Objectives:

• To learn that the molecules of a gas are in constant random motion.
• To identify the link between the temperature of a gas and the kinetic energy of the molecules.
• To understand that when the molecules collide with the wall of their container they exert a force on the wall. The total force exerted by all of the molecules inside the container on a unit area of the walls is the gas pressure.
• To appreciate that changing the temperature of a gas, held at constant volume, changes the pressure exerted by the gas.

Gases can be difficult to see; take air for example, we breath it and require it to live but we see right through it (fortunately!), it is transparent. Therefore we have to rely on the effect that air has on other particles/ gases around it to observe the motion of the particles.

Brownian Motion

A quite effective method for observing the motion of gas particles is using a smoke cell underneath a microscope. Smoke from a match of a wick of some kind can be channelled into a container that is previously full of air (or using everyday terminology – is empty). The smoke cell should have a light source in it that is directed at the smoke particles, since air is transparent it transmits light through it, the smoke however will reflect the light and allow it to go up and out of the smoke cell.

By placing this smoke cell under a microscope, the light that it reflected off of the smoke will be directed into an observers eye to be seen. Since the rest of the air does not reflect the light, the areas around the smoke particles will appear dark. In other words, by looking down the microscope (that is focussed appropriately) the individual smoke particles can be seen and their motion observed. The following short clip shows this quite well;

How amazing to actually be able to see and observe a single particles motion?!

The important points to note can be witnessed by watching the clip above and focusing on a single smoke particle;

1. What do you notice about its motion?
2. What is causing this motion?
3. If there is a motion this must be due to some ‘other effect’, but what?

1. What do you notice about its motion? A single particle will move completely randomly, going in one direction and then quickly changing again. It seems to be ‘jiggling around’.
2. What is causing this motion? As you know, (in Physics) for a particle to change the direction of its motion it must have a force acting upon it (Netwon’s 2nd law of motion: $F = ma$), but where is this force coming from?
3. If there is a motion this must be due to some ‘other effect’, but what? The smoke particles are of course not the only gas particles that are in the area being observed, they are surrounded by invisible air particles. The smoke particles are striking into these air particles which causes them to change direction, shortly after they strike into another particle and so on and so on. This leads to the gas particles undergoing a random motion. This random motion has been name Brownian Motion, after a microscopist named Robert Brown who observed this effect when studying pollen particles emmersed in water.

So that’s it, Brownian Motion – the random motion of gas particles. If you were to imagine being a single air particle amongst all of the other countless air particles inside a balloon lets say. You would constantly be colliding with other air particles all around you. The following attempts to show this random motion by tracing a single particle for a period of time:

This animation, shows that the particles in a gas are constantly moving and with random directions and speeds. Depending on the angle of a collision and force involved will result in different speeds of each particle. If you were to take an average speed of all of the particles in a system, what do you think governs this average speed and how could it be increased or decreased?

If you think back to the internal energy of a particle, it is equal to the sum of the kinetic and potential energy stores. The potential energy stores describes the energy in the bonds between particles, the motion or speed of the particles is described by the kinetic energy of the particle. So, by increasing the kinetic energy stores of the particle, the speeds of the particle can increased. This is shown by the equation for kinetic energy;

$E_{k} = \frac{1}{2}mv^{2}$

where;
$E_{k}$ is the kinetic energy
$m$ is the mass of the particle
$v$ is the velocity of the particle

By linking back to all earlier points in the topic ‘Particle Model of Matter’, the method to increase the kinetic energy store is by heating it up. The temperature of the gas is related to the average energy in the kinetic energy stores of the gas particles. So by increasing the temperature of the system, the particles move faster; the higher the temperature, the higher the average energy.

Gases in containers

As gas particles move about at high speeds, they bang into each other and whatever else happens to get in the way. When they collide with a surface (or the wall of their container for example), they exert a force on it.

The surface will inevitably have an area, and so there is a pressure that is exerted onto the container. Pressure is force per unit area and as such the equation for it is;

$P = \frac{F}{A}$

where;
$P$ is the pressure measured in $N/m^{2}$ of $Pa$ (for Pascals)
$F$ is the force measured in Newtons, $N$
$A$ is the surface area measured in metres squared, $m^{2}$

This all means that the gas particles exert a pressure onto a surface. In a sealed container, the outward gas pressure is the total force exerted by all of the particles in the gas on a unit area of the container walls.

If the particles are forced to move faster, by increasing their temperature, there will be more collisions with the walls of the container and as such there will be a greater overall net force on the surface and so also an increased gas pressure.

For a system with a constant volume (a solid metal container for example); by increasing temperature of a system, there will be an increase in the speed and the number of collisions, this then ultimately gives rise to the pressure of the system.