Calculator Inputs
Use the responsive grid below. It shows three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
| Model | n (mol) | T (K) | V (L) | Key Coefficient | Computed Pressure (bar) |
|---|---|---|---|---|---|
| Ideal Gas | 1.00 | 298.15 | 24.79 | None | 1.000 |
| van der Waals | 1.00 | 300.00 | 10.00 | a = 0.137, b = 3.87×10⁻⁵ | 2.501 |
| Virial EOS | 1.00 | 320.00 | 15.00 | B = -1.20×10⁻⁴ | 1.743 |
| Custom Z-Factor | 2.00 | 350.00 | 40.00 | Z = 0.92 | 1.338 |
These rows are reference examples for layout and interpretation. Replace them with your own states during actual use.
Formula Used
- Ideal Gas: P = nRT / V
- van der Waals: P = nRT / (V − nb) − a n² / V²
- Virial EOS: P = (nRT / V) × (1 + Bn / V)
- Custom Z-Factor: P = Z nRT / V
- Compressibility factor: Z = PVₘ / RT, where Vₘ = V / n
- Density: ρ = mass / volume = nM / V
This calculator always uses the universal gas constant R = 8.314462618 J·mol⁻¹·K⁻¹. Input pressure, volume, and temperature are converted into SI form before solving.
When volume is the unknown for van der Waals or difficult virial conditions, the code applies a numerical root search to find a physically meaningful positive volume.
How to Use This Calculator
- Choose an equation model that matches your gas behavior.
- Select the variable you want to solve for.
- Enter the known state values and units.
- For van der Waals mode, provide coefficients a and b.
- For virial mode, enter the second virial coefficient B.
- For custom Z mode, enter the compressibility factor.
- Add molar mass if you want density in kg/m³.
- Press Calculate State to show the result above the form.
- Use the CSV button for data export and the PDF button for a report snapshot.
Frequently Asked Questions
1) What is an equation of state?
An equation of state links pressure, volume, temperature, and material amount. It helps describe gas or fluid behavior and lets you solve one missing state variable from the others.
2) When should I use the ideal gas model?
Use the ideal gas model at modest pressures and away from condensation regions. It is fast, simple, and often accurate when intermolecular forces and particle size effects are small.
3) Why do van der Waals coefficients matter?
Coefficient a accounts for attractive forces between molecules. Coefficient b accounts for finite molecular size. Together, they shift pressure and volume away from ideal predictions, especially in dense states.
4) What does the second virial coefficient mean?
The second virial coefficient measures the first real-gas correction beyond ideal behavior. Its sign and magnitude show whether pairwise interactions increase or decrease pressure at a given state.
5) Why can volume solving be harder than pressure solving?
Pressure often comes directly from a formula. Volume can appear in nonlinear terms, such as V − nb or V², which may require numerical root finding and careful selection of a physically meaningful solution.
6) What does the compressibility factor Z show?
Z compares real-gas behavior with ideal behavior. A value near 1 means nearly ideal behavior. Values above or below 1 indicate repulsive or attractive effects dominating the current state.
7) Can I enter Celsius and liters?
Yes. The calculator converts Celsius to kelvin and liters to cubic meters internally, then reports the final result back in your selected display units.
8) What units should I use for a, b, and B?
Use units consistent with SI-based pressure, temperature, and volume handling. In this file, a uses Pa·m⁶/mol², b uses m³/mol, and the second virial coefficient B also uses m³/mol.