Spinodal Line Calculator

Map thermodynamic instability using the spinodal criterion quickly. Solve cubic extrema and report two volumes. Use results to guide phase diagram modeling decisions today.

Calculator Inputs

Spinodal extrema appear for T below Tc.
Controls attractive interactions.
Represents excluded volume per mole.
Keep R consistent with a and b units.

Formula used

For a van der Waals fluid, the equation of state is:

P = RT/(V - b) - a/V^2

The spinodal line is the mechanical stability limit:

(dP/dV)_T = 0

Substitution and algebra yield a cubic in V:

RT*V^3 - 2a*V^2 + 4ab*V - 2ab^2 = 0

This calculator solves that cubic, filters physical roots with V > b, and reports pressures at each spinodal volume.

How to use this calculator

  1. Enter the temperature and choose its unit.
  2. Provide van der Waals parameters a and b.
  3. Set R so units remain consistent.
  4. Select output units for pressure and volume.
  5. Press Calculate to show results above the form.
  6. Use CSV or PDF buttons to export results.

Example data table

Case (example) T (K) a (Pa*m^6/mol^2) b (m^3/mol) Expected behavior
CO2 (illustrative) 280 0.364 4.27e-5 Two spinodal volumes when T < Tc
Generic fluid 350 0.300 3.80e-5 No roots if T is at or above Tc

Example parameters are for demonstration only. Use substance-specific values from a reliable source.

Related Calculators

Boltzmann factor calculatorPartition function calculatorCanonical ensemble calculatorGrand canonical calculatorMicrocanonical entropy calculatorChemical potential calculatorInternal energy calculatorThermal wavelength calculatorMaxwell Boltzmann speedMean speed calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.