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
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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