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Real Gases by the Numbers
Compressibility, van der Waals, corresponding states, cylinder contents, Joule–Thomson cooling and liquefied gases, worked through one laser-cutting gas supply
Size, fill, draw and check high-pressure gas supplies with real-gas numbers: compressibility, contents, temperature, throttling, vapour pressure, critical points and line flow.
Start readingAbout this book
The ideal gas law, pV = nRT, is one of the most useful equations in engineering, and at the pressures of a workshop air line it is right to a fraction of a per cent. In a modern gas cylinder at 20 or 30 MPa it is not. The molecules of a real gas take up room and pull on each other, and at high pressure those two effects change how much gas a cylinder holds, how its pressure moves with temperature, how cold it gets through a regulator, and whether it stays a gas at all. The errors run to ten or fifteen per cent, which is enough to run a production cell out of gas before the end of a shift, freeze a regulator, or let a liquefied gas cylinder build a dangerous pressure on a hot day.
This book works through real gases with numbers. It starts with the compressibility factor, the single number that says how far a gas departs from the ideal law, and uses it to find the real contents of a cylinder pack. It then explains the departure with the van der Waals model, extends it to any gas with the principle of corresponding states, and applies it to gauges and temperature, to the Joule–Thomson cooling that happens in every regulator, to liquefied gases and the critical point, and to flow in pipes and nozzles. The last chapter puts it together into a specification and a set of checks. Each chapter follows one running case, includes a plausible mistake and how it was found, and ends with an exercise and its worked answer.
It is for production, process and maintenance engineers, equipment buyers and technical students who deal with gas cylinders, cylinder packs, regulators, microbulk and bulk liquid tanks, and the machines they feed. It assumes school algebra and the ideal gas law. Cryogenic plant design, gas mixtures in detail and pipeline-scale gas engineering are outside its scope.
The running case
Every chapter follows one fictional gas supply. This is an illustration. A sheet metal shop runs a fibre-laser cutting cell that cuts stainless steel with nitrogen as the assist gas. Its supply, LN-1, is a manifolded pack of 15 cylinders of 50 litres water capacity each, 0.75 m³ in total, filled to 30.0 MPa gauge (30.1 MPa absolute) at 15 °C. A regulator on the pack drops the pressure to 1.8 MPa gauge for the line to the machine, and the laser’s own valve sets 1.6 MPa absolute behind its 2.0 mm cutting nozzle, which then passes about 36 kg of nitrogen an hour while the beam is on. The pack is changed when it falls to 2.5 MPa absolute, below which the regulator can no longer hold the line pressure. The shop cuts for about six beam-on hours a day.
All property values come from the NIST Chemistry WebBook. The shop, its machine, its supply and its problems are invented. None describes KEVOS® work or a real business.
How to use the book
Read Chapters 1 to 3 first: they set out the compressibility factor, the molecular reasons behind it and the way one gas’s behaviour predicts another’s. Chapters 4 and 5 deal with what happens to the gas in the pack and through the regulator, Chapter 6 with gases that liquefy, Chapter 7 with the low-pressure side of the supply, and Chapter 8 with specifying and checking the whole. Every calculation was checked by running it, and values are given to more figures than a shop needs so that the arithmetic can be followed. Pressures are absolute unless they are marked as gauge.
Source limits and professional responsibility
The physics in this book is standard thermodynamics, and the property data come from NIST. The pack size, flows, prices and supplier arrangements in the running case are illustrations; real supplies are specified from the gas supplier’s data and the equipment maker’s requirements. High-pressure gas stores an enormous amount of energy, liquefied gases can build pressure without limit when warmed, and inert gases can displace the oxygen in a room without warning: gas installations are designed, installed and maintained under the applicable Australian standards, the supplier’s instructions and work health and safety law, and qualified review governs real work. This book teaches how real gases behave and how to check the numbers. It is not a design for any installation.
Who this book is for
Production, process and maintenance engineers, equipment buyers and technical students who specify, run or troubleshoot high-pressure gas supplies, cylinder packs, regulators and liquefied gas tanks.
What you will learn
- Explain why gases depart from the ideal gas law at high pressure and state the departure as a compressibility factor.
- Calculate the real contents of a cylinder or pack from its pressure and temperature, and correct gauge readings for temperature.
- Use the van der Waals model and corresponding states to judge a gas for which no data table is to hand.
- Estimate the Joule–Thomson temperature drop across a regulator and decide when heating or staging is needed.
- Explain vapour pressure, filling ratio and the critical point for liquefied gases, and specify and check a gas supply.
Inside this book
Chapters
- 01Where the ideal gas law failsThe compressibility factor, nitrogen's departure from the ideal law up to 30 MPa, LN-1's real contents of 232 kg against an ideal 264 kg, and a run-time plan that ran out early.
- 02Size and attraction: the van der Waals pictureWhy 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.
- 03Corresponding states: one gas predicts anotherReduced pressure and temperature, a test of corresponding states on nitrogen, argon and oxygen, why argon holds more than ideal and hydrogen less, and an argon stocktake that used nitrogen's Z.
- 04Contents, temperature and the gaugeHow a full pack's pressure moves with temperature, why real gas moves faster than ideal, hot fills that settle short, temperature-corrected contents, and a full pack rejected on a cold morning.
- 05Throttling: the Joule–Thomson effect at the regulatorWhy gas cools through a regulator, LN-1's drop from 15 °C to −20 °C on a full pack, the inversion temperature, why hydrogen warms, CO₂ regulators that freeze, and a cold-gas alarm.
- 06Liquefied gases, vapour pressure and the critical pointVapour pressure and Clausius–Clapeyron, liquid nitrogen in a microbulk tank, why warm liquid holds less, CO₂ cylinders that go liquid-full in summer, and a tank sized at the wrong density.
- 07Real gas in pipes and nozzlesWhen the ideal law is good enough downstream of the regulator: LN-1's line velocity and pressure drop, choked flow at the 2.0 mm nozzle, reference conditions, and two flow figures that did not match.
- 08Specifying and checking a gas supplyLN-1's demand in kilograms, packs against microbulk on real-gas numbers, the specification sheet, a monthly reconciliation of gas bought and used, and a changeover set too low.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Explained in this book
Boiling Margin Check (Clausius–Clapeyron Vapour Pressure, Keep Liquid or Make It Boil)
Applies the integrated Clausius–Clapeyron equation from one known boiling point to give vapour pressure and boiling temperature at your conditions.
Used in Liquefied gases, vapour pressure and the critical point
Explained in this book
Boiling Point and Vapour Pressure at Operating Pressure (Clausius–Clapeyron Check)
Applies the integrated Clausius–Clapeyron equation from this chapter to find a liquid’s boiling point at another pressure and its vapour pressure at a temperature.
Used in Liquefied gases, vapour pressure and the critical point
Explained in this book
Gas Cylinder Contents and Duration Check (Peng–Robinson or van der Waals Real Gas)
Finds a cylinder’s contents with the van der Waals constants from the critical point, as this chapter does, beside Peng–Robinson and the ideal gas law.
Used in Size and attraction: the van der Waals picture, Contents, temperature and the gauge, Corresponding states: one gas predicts another
Explained in this book
Gas Pressure Reduction Cooling Check (Joule–Thomson Temperature Drop, Outlet Temperature, Preheat)
Estimates how cold a gas gets through a regulator from a Joule–Thomson coefficient or van der Waals constants, with the inversion temperature and the preheat needed.
Used in Throttling: the Joule–Thomson effect at the regulator
Explained in this book
Gas Throttling Temperature Check (Joule–Thomson Cooling, Regulator Outlet, Preheat)
Works out a gas’s outlet temperature through a regulator from van der Waals constants or a known Joule–Thomson coefficient, and the preheat that keeps it above a limit.
Used in Throttling: the Joule–Thomson effect at the regulator
Explained in this book
Real Gas Cylinder Contents Check (Van der Waals, Compressibility, Ideal-Gas Error)
Solves the van der Waals equation this chapter sets out for a cylinder’s molar volume, contents and compressibility factor.
Used in Size and attraction: the van der Waals picture, Contents, temperature and the gauge, Liquefied gases, vapour pressure and the critical point
Explained in this book
Vapour Pressure and Boiling Check (Clausius–Clapeyron, Boiling Point at Pressure, Margin)
Applies the Clausius–Clapeyron relation this chapter explains to find vapour pressure and boiling temperature from one known point.
Used in Liquefied gases, vapour pressure and the critical point
Related Tools and Examples
Useful alongside
Boiling Point Under Vacuum (Clausius–Clapeyron Boiling Temperature, Pressure for a Temperature Limit)
Applies the Clausius–Clapeyron equation to find the boiling temperature of a liquid at another pressure from one known boiling point.
Related to Liquefied gases, vapour pressure and the critical point
Useful alongside
Liquid Throttling Temperature Rise (Valve and Orifice Heating, Joule–Thomson for Liquids)
Applies the same constant-enthalpy throttling relation to a liquid, where it gives heating: dT = v(1 − Tβ)dp/cp across a valve or orifice.
Related to Throttling: the Joule–Thomson effect at the regulator
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 27 October 2026.
- H. Gould and J. Tobochnik. Thermal and Statistical Physics (draft edition) (2006). Supplied source, in copyright (later published by Princeton University Press). Read as a subject map for equations of state, the van der Waals model, the second virial coefficient, the Joule and Joule–Thomson processes, phase equilibrium, the Clausius–Clapeyron equation and the liquid–gas critical point. No text, derivations as set out, figures, tables or problems are reproduced; the treatment, case, numbers and exercises in this book are its own.
- E. W. Lemmon, M. O. McLinden and D. G. Friend, National Institute of Standards and Technology. Thermophysical Properties of Fluid Systems, NIST Chemistry WebBook, SRD 69 (2026). Source of every density, enthalpy, Joule–Thomson coefficient, saturation pressure and critical point in the book, for nitrogen, argon, oxygen, hydrogen, helium and carbon dioxide. Values retrieved on the date checked; compressibility factors were calculated from the tabulated densities.
- National Institute of Standards and Technology. CODATA value: molar gas constant (2019). The exact SI value of the molar gas constant, 8.314462618 J/(mol·K), used to calculate every ideal-gas density and compressibility factor.
- Standards Australia. AS 4332 The storage and handling of gases in cylinders (edition as called up). Named by number and scope as the Australian standard for storing and handling gas cylinders. No values are quoted from it.
- Standards Australia. AS 2030 Gas cylinders (series) (edition as called up). Named by number and scope as the Australian series covering the design, filling, inspection and testing of gas cylinders, including filling limits for liquefied gases. No values are quoted from it.
- Safe Work Australia. Model Code of Practice: Confined spaces (current edition). Named in Chapter 8 as the starting point for assessing oxygen depletion where inert gas could accumulate. No values are quoted from it; the oxygen-depletion figures in the chapter are the book's own mixing calculation.
- International Organization for Standardization. ISO 13443 Natural gas: Standard reference conditions (edition as called up). Named in Chapter 7 by number and scope as the standard that sets 15 °C and 101.325 kPa as reference conditions for natural gas. No other content is quoted.