Thermodynamics / gas state

Ideal gas law

Solve PV = nRT for the amount, mass and density of a gas at any pressure and temperature. Absolute units are enforced internally, which is where most hand calculations go wrong.

Temperature293.15 KPressure101.325 kPaMolar mass28.970 g/mol

Amount of substance

41.5712 mol

2.503e+25 molecules

Mass

1.2043 kg

1204.32 g of Air

Density

1.2043 kg/m³

ρ = PM/RT

Specific volume

0.8303 m³/kg

Volume occupied per kilogram

Gas properties at these conditions

Density and specific volume for each gas at the entered pressure and temperature.

Air

Gas properties at these conditions
Gas	Molar mass	Density (kg/m³)	Specific volume (m³/kg)
Air	28.970 g/mol	1.2043	0.8303
Nitrogen	28.013 g/mol	1.1645	0.8587
Oxygen	31.999 g/mol	1.3302	0.7517
Carbon dioxide	44.010 g/mol	1.8295	0.5466
Helium	4.003 g/mol	0.1664	6.0093
Hydrogen	2.016 g/mol	0.0838	11.9321
Methane	16.043 g/mol	0.6669	1.4994
Argon	39.948 g/mol	1.6607	0.6022

Density is proportional to molar mass at fixed pressure and temperature — helium is about seven times lighter than air.

Density by gas

At the entered pressure and temperature, density tracks molar mass.

Pressure vs temperature at fixed volume

Isochoric heating: pressure rises linearly with absolute temperature.

Canonical equations

The exact relationships implemented by this engine.

PV = nRT · absolute pressure and temperature only

n = PV/(RT) · P in Pa, V in m³, T in K

ρ = PM/(RT) · the form used for gas sizing

m = nM · M in g/mol gives grams

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

PV = nRT relates pressure, volume, temperature and amount for an ideal gas. It is exact enough for air and combustion products at ordinary conditions, and it is the fastest way to get from a vessel size to a mass of gas. The only rule that matters is that pressure and temperature must be absolute.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the absolute pressure in kilopascals.

Enter the volume in cubic metres.

Enter the temperature in degrees Celsius; the engine converts to kelvin.

Select the gas to set its molar mass.

Read the moles, mass, density and specific volume.

Compare densities across gases in the table — the ratio is just the molar mass ratio.

Worked example

1 m³ of air at 101.325 kPa and 20 °C (default inputs)

Inputs

Pressure 101.325 kPa absolute.
Volume 1 m³.
Temperature 20 °C.
Gas: air, M = 28.97 g/mol.

Calculation path

1
Convert to absolute units: 101,325 Pa and 293.15 K.
2
Moles: (101,325 × 1) / (8.3145 × 293.15) = 41.57 mol.
3
Mass: 41.57 × 28.97 = 1,204.3 g = 1.204 kg.
4
Density: 1.204 kg/m³; specific volume 0.830 m³/kg.

Result

41.57 mol · 1.204 kg · 1.204 kg/m³ · 0.830 m³/kg.

Assumptions & limitations

The gas is ideal: no intermolecular forces and negligible molecular volume.

Absolute pressure and absolute temperature are used throughout; gauge pressure must have atmospheric added.

The gas is pure and its molar mass is known. Mixtures need a mole-weighted molar mass.

No phase change occurs. Near saturation, the ideal law fails badly.

Compressibility factor Z = 1. Real gases deviate above about 10 bar or near the critical point.

Frequently asked questions

Why must I use absolute pressure?

Because the law is derived from kinetic theory with a zero at vacuum. Using gauge pressure omits the 101.325 kPa of atmosphere already acting on the gas, which understates the amount by about 15% at low gauge pressures.

When does the ideal gas law break down?

At high pressure, low temperature, or near the critical point — anywhere the molecules are close enough to interact. Use a compressibility factor Z or a cubic equation of state such as Peng-Robinson there.

Does this work for steam?

Only far from saturation. Steam near its dew point behaves very non-ideally, and steam tables or the IAPWS formulation are the right tool.

What is the difference between STP and NTP?

STP is 0 °C and 101.325 kPa (22.414 L/mol); NTP is 20 °C and 101.325 kPa (24.05 L/mol). Some standards use 15 °C. Always confirm which one a specification means.

How do I handle a gas mixture?

Compute a mole-weighted molar mass and use it in the same equations. Dalton’s law lets you sum partial pressures if you prefer to work per component.

How do I get mass flow from volumetric flow?

Multiply volumetric flow by density at the operating conditions. This is why the density readout matters more than the moles for HVAC and process work.