# Molecular basis for pressure and the ideal-gas law.

If a molecule, with radius r, averages n collisions as it travels distance L, then the average distance between collisions is L/n, and is called the mean free path λ, ﻿$\lambda =\frac{1}{4\sqrt{2}\pi (\frac{N}{V})r^{2}}$.

The mean free path is independent of temperature.

The mean time between collisions is temperature dependent.

Assumptions for ideal gas:

• # of molecules N is large
• They obey Newton’s laws
• Short-range interactions with elastic collisions
• Elastic collisions with walls  (an impulse…..pressure)
• What we call temperature T is a direct measure of the average translational kinetic energy
• What we call pressure p is a direct measure of the number density of molecules, and how fast they are moving (vrms)