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

Reduced (P_r,V_r,T_r) curves; critical point; subcritical wiggle vs Maxwell plateaus (qualitative).

About this model

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.

Continue with similar topics in this category — or all 46 in Thermodynamics.

View category →

School

Phase Diagram

Launch Simulator

Temperature-pressure diagram with phase transitions.

NewSchool

Leidenfrost Effect (Toy)

Launch Simulator

T_plate vs ~200 °C threshold: vapor gap and lifetime curves — pedagogical, not measured boiling data.

NewSchool

Vapor-Compression Refrigeration Cycle

Launch Simulator

Compressor, condenser, expansion valve, evaporator: COP, cooling capacity, pressure ratio, and p-h sketch with states 1-2-3-4.

NewUniversity / research

Maxwell’s Demon (Toy)

Launch Simulator

2D billiards + gate: fast |v| crosses; ⟨|v|⟩ left/right + Landauer note.

NewSchool

Stirling Cycle

Launch Simulator

PV: two isotherms and two isochores; ideal η equals Carnot with a perfect regenerator.

NewSchool

Open-Channel Flow & Hydraulic Jump

Launch Simulator

Rectangular-channel Froude number, critical depth, conjugate depths, energy loss, and subcritical/supercritical regimes.

van der Waals Isotherms

About this model

How it works

Key equations

Frequently asked questions

Related simulators

Phase Diagram

Leidenfrost Effect (Toy)

Vapor-Compression Refrigeration Cycle

Maxwell’s Demon (Toy)

Stirling Cycle

Open-Channel Flow & Hydraulic Jump

van der Waals Isotherms

About this model

How it works

Key equations

Frequently asked questions