γ–φ equilibrium · second virial vapor
Beyond ideal vapor.
Supply your coefficients.
Compare bubble pressure, dew pressure and TP flash with the same liquid model and two vapor descriptions. Enter pure and cross virial coefficients explicitly.
Same liquid. Different vapor.
Verify the selected virial state
Equations and standard states Pressure-form second-virial approximation
Z = 1 + Bmix P/(RT)
ln φᵢ = [2Σⱼ yⱼBᵢⱼ − Bmix] P/(RT)
ln φᵢsat = Bᵢᵢ Pᵢsat/(RT)
ln Πᵢ = vᵢL(P − Pᵢsat)/(RT)
This implements the pressure expansion truncated after its first pressure term, with Bij expressed as volume per mole. It does not solve the density form Z=1+Bρ as an exact finite-density equation. B12 is supplied independently; no cross mixing rule is silently assumed.
The Gibbs reference uses the same pure-liquid standard state for both phases. Saturated-vapor and Poynting corrections appear in the reference offsets, so zero virial coefficients recover ideal-vapor behavior and a pure component at P=Psat satisfies saturation equality.
Bubble and dew pressures bracket a tangent-distance zero in the admitted pressure interval. TP flash isolates all common tangents between strictly convex liquid and vapor Gibbs curves. Candidate intervals are divided at equal-composition stationary points: a quadratic for Margules and a rational-polynomial numerator for NRTL. Both material balance and fugacity equality are checked independently.
Validity and interpretation No universal pressure cutoff
The lab uses a conservative numerical teaching guard: max|Bij| × max(P, Psat1, Psat2)/(RT) ≤ 0.1. This limits cancellation between coefficients, but does not establish that neglected higher virial terms are small. A small Z−1 alone cannot validate the approximation. Use coefficients from a reliable source and their stated temperature and density range.
Operating pressure is restricted to 1–200 kPa. A boundary outside that interval or the guard is reported unavailable. Nonconvex liquid states are rejected rather than reported as stable two-phase VLE. This module has no PR/SRK EOS, dense-vapor model, LLE/VLLE, temperature-boundary solver or energy-balanced virial flash.
DeVoe: gas-mixture virial coefficients and fugacity · Calculation source · Regenerate figures.