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
Picture 3.4. Measuring pressure against volume. Pulling the plunger out reduces the pressure.
Pressure µ 1/volume
we can write this as:
P = constant/V
P.V = constant
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 Boyles 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. Lets 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.
Picture 3.6. Graph of Charles Law. Volume is proportional to absolute temperature.
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
Volume µ Temperature
we can write this as:
V = constant.T
V/T = constant
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.