# Thermal Expansion - How it works

### Molecular Translational Energy

In scientific terms, heat is internal energy that flows from a system of relatively high temperature to one at a relatively low temperature. The internal energy itself, identified as thermal energy, is what people commonly mean when they say "heat." A form of kinetic energy due to the movement of molecules, thermal energy is sometimes called molecular translational energy.

Temperature is defined as a measure of the average molecular translational energy in a system, and the greater the temperature change for most materials, as we shall see, the greater the amount of thermal expansion. Thus, all these aspects of "heat"—heat itself (in the scientific sense), as well as thermal energy, temperature, and thermal expansion—are ultimately affected by the motion of molecules in relation to one another.

#### MOLECULAR MOTION AND NEWTONIAN PHYSICS.

In general, the kinetic energy created by molecular motion can be understood within the framework of classical physics—that is, the paradigm associated with Sir Isaac Newton (1642-1727) and his laws of motion. Newton was the first to understand the physical force known as gravity, and he explained the behavior of objects within the context of gravitational force. Among the concepts essential to an understanding of Newtonian physics are the mass of an object, its rate of motion (whether in terms of velocity or acceleration), and the distance between objects. These, in turn, are all components central to an understanding of how molecules in relative motion generate thermal energy.

The greater the momentum of an object—that is, the product of its mass multiplied by its rate of velocity—the greater the impact it has on another object with which it collides. The greater, also, is its kinetic energy, which is equal to one-half its mass multiplied by the square of its velocity. The mass of a molecule, of course, is very small, yet if all the molecules within an object are in relative motion—many of them colliding and, thus, transferring kinetic energy—this is bound to lead to a relatively large amount of thermal energy on the part of the larger object.

#### MOLECULAR ATTRACTION AND PHASES OF MATTER.

Yet, precisely because molecular mass is so small, gravitational force alone cannot explain the attraction between molecules. That attraction instead must be understood in terms of a second type of force—electromagnetism—discovered by Scottish physicist James Clerk Maxwell (1831-1879). The details of electromagnetic force are not

B ECAUSE STEEL HAS A RELATIVELY HIGH COEFFICIENT OF THERMAL EXPANSION , STANDARD RAILROAD TRACKS ARE CONSTRUCTED SO THAT THEY CAN SAFELY EXPAND ON A HOT DAY WITHOUT DERAILING THE TRAINS TRAVELING OVER THEM . (
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important here; it is necessary only to know that all molecules possess some component of electrical charge. Since like charges repel and opposite charges attract, there is constant electromagnetic interaction between molecules, and this produces differing degrees of attraction.

The greater the relative motion between molecules, generally speaking, the less their attraction toward one another. Indeed, these two aspects of a material—relative attraction and motion at the molecular level—determine whether that material can be classified as a solid, liquid, or gas. When molecules move slowly in relation to one another, they exert a strong attraction, and the material of which they are a part is usually classified as a solid. Molecules of liquid, on the other hand, move at moderate speeds, and therefore exert a moderate attraction. When molecules move at high speeds, they exert little or no attraction, and the material is known as a gas.

### Predicting Thermal Expansion

#### COEFFICIENT OF LINEAR EXPANSION.

A coefficient is a number that serves as a measure for some characteristic or property. It may also be a factor against which other values are multiplied to provide a desired result. For any type of material, it is possible to

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calculate the degree to which that material will expand or contract when exposed to changes in temperature. This is known, in general terms, as its coefficient of expansion, though, in fact, there are two varieties of expansion coefficient.

The coefficient of linear expansion is a constant that governs the degree to which the length of a solid will change as a result of an alteration in temperature For any given substance, the coefficient of linear expansion is typically a number expressed in terms of 10 −5 /°C. In other words, the value of a particular solid's linear expansion coefficient is multiplied by 0.00001 per °C. (The °C in the denominator, shown in the equation below, simply "drops out" when the coefficient of linear expansion is multiplied by the change in temperature.)

For quartz, the coefficient of linear expansion is 0.05. By contrast, iron, with a coefficient of 1.2, is 24 times more likely to expand or contract as a result of changes in temperature. (Steel has the same value as iron.) The coefficient for aluminum is 2.4, twice that of iron or steel. This means that an equal temperature change will produce twice as much change in the length of a bar of aluminum as for a bar of iron. Lead is among the most expansive solid materials, with a coefficient equal to 3.0.

#### CALCULATING LINEAR EXPANSION.

The linear expansion of a given solid can be calculated according to the formula δ L = aL O Δ T. The Greek letter delta (d) means "a change in"; hence, the first figure represents change in length, while the last figure in the equation stands for change in temperature. The letter a is the coefficient of linear expansion, and L O is the original length.

Suppose a bar of lead 5 meters long experiences a temperature change of 10°C; what will its change in length be? To answer this, a (3.0 · 10 −5 /°C) must be multiplied by L O (5 m) and δ T (10°C). The answer should be 150 & 10 −5 m, or 1.5 mm. Note that this is simply a change in length related to a change in temperature: if the temperature is raised, the length will increase, and if the temperature is lowered by 10°C, the length will decrease by 1.5 mm.

#### VOLUME EXPANSION.

Obviously, linear equations can only be applied to solids. Liquids and gases, classified together as fluids, conform to the shape of their container; hence, the "length" of any given fluid sample is the same as that of the solid that contains it. Fluids are, however, subject to volume expansion—that is, a change in volume as a result of a change in temperature.

To calculate change in volume, the formula is very much the same as for change in length; only a few particulars are different. In the formula δ V = bV O δ T , the last term, again, means change in temperature, while δ V means change in volume and V O is the original volume. The letter b refers to the coefficient of volume expansion. The latter is expressed in terms of 10 −4 /°C, or 0.0001 per °C.

Glass has a very low coefficient of volume expansion, 0.2, and that of Pyrex glass is extremely low—only 0.09. For this reason, items made of Pyrex are ideally suited for cooking. Significantly higher is the coefficient of volume expansion for glycerin, an oily substance associated with soap, which expands proportionally to a factor of 5.1. Even higher is ethyl alcohol, with a volume expansion coefficient of 7.5.