Van der Waals Gas 🌡️

Real gas P–V isotherms, Maxwell construction, and liquid-gas critical point

Temperature T
647 K (1.00 T_c)

Show isotherms
7

Maxwell construction
enabled

Critical Temp T_c

647.1 K

Critical Pressure P_c

220.6 bar

Critical Volume V_c

0.0915 L/mol

T / T_c (reduced)

1.00

VdW constant a

0.5536 Pa·m⁶

VdW constant b

0.03049 L/mol

Physics & equations

Van der Waals equation: (P + a/V_m²)(V_m − b) = RT

where a accounts for intermolecular attractive forces and b for finite molecular volume. For an ideal gas, a = b = 0.

Critical point (inflection of isotherm): T_c = 8a/(27Rb), P_c = a/(27b²), V_c = 3b

Below T_c the van der Waals isotherm develops a non-physical loop. The Maxwell equal-area construction replaces the loop with a horizontal tie-line at the equilibrium saturation pressure — the areas above and below the tie-line are equal.

The reduced equation of state with P_r=P/P_c, V_r=V/V_c, T_r=T/T_c: (P_r + 3/V_r²)(3V_r−1) = 8T_r — universal for all vdW gases.