Why are negative pressures drawn?

The mean-field continuation can go below zero in the unphysical spinodal region; the plot clips deeply negative values but may still show shallow negative segments for pedagogy.

Is this equation accurate near the critical point?

Qualitative only; modern engineering uses accurate multiparameter equations of state and critical scaling exponents beyond mean-field vdW.

van der Waals Isotherms

The van der Waals equation (P + a/V_m²)(V_m − b) = RT adds mean-field attraction and covolume to capture liquid–vapor behavior qualitatively. In reduced coordinates (P_r, V_r, T_r) relative to the critical point, all fluids share the same dimensionless shape—law of corresponding states at this level of modeling. Below T_r = 1, isotherms on a P–V diagram develop a non-monotonic region; Maxwell’s equal-area rule replaces the wiggle with a flat coexistence segment at the vapor pressure. This simulator plots several T_r curves and marks (1,1) but does not construct the Maxwell plateau—keeping the famous loop visible for discussion.

Who it's for: Physical chemistry and engineering thermodynamics when introducing real fluids and criticality.

Key terms

van der Waals
Critical point
Reduced variables
Law of corresponding states
Spinodal
Maxwell construction
Liquid–vapor coexistence

How it works

The van der Waals equation adds molecular attraction (∝ 1/V²) and excluded volume to the ideal gas. In reduced variables it has a universal shape with a critical point (T_r = P_r = V_r = 1). Below T_c, isotherms develop an unphysical wiggle; the Maxwell equal-area rule replaces it with a flat coexistence segment — not drawn here, but the yellow dot marks (1,1) for orientation.

Key equations

(P_r + 3/V_r²)(3V_r − 1) = 8T_r · V_r = V_m/V_c, etc.

Frequently asked questions

Why are negative pressures drawn?: The mean-field continuation can go below zero in the unphysical spinodal region; the plot clips deeply negative values but may still show shallow negative segments for pedagogy.
Is this equation accurate near the critical point?: Qualitative only; modern engineering uses accurate multiparameter equations of state and critical scaling exponents beyond mean-field vdW.

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