Thermal Properties of Matter:
Some Basic Concepts

• Pressure is produced by molecular collisions between a gas and its surroundings. The kinetic theory of gases relates the observable (macroscopic) properties of a gas (such as pressure) to the unobservable (microscopic).
• Pressure is a function of the average speed of molecules in an ideal gas in two independent ways, hence P is proportional to (v_av)². The two independent ways are
  • through the momentum mv_av of each molecule that hits a container wall
  • through the fact that the frequency with which the molecules hit the container wall increases as their average speeds increase.
  Thus we can conclude that pressure is proportional to average kinetic energy (1/2)m(v_av)².
• An ideal gas has molecules with no spatial size that collide only with the wall of the container and not with each other. A real gas approaches "ideal" conditions at low temperature and pressure (such as in a constant-volume gas thermometer).
• Temperature in an ideal gas is also proportional to the average kinetic energy of molecules. Since kinetic energy is never negative, the equations relating these two things are based on absolute (Kelvin) temperature T:
  • PV = nRT
  • (1/2)m(v_av)² = (3/2)kT.
• Since kinetic energy is always being transferred between molecules and the environment, a gas can never be chilled all the way to absolute zero Kelvin temperature (you would have to have something already at absolute zero to which you can conduct away the remaining heat energy!).
• Root mean-squared speed of certain molecules in a mixed gas at temperature T is defined as:
  Ö(v²)_av = v_rms = Ö[(3kT)/m].
  According to this equation, lighter molecules travel faster than heavier ones when they are together at the same temperature.
• At standard atmospheric temperature and pressure (S.T.P), v_rms is several hundred to several thousand meters per second. The speed of sound at S.T.P. is 330 m/s. It makes sense for the speed of sound to be slower than the average speed of molecules communicating the sound energy by collisions.