Kinetic TheoryIntroduction
Riya's cycle tyre is flat, so she borrows the pump at the puncture shop near her school. Out of curiosity she presses her thumb over the nozzle and pushes the handle down. The handle gets harder and harder to push, and the air shoves her thumb back. Nothing she can see is pushing. So what is?
Boyle, Newton and others already suspected the answer in the 1600s: a gas is made of tiny particles. The full theory, called kinetic theory, was built in the nineteenth century by Maxwell, Boltzmann and others. It pictures a gas as a crowd of molecules rushing about at random. The forces between them matter in solids and liquids, but in a gas the molecules are so far apart that we can almost ignore them.
Below is a box of such molecules. Every kick they give the walls adds to the pressure.
Molecules:
The molecules never stop hitting the walls, and each hit is a small push. Add up millions of millions of pushes every second and you get the steady pressure shown by the purple bar. More molecules means more hits; hotter molecules move faster, so they hit more often and harder.
This chapter turns that picture into physics. It explains pressure and temperature in terms of molecules, agrees with the gas laws and Avogadro's hypothesis, predicts the specific heats of many gases, and even estimates how big a molecule is.
The Plan for This Chapter
First we look at the evidence that matter is made of atoms and molecules, and recall how gases behave: the ideal-gas equation, Boyle's, Charles' and Dalton's laws, and why real gases are not quite ideal. Then we derive the pressure of a gas from molecules bouncing off a wall and discover what temperature really measures. The law of equipartition of energy shares that energy out among the ways a molecule can move, which predicts specific heats. Finally, the mean free path tells us how far a molecule gets before it bumps into another one.
A sealed steel tin of air is warmed from 27 °C to 327 °C. Its volume hardly changes. What happens to the pressure of the air inside?
27 °C is 300 K and 327 °C is 600 K, so the absolute temperature doubles, and so does the pressure. Why the kelvin temperature is the one that counts is one of the big results of this chapter.