Points to Ponder

Pressure is not a surface-only phenomenon. It exists at every point inside a fluid. A thin layer of gas anywhere inside a container is in equilibrium because the pressure on both sides of that layer is equal — the layer does not get pushed one way or the other.

Don't overestimate how far apart gas molecules are. At ordinary pressure and temperature, the average distance between neighbouring molecules in a gas is only about 10 times the interatomic spacing in solids or liquids. What is dramatically larger is the mean free path — in a gas, it is roughly 100 times the interatomic distance and about 1000 times the size of a molecule.

The law of equipartition of energy says: for a system in thermal equilibrium, each degree of freedom contributes $\frac{1}{2} k_B T$ to the total energy. A degree of freedom is any quadratic term in the expression for a molecule's total energy. So a vibrational mode counts as two degrees of freedom (one for kinetic energy, one for potential energy), giving it an energy of $2 \times \frac{1}{2} k_B T = k_B T$.

Air molecules in a room do not all fall to the floor under gravity because they move at very high speeds and collide constantly. In equilibrium, there is only a tiny increase in density near the floor — the effect is small because the gravitational potential energy $mgh$ for ordinary heights is much smaller than the average kinetic energy $\frac{1}{2} m v^2$ of the molecules. …