# Charles' Law

Charles' Law, named after Jacques Charles, says that for a gas confined in a flexible container, the volume is directly proportional to the temperature. In English this means that as a gas is heated, it expands and as it cools, it contracts. This, of course, only works in a container that can change volume easily. As we have already said, the volume of gas in a 2-liter bottle is two liters and temperature cannot affect that. So, Charles' Law only works in containers like hot air balloons (with soft, non-stretchy sides) or pistons that move freely.

Charles' Law can be stated mathematically:

and it can be shown graphically:

Note that this graph is similar to the one for Gay Lussac's Law (with temperature on the horizontal axis). That means that in this case (as in the case for Gay Lussac's Law) we can use this graph to determine absolute zero. By extrapolating back to the temperature at which the volume would be zero, we can determine the temperature at which the particles stop moving (the only way they would not take up their entire container). This temperature, as it is for Gay Lussac's Law, is -273.15 oC, the base of the Kelvin scale.

Why are temperature and volume directly related? The answer here is more complex than it is for Gay Lussac's Law or Boyle's Law. In fact, you need to understand each of those laws to make sense of Charles' Law. So, if you aren't sure about the why's behind those two laws, go back and read them now.

To understand Charles' Law we need to have an appropriate situation in mind. Let's picture a hot air balloon – soft flexible sides and a burner underneath that can be turned on and off to control the temperature. Now, if the balloon is not currenly getting bigger or smaller, then we know that the force on the walls of the balloon are equal. That is, we know that the air inside is pushing out exactly as hard as the air outside is pushing in. If the forces weren't equal, the sides would be moving and the volume would change as a consequence.

If the burner at the bottom of the balloon is turned on the gas trapped in the balloon will get hotter. As a result, the particles will move faster and hit the walls of the balloon harder and more often (Gay Lussac's Law). As a result, the force pushing out on the walls of the balloon will become larger than the force pushing in on those walls. With unbalanced forces, the walls will begin to move out.

As the walls of the balloon move out, the volume of the balloon increases. This means that it will take longer for the particles to get from wall to wall, they will hit the walls less often and the pressure inside the balloon will go down. This will continue until the force in (from the atmosphere) and the force out (from the air in the balloon) are once again equal.

In the end, the pressure will be what it was before and the only changes will have been the temperature and the volume.

Putting that all together, increasing the temperature causes an initial increase in pressure (Gay Lussac's Law). This increase in pressure will cause the walls to move out (increasing volume) until the pressure drops back down (Boyle's Law) to what it was before. Of course this can all happen so quickly that no change in pressure may be observed, but there is no other way to explain why the volume increases.