How does the ideal gas law work?

[pelmel92]

So here's what has me all confuzzled about the relationship between temperature and pressure:

Temperature is proportionate to average kinetic energy... but why does expanding a container lower the KEavg of the container's gaseous contents? Shouldn't the conservation of momentum keep all the particles moving along at the same average velocity? What exactly is slowing them down, or in the case of reduced container volume, speeding them up?

 

[Ygggdrasil]

Since PV = nRT, if you expand a container without changing the pressure or number of moles of gas, the average kinetic energy of the gas molecules will increase, not decrease.

This makes sense when you consider the requirement for constant pressure. To maintain a constant pressure, the gas molecules must exert the same force per unit area against the walls of the container. However, if the gas expands and the number of moles of gas remain the same, collisions with the walls of the container will be less frequent (in part because you've increased the area of the container). Therefore, to maintain the same pressure, these collisions must be more forceful, requiring the gas molecules to have a higher kinetic energy. Expanding a gas at constant pressure therefore requires an input of heat energy into the gas.

Now, this refers to just one way of making a gas expand. There are many other ways to make a gas expand. For example, it is possible to make a gas expand and decrease its temperature if you decrease the pressure enough. As you note, however, a decrease in temperature means a decrease in the kinetic energy of the gas. Where does that lost kinetic energy go? In this case, the expanding gas is performing work on the environment (imagine an expanding gas pushing a piston against a load). Therefore, the "lost" kinetic energy is really being used to perform work.