• id: JTHERM-02-N12
• title: Deviations from Ideal Behaviour
• tags: real-gas, van-der-waals, intermolecular-forces

Real gases deviate from $PV = nRT$ at high pressures and low temperatures, where intermolecular forces and molecular volume become significant. The van der Waals equation corrects for both: $(P + a n^2/V^2)(V - nb) = nRT$. Here $a$ accounts for attractive intermolecular forces (reduces effective pressure), and $b$ accounts for finite molecular volume (reduces available volume). The critical constants: $T_c = 8a/(27Rb)$, $P_c = a/(27b^2)$, $V_c = 3nb$. At the critical point, the gas-liquid distinction vanishes. The Boyle temperature $T_B = a/(Rb)$ is where $PV$ vs $P$ shows ideal behaviour over a range of pressures.