Lesson 2 - Gas Laws

The relationships between pressure, volume, and the temperature of gases have been studied for many years. One of the results of this study is the concept of a perfect or ideal gas. This is essentially a concept of a gas which behaves predictably to a set of mathematical laws (or equations): the so-called ‘ideal gas’ laws. Many actual gases can be considered ideal for most practical purposes under certain conditions of pressure and temperature.

Boyle’s law suggests that for a fixed mass of gas at a fixed temperature, the pressure (P) is inversely proportional to its volume (V). This is shown below:

What does this mean? If we trap a mass of gas and increase the pressure on it, the volume will reduce by the same proportion.

Why not try it for yourself? Get a syringe (without the needle), or a bicycle pump and draw up the plunger to fill the cylinder with a mass of air. Put your finger over the end of the syringe and start to push the plunger down, thereby reducing the volume of the air trapped in the syringe. What do you notice? You have to apply more force on the plunger to apply more pressure on the air. Reducing the air volume, or compressing it, requires an increase in pressure.

If we rearrange the above situation, it would suggest that for a fixed mass of gas at a constant temperature, the pressure P and volume V before and after compression are related:

We should note here that we use the absolute pressure values for P₁ and P₂.

If we double the pressure on a gas, its volume is halved and so on. Let’s look at an example of this.

Example:

A bicycle pump is filled with 1 L of air at a pressure of 100 kPa a, by fully pulling back the plunger. At this point, the end of the pump is sealed, and the plunger is pushed in to decrease the volume to 0.8 L. Temperature can be assumed to be fixed, and no air is lost. What would the pressure be when the volume is 0.8 L?

Using Boyle’s law and rearranging for the parameter we are interested in – P₂:

Substituting the values, we know:

Please note we have used absolute pressure in pascals, and volume in m³.

Boyle’s law deals with the relationship between gas pressure and volume.

Robert Boyle (1627-1691) was an Anglo-Irish chemist, physicist, inventor, and theologian. Amongst many other fields of interest, he was concerned with the behaviour of air and how its pressure and volume were related. He and his assistant Robert Hooke built an apparatus to investigate it – the rather grandly titled ‘Pneumatical Engine’. Boyle published the results in an article titled Touching the Spring of Air and Its Effects, suggesting that the volume of air would reduce (or compress) under the action of pressure (or an applied force).

It is probably not due to chance that Robert Hooke proceeded to define his own law in which the force applied to a mechanical spring can be related to the spring’s compression.

Let us now consider the relationship between volume and temperature.