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# Kinetic Theory of Matter

by Ron Kurtus (revised 26 November 2011)

The Kinetic Theory of Matter states that matter is composed of a large number of small particles—individual atoms or molecules—that are in constant motion. This theory is also called the Kinetic Molecular Theory of Matter and the Kinetic Theory.

By making some simple assumptions, such as the idea that matter is made of widely spaced particles in constant motion, the theory helps to explain the behavior of matter. Two important areas explained are the flow or transfer of heat and the relationship between pressure, temperature, and volume properties of gases.

Questions you may have include:

• What are the assumptions of the kinetic theory of matter?
• How does this explain heat flow?
• How does the theory explain pressure and volume?

This lesson will answer those questions.

Useful tool: Metric-English Conversion

## Assumptions of theory

The Kinetic Theory of Matter is a prediction of how matter should behave, based on certain assumptions and approximations. The assumptions are made from observations and experiments, such as the fact that materials consist of small molecules or atoms. Approximations are made to keep the theory from being too complex. One assumption is that the size of the particles is so small that it can be considered a point.

### Matter consists of small particles

The first assumption in this theory is that matter consists of a large number a very small particles—either individual atoms or molecules.

### Large separation between particles

The next assumption concerns the separation of the particles.

• In a gas, the separation between particles is very large compared to their size, such that there are no attractive or repulsive forces between the molecules.
• In a liquid, the particles are still far apart, but now they are close enough that attractive forces confine the material to the shape of its container.
• In a solid, the particles are so close that the forces of attraction confine the material to a specific shape.

### Particles in constant motion

Another assumption is that each particle is in constant motion.

In gases, the movement of the particles is assumed to be random and free. In liquids, the movement is somewhat constrained by the volume of the liquid. In solids, the motion of the particles is severely constrained to a small area, in order for the solid to maintain its shape.

The velocity of each particle determines its kinetic energy.

### Collisions transfer energy

The numerous particles often collide with each other. Also, if a gas or liquid is confined in a container, the particles collide with the particles that make up the walls of a container.

#### Approximations

When atoms or molecules collide, energy may be given off in the form of electromagnetic radiation. Taking this into account could make the theory highly complex, and since the amount of radiation is small in most situations, an approximation is made that this effect is negligible.

Also, atoms and molecules have a discrete size. But charting the collisions of such particles would again make the theory too complex. Thus an approximation is made to say the size of the particles is a simple point, especially compared to the distances involved.

#### No energy change

Thus, an assumption is that the particles transfer energy in a collision with no net energy change. That means the collisions between the particles are perfectly elastic and no energy is gained or lost during the collision. This follows the Law of the Conservation of Energy.

In reality, the collisions are not perfect, and some energy is lost. But for the sake of simplicity in drawing conclusions, this theory makes the collisions elastic.

## Thermal energy and heat flow

The motion of a particle determines its kinetic energy, according to the equation

KE = ½mv²

where

• KE is the kinetic energy of the particle
• m is its mass
• is the square of its velocity

The total internal kinetic energy of all the particles is called its thermal energy.

The temperature of an object or collection of matter is the average kinetic energy of the particles. Faster particles means a higher temperature. A thermometer is used to measure the temperature and put it into temperature degrees instead of kinetic energy units.

The heat is the transfer of thermal energy from an object of higher temperature to one of lower temperature. For example, an object feels warm or hot if its temperature is higher than your skin temperature.

The Kinetic Theory of Matter explains heat transfer by conduction, where thermal energy seems to move through a material, warming up cooler areas. This is called heat transfer or heat flow

Processes not covered in this theory are heat transfer by convection and by radiation.

### Collisions transfer energy

The Kinetic Theory of Matter states that the material's particles have greater kinetic energy and are moving faster at higher temperatures. When a fast moving particle collides with a slower moving particle, it transfers some of its energy to the slower moving particle, increasing the speed of that particle.

If that particle then collides with another particle that is moving faster, its speed will be increased even more. But if it hits a slow moving particle, then it will speed up the third particle.

With billions of moving particles colliding into each other, an area of high energy or high heat will slowly diffuse across the material, making other areas warm too. By the Conservation of Energy, the total energy or total heat of the object will remain the same, but the heat will be evenly distributed throughout the object.

### Rate of transfer

The rate at which the kinetic or thermal energy is transferred from one particle to another depends on the separation of the particles and their freedom to move.

In a gas, the particles are allowed to move freely, but their separation distance is great, so heat or energy transfer is slow. In a liquid, the heat transfer by conduction is faster because the particles are closer together.

In a solid, the molecules are constrained into a specific location within the material. Although the particles are closer together than in liquids, the constraints in some materials actually prevent the transfer of heat energy. A good example of that is in wood.

### Temperature

One important result of the kinetic theory is that the average molecular kinetic energy is proportional to the absolute temperature of the material. Absolute temperature is measured in the Kelvin scale. But in general, you can say that temperature is the measurement of the average internal kinetic energy of the material or object.

## Pressure, volume and temperature

If a gas is enclosed in a container, it exerts pressure on the walls of the container. The Kinetic Theory of Matter explains gas pressure as the total force exerted by gas molecules colliding against the walls of a container.

If the container can expand, like with a balloon or cylinder and piston, increasing the pressure can increase the volume. Like, the balloon will get bigger. Also, if you increase the temperature of the gas--and thus the kinetic energy of its molecules—you increase the pressure or the volume of the container.

This leads to a relationship between pressure, volume and temperature in an ideal gas. (An ideal gas is a gas that follows the assumptions of the Kinetic Theory of Matter.) The relationship is

PV = NkT

where:

• P is the pressure of the ideal gas
• V is the volume of the gas container
• N is the number of gas particles
• k is the Boltzman constant in joule per kelvin per particle
• T is the temperature in the absolute or kelvin scale

This equation has a number of implications, including:

• If you decrease the pressure and hold the volume constant, the temperature decreases (principle of a refrigerator)
• If you increase the temperature and hold the pressure constant, the volume increases (heating a balloon)

## Summary

The Kinetic Theory of Matter states that matter is composed of a large number a small particles that are in constant motion. It also assumes that particles are small and widely separated. They collide and exchange energy. The theory helps explain the flow or transfer of heat and the relationship between pressure, temperature and volume properties of gases.

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## Resources and references

Ron Kurtus' Credentials

### Websites

Kinetic Theory - HyperPhysics

Physics Resources

### Books

Introduction to Thermodynamics and Kinetic Theory of Matter by Anatoly I. Burshtein; Wiley-Interscience (1995)

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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