KEVOS® MAKEOS · Pneumatics
Real Gas Cylinder Contents Check (Van der Waals, Compressibility, Ideal-Gas Error)
How much gas is really in this cylinder or receiver at its pressure and temperature, how far off is the ideal-gas estimate, and is it enough for the job?
Contents of a gas cylinder, bank or receiver by the van der Waals equation of state with the gas constants you enter: the molar volume from the gas root of the cubic, the moles and mass held, the compressibility factor, the ideal-gas mass and its error, and the critical temperature and pressure implied by the constants (with a warning below the critical temperature, where the gas may condense), against the mass you need.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Internal (water) volume | L | Internal volume of the cylinder or receiver (the water capacity stamped on a cylinder). |
| Gauge pressure | bar | Gauge pressure of the gas. |
| Gas temperature | °C | Temperature of the gas (settled temperature, not just after filling). |
| Atmospheric pressure | kPa | Local atmospheric pressure (101.325 kPa at sea level). |
| Gas constants (from data tables) | ||
| Molar mass of the gas | g/mol | Molar mass of the gas (nitrogen 28.014 g/mol). |
| Van der Waals constant a | Pa·m⁶/mol² | Van der Waals attraction constant for the gas, from data tables such as the CRC Handbook of Chemistry and Physics (1 L²·bar/mol² = 0.1 Pa·m⁶/mol²). |
| Van der Waals constant b | cm³/mol | Van der Waals excluded-volume constant (1 L/mol = 1000 cm³/mol). |
| Requirement | ||
| Mass of gas needed | kg | Mass of gas the job needs. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Internal (water) volume
- What it is
- The internal volume of the cylinder, bank or receiver that holds the gas, the water capacity rather than the outside size.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 10000000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The moles and mass of gas held rise in proportion.
- Get it right
- Use the water capacity stamped on the cylinder in litres; add the volumes for a bank of cylinders.
What this means: Gauge pressure
- What it is
- The pressure of the gas above atmospheric, as read on the cylinder or receiver gauge.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 1500 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pressure holds more gas, and the ideal-gas error grows at high pressure.
- Get it right
- Read it after the gas has settled to room temperature; a warm cylinder just after filling reads high.
What this means: Gas temperature
- What it is
- The temperature of the gas inside the cylinder, which with the pressure sets how many moles the volume holds.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -150 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A warmer gas holds fewer moles at the same pressure.
- Get it right
- Use the settled gas temperature; a cylinder in the sun can be well above the air temperature.
What this means: Atmospheric pressure
- What it is
- The local air pressure added to the gauge reading to give the absolute pressure used in the equation of state.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 50 kPa to 110 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 101.325 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds a small amount to the absolute pressure and so to the mass.
- Get it right
- Sea level is 101.325 kPa; high-altitude sites are lower. It hardly matters at cylinder pressures.
Gas constants (from data tables)
What this means: Molar mass of the gas
- What it is
- The mass of one mole of the gas, converting the moles held into kilograms.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 500 g/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 28.014 g/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass held rises in proportion; the moles held do not change.
- Get it right
- Enter grams per mole: nitrogen 28.014, argon 39.948, carbon dioxide 44.01.
What this means: Van der Waals constant a
- What it is
- The van der Waals constant describing the attraction between the gas molecules, which lets a real gas pack more tightly than an ideal one.
- Units and format
- Enter a number in Pa·m⁶/mol²: Pa·m⁶/mol². The form accepts 0 Pa·m⁶/mol² to 10 Pa·m⁶/mol². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.137 Pa·m⁶/mol² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger value lowers the molar volume, so the cylinder holds more gas.
- Get it right
- Data tables often give it in L²·bar/mol²: divide by 10 to get Pa·m⁶/mol². Enter 0 to model an ideal gas.
What this means: Van der Waals constant b
- What it is
- The van der Waals constant for the volume the gas molecules themselves occupy, which makes a real gas harder to compress than an ideal one.
- Units and format
- Enter a number in cm³/mol: cm³/mol. The form accepts 0 cm³/mol to 1000 cm³/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 38.7 cm³/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger value raises the molar volume at high pressure, so the cylinder holds less gas.
- Get it right
- Tables give it in L/mol: multiply by 1000 to get cm³/mol. Enter 0 to model an ideal gas.
Requirement
What this means: Mass of gas needed
- What it is
- The mass of gas the job needs, such as for a purge, a pressure test or a run of welding, against which the contents are compared.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line; the contents do not change.
- Get it right
- Allow for the gas that stays in the cylinder at its lowest usable pressure; it cannot be used.
Method and formulas
- Absolute pressure p = gauge + atmospheric; van der Waals (p + a ÷ v²)(v − b) = R T (Fermi eq 99), solved as p v³ − (p b + R T) v² + a v − a b = 0 for the largest (gas) root by Newton’s method from v = b + R T ÷ p.
- Moles n = V ÷ v; mass = n M; compressibility Z = p v ÷ (R T); ideal-gas mass = p V M ÷ (R T) and its error against the van der Waals mass.
- Critical point of the constants: T_c = 8a ÷ (27 R b), p_c = a ÷ (27 b²); below T_c the gas may condense.
- Example: the cylinder holds 11.742 kg (Z = 1.0009); the ideal-gas law says 11.752 kg.
Limitations
- Van der Waals is a two-constant model: it is close for permanent gases at moderate pressures, but at cylinder pressures of 200 bar and above, and near the critical point, it can be several per cent out; use measured compressibility data or a better equation of state where the quantity matters.
- Screening aid only: cylinders, receivers and their filling are pressure equipment, and the rated pressure, regulations and qualified review govern real work.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check how much nitrogen or argon a cylinder bank really holds
- See how wrong the ideal-gas law is at high pressure
- Check a receiver holds enough gas for a purge or test
Who it is for
- Process and plant engineers
- Welding and gas supervisors
- Pneumatic system designers
What you get
- Molar volume, moles and mass of gas held
- Compressibility factor and ideal-gas error
- Critical temperature and pressure from the constants
- Contents against the mass needed
Interpreting the result
- Z above 1 means the gas is harder to compress than an ideal gas, so the cylinder holds less than the ideal-gas law predicts; Z below 1 means it holds more.
References
- Fermi E., Thermodynamics (Dover Publications, 1956; first published by Prentice-Hall, 1937), pp. 69–76. Method reference; no text, examples or tables are reproduced.
- CRC Handbook of Chemistry and Physics (CRC Press): van der Waals constants for gases; values are entered by the user.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Size and attraction: the van der Waals picture
What it covers: Why molecules push the compressibility factor both ways, van der Waals constants for nitrogen from its critical point, the model in LN-1's pack, and a contents check it got wrong.
Also in Contents, temperature and the gauge, Liquefied gases, vapour pressure and the critical point
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.