Summarizing Kinetic Theory

Summary

• Kinetic theory is the atomistic description of gases as well as liquids and solids.
• Kinetic theory models the properties of matter in terms of continuous random motion of atoms and molecules.
• The ideal gas law can also be expressed as

  \(\text{PV}=\cfrac{1}{3}\text{Nm}\overline{{v}^{2}},\)

  where \(P\) is the pressure (average force per unit area), \(V\) is the volume of gas in the container, \(N\) is the number of molecules in the container, \(m\) is the mass of a molecule, and \(\overline{{v}^{2}}\) is the average of the molecular speed squared.
• Thermal energy is defined to be the average translational kinetic energy \(\overline{\text{KE}}\) of an atom or molecule.
• The temperature of gases is proportional to the average translational kinetic energy of atoms and molecules.

  \(\overline{\text{KE}}=\cfrac{1}{2}m\overline{{v}^{2}}=\cfrac{3}{2}\text{kT}\)

  or

  \(\sqrt{\overline{{v}^{2}}}={v}_{\text{rms}}=\sqrt{\cfrac{3\text{kT}}{m}}\text{.}\)

• The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.

Glossary

thermal energy

\(\overline{\text{KE}}\), the average translational kinetic energy of a molecule