Ideal Gas — Molecules in a Box, and Internal Energy, Enthalpy, and Entropy

Here we rebuild the PV = nRT you learned in high school from the motion of each individual molecule. In ① you watch molecules flying around in a box and actually measure that pressure is the “impulse delivered to the walls”. In ② you heat the gas at constant volume and constant pressure and see how U, H, S and the specific heat change.

All thermodynamic quantities are computed from the partition function (translation + rotation + vibration + electronic degeneracy). The standard entropy at 298.15 K and 1 bar agrees with the NIST-JANAF measured values to within 0.02 J/(mol·K) for the six gases other than hydrogen (hydrogen alone comes out about 0.14 J/(mol·K) lower).