Ideal Gas vs. Van der Waals Real Gas Equation of State Calculator

Compute real gas pressure and compressibility deviation from PV = nRT.

Van der Waals Real Gas Pressure
39.98 bar
Ideal Gas Law Pressure (PV=nRT) 49.89 bar
Compressibility Factor (Z = P_real/P_ideal) 0.8 Z
Pressure in PSI 579.93 psi
Inputs
mol
Amount of gas (n) in moles.
L
Container volume (V) in liters.
K
Absolute gas temperature (T) in Kelvin.
L²·bar/mol²
Van der Waals attraction parameter a (L²·bar/mol², 3.64 for CO₂).
L/mol
Van der Waals covolume parameter b (L/mol, 0.0427 for CO₂).
Results & Graph
Van der Waals Real Gas Pressure
39.98 bar
Ideal Gas Law Pressure (PV=nRT)
49.89 bar
Compressibility Factor (Z = P_real/P_ideal)
0.8 Z
Pressure in PSI
579.93 psi

Van der Waals Real Gas Pressure

Graph 1 • Moles Gas N Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 bar 28.7 bar 57.3 bar 50%: 22.42 bar 22.4 50% 75%: 31.79 bar 31.8 75% 100%: 39.98 bar 40.0 100% 125%: 47.06 bar 47.1 125% 150%: 53.06 bar 53.1 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Van der Waals Real Gas Pressure 39.98 bar Ideal Gas Law Pressure (PV=nRT) 49.89 bar Compressibility Factor (Z = P_real/P_ideal) 0.8 Z Pressure in PSI 579.93 psi
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Van der Waals Real Gas Pressure39.98 barIdeal Gas Law Pressure (PV=nRT)49.89 barCompressibility Factor (Z = P_real/P_ideal)0.8 ZPressure in PSI579.93 psi
Summary: For 10 mol in 5 L at 300 K, Van der Waals pressure is 39.98 bar vs. 49.89 bar Ideal Gas pressure.
Summary: For 10 mol in 5 L at 300 K, Van der Waals pressure is 39.98 bar vs. 49.89 bar Ideal Gas pressure.
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Formula & Mathematical Methodology: Van der Waals Real Gas Physics & Engineering Equation

Pideal = nRT / V
PvdW = [ nRT / (V − n·b) ] − a × (n / V)²
P_ideal = nRT / V; P_vdW = [ nRT / (V − n·b) ] − a × (n / V)²
  • molesGasN: Moles Gas N (mol)
  • volumeLiters: Volume Liters (L)
  • temperatureKelvin: Temperature Kelvin (K)
  • attractionConstA: Attraction Const A (L²·bar/mol²)
  • excludedVolumeB: Excluded Volume B (L/mol)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Van der Waals Real Gas

Compute real gas pressure and compressibility deviation from PV = nRT.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: P_ideal = nRT / V; P_vdW = [ nRT / (V − n·b) ] − a × (n / V)².
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Van der Waals Real Gas via P_ideal = nRT / V; P_vdW = [ nRT / (V − n·b) ] − a × (n / V)².

Frequently Asked Questions

What equation powers the Ideal Gas vs. Van der Waals Real Gas Equation of State Calculator?

It evaluates P_ideal = nRT / V; P_vdW = [ nRT / (V − n·b) ] − a × (n / V)² using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Thermodynamics & Heat Transfer

Ideal Gas vs. Van der Waals Real Gas Equation of State Calculator: inputs, method, and how to read the result

Compute real gas pressure and compressibility deviation from PV = nRT.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Moles Gas N: Amount of gas (n) in moles.
  • Volume Liters: Container volume (V) in liters.
  • Temperature Kelvin: Absolute gas temperature (T) in Kelvin.
  • Attraction Const A: Van der Waals attraction parameter a (L²·bar/mol², 3.64 for CO₂).

What the calculation includes

With the default values shown, Van der Waals Real Gas Pressure is 39.98 bar. The calculation follows Van der Waals Real Gas Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Moles Gas N from 10 mol to 11 mol changes Van der Waals Real Gas Pressure from 39.98 bar to 42.95 bar. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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