If you were caught out in a heavy hail storm you might complain of getting pummelled by the hail; you might say that you felt a force or pressure due to the hail hitting you. Well that is how containers of gas feel when gas particles repeatedly collide with their sides; they feel under pressure.

In the previous two sections of this chapter (Sections 4.3.1 and 4.3.2) we made 2 important statements about the particles within a gas:

They are in "constant random motion" (because they are so far apart that they do not influence or interfere with each other with any forces), and

their speed of movement was related to their internal kinetic energy which depends on the temperature of the gas.

But how does Pressure come into this picture of a gas where its particles are moving around randomly?

Well, if the gas is inside some container, say a box with a lid, as shown below, then the particles will randomly, but regularly, hit against the walls of the container. The force that they exert over an area of the container will be felt by the container as a......pressure!

So, a gas in a contained space will always exert a pressure on its container.

What happens if the gas is heated?

If the temperature of the gas rises then the speed of movement of the gas particles will increase (their kinetic energy will increase); we stated this above. But what will this do to the pressure exerted on the container?

Well, if the particles move faster then they will collide with the sides of the container more often; more collisions will be felt as more pressure.

So, it is simple, as the temperature of a gas is increased (in a fixed volume container) the pressure it exerts will increase.

This is why heating gases in containers can be dangerous and can often cause them to "blow", in dramatic fashion!

What happens if the volume of the container is reduced?

If the dimensions of the container are reduced, as shown below, then since there is less distance to travel, the particles will hit the sides more often, won't they?

If the particles are hitting the sides more often then the sides will feel more pressure.

So, reducing the volume of the container (whilst keeping the temperature constant; let's not change too many things at once!) increases the pressure.

Or, Pressure increases as Volume decreases.

This is why balloons burst when you squeeze them, reducing their volume, increasing the pressure of the air within until the material gives way.

Alternatively, if we increase the volume of the container then the particles will have further to travel before they collide with the sides, so there will be less collisions and so less pressure.

Therefore, Pressure decreases as Volume increases.

In the section above we explained briefly why a gas produces a pressure within a container and why the pressure increases/decreases as the volume decreases/increases. In this section we need to delve a little deeper into what is happening and learn how to calculate how the pressure changes with volume. But don't worry; its not difficult.

We can rewrite the statement in bold, above, as:

Pressure is inversely proportional to Volume, when a gas is at constant temperature.

As an equation we can write this as:

What this equation tells us is that the product of pressure and volume always remains constant for a gas (at a fixed temperature). So, if either the pressure or the volume is changed, the product will not change!

This simple equation allows us to do some clever calculations concerning gases.

The basic technique is:

1. Work out, using the equation, the constant (the product *p x V*) with the provided "before" data.

2. Work out, using the same equation, either the new value for pressure or the new value for volume using the constant and the "after" data.

Its time for you to have a go at a few questions by yourself.

Finally, in this section, we need to learn that the overall effect of lots of particles colliding with a surface is that a force is produced at right angles to the surface. This simplifies how we view the forces acting as a result of a gas within a container.

For example, in the diagram below, the overall effect of the yellow particles striking the right side of the container is a force at right angles to that side as shown.

(Why are there 2 green force arrows?

Well, the particles push on the side but the side must push back, mustn't it? Otherwise it would move or break/burst, which could happen if the pressure becomes too great.)

We have already described how increasing the temperature of a fixed volume of gas will increase its pressure.

Reminder: Increasing the temperature of the gas increases the kinetic energy of the particles which increases their speed and since they then collide with the walls of the container more often, the container feels a greater pressure

So, one way to increase the pressure of a gas is to fix the volume of its container but increase its temperature.

Another way to increase the pressure of a gas is to do the obvious thing which is to squash it, to decrease the volume of its container.

This is a mechanical way of increasing the pressure and to do so we have to exert a force on the gas. When we exert a force on the gas we move it (squash it inwards).

This means that we do Work on the gas!

Remember, Work is the transfer of energy by a force.

So, not surprisingly, we do Work or we use Energy, when we exert a force on a gas to try to squash it. OK?

So far so good.

What happens to the gas when we do this?

Well, if we put Energy into the system by doing Work on it, then that system must somehow show signs of gaining Energy.

If the container is not allowed to expand, then the only other way that the system will reveal an increase in its Energy is that the Internal Energy of the gas particles will increase which we will see as an increase in the gas temperature.

If the container is allowed to expand then we would most likely see both an increase in the volume of the gas and some rise in its internal energy and temperature. A good example of this is when we pump up a bicycle tyre; the inner tube of the tyre is allowed to expand but only up to a limit, so as we pump and pump, the tyre gets harder and the air inside the pump and the inner tube gets hotter (if you touch the valve within seconds after pumping, it will feel distinctly hot).