Second Virial Calculator

Calculator

Select a method, enter inputs, and calculate the second virial coefficient. The output unit applies to both methods.

Method

Choose an experimental or correlation approach.

Output unit for B(T)

Virial B has molar-volume units.

Sign convention

Interpretation depends on temperature range.

PVT method Uses Z = PVm/RT and B = (Z−1)Vm.

Temperature

Use absolute temperature for stability.

Pressure

Low pressure improves the approximation.

Molar volume, Vm

Example near 298 K and 1 atm: ~24.465 L/mol.

Virial equation (molar volume form):

Z = PVm / (RT) ≈ 1 + B(T)/Vm + C(T)/Vm² + …

PVT-based low-density estimate:

B(T) ≈ (Z − 1) Vm

Pitzer correlation (generalized):

B(T) = (R Tc / Pc) [ B0(Tr) + ω B1(Tr) ]

Tr = T/Tc, B0 = 0.083 − 0.422/Tr^1.6, B1 = 0.139 − 0.172/Tr^4.2

Notes: B(T) is a second-order correction capturing pair interactions. For accurate work near saturation or high pressure, use multi-parameter EOS or fitted virial data.

Select a method: experimental PVT or generalized correlation.
Enter temperature and unit; the tool converts to kelvin.
For PVT, input pressure and molar volume at the same state.
For correlation, input Tc, Pc, and acentric factor ω.
Choose your preferred B(T) unit and calculate.
Use CSV or PDF export for quick reporting.

Method	T	P	Vm	Tc	Pc	ω	Output B(T)
PVT	300 K	101.325 kPa	24.465 L/mol	-	-	-	Near 0 at low pressure
Pitzer	300 K	-	-	190.56 K	4.5992 MPa	0.011	Computed by correlation

The first row uses near-ideal conditions, so B(T) trends toward zero. The second row demonstrates typical correlation inputs for methane-like properties.

1) Why the second virial coefficient matters

B(T) is the first correction to ideal-gas behavior caused by pairwise intermolecular interactions. In the virial expansion, it controls the initial curvature of Z versus density, so it strongly influences low-pressure compressibility, residual enthalpy trends, and fugacity at dilute conditions.

2) Link to measurable PVT data

When you provide T, P, and molar volume Vm, the calculator forms Z = PVm/(RT). At low density, Z ≈ 1 + B/Vm, so B ≈ (Z−1)Vm. Practically, this works best when pressures are modest and Vm is large, because measurement noise in Z is amplified when Vm is small.

3) Typical magnitude and physical meaning

For many nonpolar gases near room temperature, B often falls in the range of tens to a few hundred cm³/mol. Negative values indicate net attractive forces dominate, lowering Z below one. Positive values indicate repulsive forces dominate, raising Z above one, which is common at higher temperatures.

4) Boyle temperature and sign changes

The Boyle temperature is where B(T) crosses zero, making the gas nearly ideal over a wider pressure range. Below it, attractions dominate (B<0). Above it, repulsions dominate (B>0). Tracking this sign change helps validate datasets and quickly flags unit mistakes.

5) Correlation mode for quick engineering estimates

The Pitzer method uses critical properties and the acentric factor to form Tr = T/Tc and then estimates B with generalized functions B0(Tr) and B1(Tr). This approach is convenient when experimental Vm is unavailable, and it provides a consistent baseline for screening conditions.

6) Accuracy expectations and best practices

Virial-based estimates are most reliable at low pressure and away from saturation. If you are near phase boundaries or at high density, higher-order terms (C, D, …) matter and B alone is insufficient. For PVT mode, prefer multiple data points and compare B across nearby pressures.

7) Units and reporting workflow

B has units of molar volume. This calculator converts between m³/mol, L/mol, and cm³/mol, and also reports Bp = B/(RT) in 1/Pa for pressure-form virial work. Use the CSV export for lab notebooks and the PDF export for formal reports.

8) Practical interpretation in modeling

In mixture thermodynamics, second virial terms support dilute-gas mixing rules and help estimate deviations from ideality in transport and equilibrium calculations. Even when a full equation of state is used, B(T) provides a fast sanity check: the sign and scale should match your fluid family and temperature range.

1) What does a negative B(T) indicate?

Negative B(T) means attractive intermolecular forces dominate at that temperature, typically producing Z<1 at low pressure. It is common below the Boyle temperature for many gases.

2) Which method should I choose?

Use PVT mode when you have measured P, T, and Vm for the same state. Use the correlation mode when Vm is unavailable and you have Tc, Pc, and the acentric factor.

3) Why does PVT mode require low pressure?

The approximation B ≈ (Z−1)Vm comes from the low-density virial truncation. At higher density, neglected terms like C/Vm² contribute, so the inferred B becomes biased.

4) What is Bp = B/(RT) used for?

Bp is the pressure-form coefficient that appears in low-pressure expansions such as Z ≈ 1 + Bp·P. It is useful when your data are organized by pressure rather than molar volume.

5) Can I use this for liquids or near saturation?

This tool is intended for gases and dilute conditions. Near saturation or in liquids, density is high and higher-order terms dominate. Use a multi-parameter equation of state for those regimes.

6) What units are recommended for reporting?

cm³/mol is common in thermodynamics tables, while L/mol is convenient for lab work. Use m³/mol for SI consistency. The calculator lets you switch units without re-entering data.

7) Why do my results look close to zero?

At very low pressure, many gases behave nearly ideally, so Z approaches 1 and the inferred B becomes small. Also verify Vm units, temperature units, and that P and Vm refer to the same state.