Gas: Pressure, volume, and temperature

Michael and Leon are playing table tennis. Oops! I stepped on the ball. Look, it’s dented. We can’t play with this, it’s broken!

Well actually, the ball isn't broken, the plastic is just dented — there's no hole, so the air is still in there. Oh, I know how to fix that! We just need to put it in hot water! Leon is right, heating the dented ball can fix it. But how does that work?

It works because of the relationship between pressure, volume, and temperature of the gas that fills the ball. Let’s take volume and temperature first. The ping pong ball is a plastic sphere that contains a certain amount of air. The air can’t move in or out of the ball. When you put the dented ball in hot water, the air inside heats up and expands.

The expanding air takes up more space, so it pushes on the inner walls of the ball and forces the dented plastic outwards. This makes the ball round in shape again. This relationship between the volume and temperature of a gas is known as Charles’s law. According to this law, the ratio of volume to temperature of a given amount of gas, is constant when the pressure is constant. This means that, if the pressure remains the same, the volume of a certain amount of gas increases proportionally to the increase in temperature.

A decrease in temperature, on the other hand, will cause a proportional decrease in volume. Okay, so we now know how temperature and volume relate to each other. What about temperature and pressure? For this one, we’ll need another example. Have you noticed that aerosol cans, such as spray paints, have a warning that says you should keep them away from sources of heat?

Have you ever wondered why? Aerosol cans contain ingredients that are highly-pressurised. When exposed to high temperatures, the pressure of the gas inside the can increases. After some time, the gas exerts so much pressure on the walls of the container that it explodes. This example illustrates that when volume is constant, increasing temperature causes pressure to increase.

The relationship between pressure and temperature of a gas is described by Amonton's law, also referred to as Gay-Lussac's law. This law states that pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature. In other words, the ratio of pressure to temperature is constant when volume is constant. Now, what about pressure and volume? Let’s take that spray can again.

Inside the can, there are two main ingredients: a gas and a paint material. The gas is highly compressed, so it takes up a small amount of space. But when you press the nozzle, the pressure decreases drastically and the volume of the gas increases. That’s why you can cover a large surface with just one can of spray paint. This example shows that decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure.

And when the pressure decreases, the volume increases. This relationship is stated in Boyle’s law: The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured. The relationships described by Charles’s law, Gay-Lussac's law, and Boyle’s law are three of the so-called gas laws. The gas laws can be applied in approximation to all gases. The ball is fixed!

One more game, Michael? Sure!