An easy toy system is a collection of perfect billiard balls on a perfect pool table, that is, one without rolling friction and where all collisions conserve energy. For a few billiard balls it would be quite easy to extract all of their energy as work if you know their initial positions and velocities. There are plenty of ways to do it, and it’s fun to think of them. This means they are at 0 temperature.
If you don’t know the microstate, but you do know the sum of the square of their velocities, which is a constant in all collisions, you can still tell some things about the process. For instance, you can predict the average number of collisions with one wall and the corresponding energy, related to the pressure. If you stick your hand on the table for five seconds, what is the chance you get hit by a ball moving faster than some value that will cause pain? All these things are probabilistic.
In the limit of tiny billiard balls compared to pool table size, this is the ideal gas.
An easy toy system is a collection of perfect billiard balls on a perfect pool table, that is, one without rolling friction and where all collisions conserve energy. For a few billiard balls it would be quite easy to extract all of their energy as work if you know their initial positions and velocities. There are plenty of ways to do it, and it’s fun to think of them. This means they are at 0 temperature.
If you don’t know the microstate, but you do know the sum of the square of their velocities, which is a constant in all collisions, you can still tell some things about the process. For instance, you can predict the average number of collisions with one wall and the corresponding energy, related to the pressure. If you stick your hand on the table for five seconds, what is the chance you get hit by a ball moving faster than some value that will cause pain? All these things are probabilistic.
In the limit of tiny billiard balls compared to pool table size, this is the ideal gas.