Boltzman and Temperature

A typical Boltzman Diagram looks like this:

But what happens when the temperature is changed? We know that temperature is a measure of the average kinetic energy and that kinetic energy and speed are related. So if we raise the temperature, the average speed goes up, but what happens to the rest of the molecules?

Using the highway analogy with which we introduced the Boltzmann diagram, we can imagine what would happen if the speed limit were increased.

With a higher speed limit the average driver will be going faster, however not all cars are equally capable of going faster. Those drivers with cars capable of going at high speeds will move at higher speeds but many drivers will not be able to speed up proportionately. This is especially true of those drivers entering or leaving the highway who will be just speeding up or slowing down and of course a driver pulling off with a flat tire will of course be barely moving. This means that the average increases, but that the spread of speeds increases. In other words, the same number of cars are now spread over a larger range of speeds.

Again, this is not about cars, but molecules. At higher temperatures, molecules move faster, but not all molecules more proportionally faster. Like the cars, the range of speeds of the molecules grows with a few still going very slowly and some going very fast. Because the same molecules are now covering a broader range, not as many molecules are going at the average speed.

The final result is that at a higher temperature, the graph shifts to the right and gets lower.

When the temperature is decreased the opposite happens – the average goes down, the graphs shrinks horizontally to the left and increases vertically.