## Boltzmann Diagrams

If you pay attention to the cars on the highway, you will notice that they are not all moving at the same speed (pretty obvious), but what you may not have noticed is that most of them are going about the same speed.) If the average speed on the highway is 72 miles per hour (mph) (a fairly common speed ona highway with a speed limit of 65) you'll see that lots of people are going about that speed, some a few mph over 72 and some a few mph under 72. In fact if you drive at the average speed for a long distance, you'll find yourself passing and being passed by the same other cars over and over again.

Of course not everyone goes at the average speed. There are some cars and trucks that drive faster, some considerably faster, but far fewer of them. Not that many cars are built to go considerably above 80 mph and very few can handle speeds over 90. Even those cars that can do such speeds are usually driven by people who don't like to pay speeding tickets and therefore don't push their engines that much.

At the same time there are people who are driving slower. There is a sizable group of people who will be going about 65 mph (it is the speed limit after all), and a much smaller group going around 40 mph (the lower speed limit on many highways), and there are always a few cars pulling onto or off of the highway, or slowly drifting onto the berm to deal with a flat tire.

The result is that a graph of the number of cars v. speed would look something like this:

This bell shaped curve shows in a simple graphical form all of the things said above. There are lots of cars traveling close the average speed, with far fewer traveling much faster or much slower. The highest point on the graph occurs at the average speed.

Of course this isn't really about cars on the highway at all. This is about molecules. In any group of molecules (the water in a glass, the air in your room, the metal in the leg of your school desk), there are different speeds. Some molecules are moving very fast and some very slow, but most of them are moving at about the average speed. This relationship was first discussed by Boltzmann and this curve (at least when applied to molecules) is called the Boltzmann diagram.

It is also important to understand how temperature affects the movement of molecules and therefore the Boltzmann curve.