Calculator Inputs
Use measured PVT data or estimate B(T) from van der Waals constants.
Formula Used
The virial equation expands real-gas behavior in powers of density or pressure. The second virial coefficient, B, measures the first correction beyond ideal gas behavior.
PVT route: Z = \frac{PV_m}{RT} and B = \frac{(Z-1)RT}{P}
van der Waals estimate: B(T) = b - \frac{a}{RT}
Interpretation: Negative B suggests attractive forces dominate. Positive B suggests repulsive or excluded-volume effects dominate. At the Boyle temperature, B becomes approximately zero.
How to Use This Calculator
- Choose Experimental PVT if you know pressure, temperature, and measured molar volume.
- Choose van der Waals if you know the gas constants a and b.
- Enter the working temperature and pressure for your case.
- Set graph limits to study trends across pressure or temperature.
- Press Calculate Second Virial to show results beneath the header and above the form.
- Use the export buttons to save a CSV summary or a PDF report.
Example Data Table
| Case | Method | Temperature (K) | Pressure (bar) | Vm or b (L/mol) | a (L²·bar/mol²) | Estimated B (L/mol) |
|---|---|---|---|---|---|---|
| Example A | PVT | 350 | 12 | 2.55 | — | -0.131405 |
| Example B | van der Waals | 320 | 10 | 0.0391 | 1.390 | -0.013150 |
| Example C | van der Waals | 450 | 15 | 0.0391 | 1.390 | 0.001956 |
Frequently Asked Questions
1. What does the second virial coefficient represent?
It measures the first real-gas correction to ideal behavior. It captures how intermolecular attractions and repulsions shift the compressibility factor away from one.
2. Why can B be negative?
A negative value usually means attractive forces dominate at the chosen temperature. Molecules pull together more than excluded volume pushes them apart.
3. Why can B become positive?
At higher temperatures, repulsive effects and molecular size can dominate. Then the coefficient becomes positive, showing nonideal behavior driven more by excluded volume.
4. What is the Boyle temperature?
It is the temperature where the second virial coefficient is approximately zero. Near that point, a gas behaves more ideally over a limited pressure range.
5. When should I use the PVT method?
Use it when you have measured pressure, temperature, and molar volume for a real gas state. It gives B directly from experimental information.
6. When should I use the van der Waals method?
Use it for a fast estimate when you know constants a and b. It is convenient for trend analysis but less reliable than quality experimental data.
7. Which units does this calculator use?
The page uses Kelvin, bar, liters per mole, and the gas constant in L·bar/mol·K. Output is shown in both L/mol and m³/mol.
8. Why is the graph useful?
The graph reveals how compressibility or second virial values change with pressure or temperature. That makes trends easier to interpret than single-point results.