermal expansion for solids is ​α​, the coefficient for liquids is ​β​ and the thermal expansion of gases is the ideal gas law

PV=nRT

for pressure ​P​, volume ​V​, number of moles ​n​, gas constant ​R​ and temperature ​T​.