WHAT IS VOLUMETRIC DILATION? (WITH EXAMPLES) - PHYSICAL - 2025

The volume expansion is a physical phenomenon involving a change in the three dimensions of a body. The volume or dimensions of most substances increase when they are subjected to heat; This is a phenomenon known as thermal expansion, however there are also substances that contract when heated.

Although the volume changes are relatively small for solids, they are of great technical importance, especially in situations where it is desired to join materials that expand differently.

The shape of some solids is distorted when heated and can expand in some directions and contract in others. However, when there is only dilation in a certain number of dimensions, there is a classification for such expansions:

• Linear dilation occurs when variation in a particular dimension predominates, such as the length, width, or height of the body.
• Surface dilation is one where variation in two of the three dimensions predominates.
• Finally, volumetric dilation implies a variation in the three dimensions of a body.

Basic concepts related to thermal expansion

Thermal energy

Matter is made up of atoms that are in continuous motion, either moving or vibrating. The kinetic (or motion) energy with which atoms move is called thermal energy, the faster they move, the more thermal energy they have.

Hot

Heat is the thermal energy transferred between two or more substances or from one portion of substance to another on a macroscopic scale. This means that a hot body can give up part of its thermal energy and affect a body close to it.

The amount of heat energy transferred depends on the nature of the nearby body and the environment that separates them.

Temperature

The concept of temperature is fundamental to study the effects of heat, the temperature of a body is the measure of its ability to transfer heat to other bodies.

Two bodies in mutual contact or separated by a suitable medium (heat conductor) will be at the same temperature if there is no heat flow between them. Similarly, a body X will be at a higher temperature than a body Y if heat flows from X to Y.

What are the basic properties of thermal expansion?

It is clearly related to a change in temperature, the higher the temperature, the greater the expansion. It also depends on the internal structure of the material, in a thermometer, the expansion of mercury is much greater than the expansion of the glass that contains it.

What is the fundamental cause of thermal expansion?

An increase in temperature implies an increase in the kinetic energy of the individual atoms in a substance. In a solid, unlike a gas, the atoms or molecules are closely together, but their kinetic energy (in the form of small, rapid vibrations) separates the atoms or molecules from each other.

This separation between neighboring atoms becomes greater and greater and results in an increase in the size of the solid.

For most substances under ordinary conditions, there is no preferred direction in which thermal expansion occurs, and increasing temperature will increase the size of the solid by a certain fraction in each dimension.

Linear dilation

The simplest example of dilation is expansion in one (linear) dimension. Experimentally it is found that the change in length ΔL of a substance is proportional to the change in temperature ΔT and the initial length Lo (Figure 1). We can represent this in the following way:

DL = aLoDT

where α is a coefficient of proportionality called the coefficient of linear expansion and is characteristic of each material. Some values ​​of this coefficient are shown in table A.

The coefficient of linear expansion is higher for materials that experience greater expansion for each degree Celsius that their temperature rises.

Superficial dilation

When a plane is taken within a solid body, so that this plane is the one that undergoes thermal expansion (Figure 2), the change in area ΔA is given by:

DA = 2aA0

where ΔA is the change in initial area Ao, T is the change in temperature, and α is the coefficient of linear expansion.

Volumetric dilation

As in the previous cases, the change in volume ΔV can be approximated with the relationship (Figure 3). This equation is usually written as follows:

DV = bVoDT

where β is the coefficient of volumetric expansion and is approximately equal to 3∝ Λ∝ τ∝ ßλ∝ 2, the values ​​of the coefficients of volumetric expansion for some materials are shown.

In general, substances will expand under an increase in temperature, water being the most important exception to this rule. Water expands when its temperature increases when it is greater than 4ºC.

However, it also expands when its temperature decreases in the range of 4 ° C to 0 ° C. This effect can be observed when water is put into a refrigerator, the water expands when it freezes and it is difficult to remove the ice from its container due to this expansion.

Examples

Differences in volumetric expansion can lead to interesting effects at a gas station. An example is gasoline dripping into a tank that has just been filled on a hot day.

The gasoline cools the steel tank when it is poured, and both the gasoline and the tank expand with the temperature of the surrounding air. However, gasoline expands much faster than steel, causing it to leak out of the tank.

The difference in expansion between gasoline and the tank containing it can cause problems when reading the fuel level gauge. The amount of gasoline (mass) remaining in a tank when the gauge reaches empty is much less in the summer than in the winter.

Gasoline has the same volume in both stations when the warning light comes on, but because gasoline expands during the summer, it has a lower mass.

As an example, you can consider a full steel gas tank, with a capacity of 60L. If the temperature of the tank and gasoline is 15ºC, how much gasoline will be spilled by the time they reach a temperature of 35ºC?

The tank and gasoline will increase in volume with the increase in temperature, but the gasoline will increase more than the tank. So the spilled gasoline will be the difference in your volume changes. The volumetric expansion equation can then be used to calculate the volume changes:

The volume spilled by the increase in temperature is then:

Combining these 3 equations in one, we have:

From table 2 the values ​​of the volumetric expansion coefficient are obtained, substituting values:

Although this amount of spilled gasoline is relatively insignificant compared to a 60L tank, the effect is surprising, as gasoline and steel expand very quickly.

Bibliography

1. Yen Ho Cho, Taylor R. Thermal Expansion of Solids ASM International, 1998.
2. H. Ibach, Hans Lüth Solid-State Physics: An Introduction to Principles of Material Science Springer Science & Business Media, 2003.
3. Halliday D., Resnick R., Krane K. Physics, Volume 1. Wiley, 2001.
4. Martin C. Martin, Charles A. Hewett Elements of Classical Physics Elsevier, 2013.
5. Zemansky Mark W. Heat and Thermodynamics. Editorial Aguilar, 1979.