3. The gas laws
Boyle's Law and Charles' Law P.15
Graph of pressure against volume
Picture 3.3. Graph of pressure against volume. As you double the volume, the pressure halves. Four times the volume and the pressure quarters. Pressure is inversely proportional to volume.
Boyle’s Law
This is a gas law that relates the volume of a gas to the pressure. We find that the pressure produced by a fixed mass of gas increases as the volume decreases. The gas is held at a constant temperature. More precisely, we find that:
pressure is inversely proportional to the volume
Graph of pressure against volume
Picture 3.4. Measuring pressure against volume. Pulling the plunger out reduces the pressure.
in symbols Pressure µ 1/volume
we can write this as:  P = constant/V
or P.V = constant
Reducing volume increases pressure
Picture 3.5. The particles in a pump collide with the walls. If the volume is halved, each particle collides twice as often. (The temperature (and therefore the speed) of the particles is the same throughout.

Making sense of Boyle’s law
Imagine some gas trapped inside a container - say a bicycle pump. The gas produces a pressure because its particles are colliding with the walls. Now think of just one of its particles, moving back and forth. Let’s say it makes 300 collisions every second;
  • now, we halve the width of the box
  • this halves its volume.
  • Now the particle has half as far to travel;
  • so it makes twice as many collisions with the walls.
  • Each collision is the same strength as before.
  • So the pressure is doubled.

Note that the volume has to be reduced gently so as not to increase the temperature of the gas (see page 12). This sort of change is called isothermal.

Graph of volume agains temperature
Picture 3.6. Graph of Charles Law. Volume is proportional to absolute temperature.
Charles’ law
The final gas law relates the volume to the temperature (at constant pressure). We can set up an experiment to measure the effect of increasing temperature on a fixed mass of gas. We find that, as the temperature rises, so the volume increases. In fact
volume is proportional to absolute temperature
in symbols Volume µ Temperature
we can write this as:  V = constant.T
or V/T = constant
Charles law appartus
Picture 3.7. Lab apparatus for Charles' Law. Increasing the temperature (on the right) increases the volume.
Making sense of Charles’ law
The best way to think of Charles’ law is to think of the other two laws combining to try to keep the pressure constant.
  • So, if we double the temperature (with the volume constant)
  • The pressure will double
  • To get back to the original pressure, we need to allow the volume to double.
  • So doubling the temperature will make the volume double whilst keeping the pressure constant.
Question 12
Butane has the formula C4H10. It is based on a chain of 4 carbon atoms. This means that it can have rotational kinetic energy as well as translational KE. That means, when we heat it up, its molecules will spin around faster as well as moving faster.

a) What effect do you think this will have on how its pressure behaves with temperature?

Click shift/return to get a line break in your answer
b) Explain your answer.

top start units pages

Summary                                           Close
  • an ideal gas obeys the gas laws, including . . .
  • volume is proportional to absolute temperature
  • pressure is inversely proportional to volume