Specific Gas Constant Calculator

Background.

The ideal gas law is usually written per mole, pV = nRT, with one universal constant R that is the same for every gas. Engineers rarely count moles. They weigh gas, meter it in kilograms and work with density, so they divide R by the gas's molar mass to get a constant per kilogram instead: the specific gas constant. With it the law becomes p = ρRT, linking pressure, density and temperature without any mention of amount of substance.

Because R is fixed, the specific constant depends on nothing but molar mass, and inversely: light gases have large constants, heavy ones small. Dry air, at a molar mass of about 0.029 kg/mol, comes out near 287 J/(kg·K), the figure behind most aerodynamics and ventilation calculations. Helium is about seven times lighter and has a constant about seven times larger, which is why a kilogram of helium takes up so much more room than a kilogram of air at the same temperature and pressure.

The universal constant used here is 8.31446261815324 J/(mol·K), exact since the 2019 redefinition of the SI fixed both the Boltzmann and Avogadro constants. The only uncertainty in the answer is therefore the molar mass you supply. For a pure substance that comes from atomic weights; for a mixture such as natural gas, flue gas or humid air it must be the average of the components weighted by mole fraction.

The result is an ideal-gas quantity. It describes real gases well at ordinary pressures and well away from their condensation point, and less well for steam near saturation, refrigerants, or gases compressed to high pressure, where a compressibility factor or a full equation of state is needed.

What is specific gas constant calculator?

The specific gas constant of a gas is the universal molar gas constant divided by that gas's molar mass, R_specific = R/M, in joules per kilogram per kelvin. It is the ideal-gas constant on a per-mass basis: the work one kilogram of the gas does when it expands at constant pressure while warming by one kelvin. For an ideal gas it also equals the difference between the specific heats at constant pressure and constant volume, cp − cv. Unlike R it differs from gas to gas, and engineering texts often write it simply as R, a frequent source of confusion.

How to use this calculator.

1. 01Enter the molar mass in kilograms per mole. Periodic tables and data sheets list grams per mole, so divide by 1,000: nitrogen's 28.0134 g/mol becomes 0.0280134.
2. 02For a mixture, multiply each component's molar mass by its mole fraction (equal to its volume fraction for ideal gases), add the products and enter the total. Do not weight by mass fraction.
3. 03Read the specific gas constant in J/(kg·K) and use it with absolute temperature in kelvin, in p = ρRT or in the speed of sound, √(γRT).
4. 04If the gas is near condensation or at high pressure, treat the ideal-gas result only as a first approximation.

The formula.

R_specific = R ÷ M, where R = 8.31446261815324 J/(mol·K) is the molar gas constant and M the molar mass in kg/mol. R is the product of the Boltzmann constant, 1.380649 × 10⁻²³ J/K, and the Avogadro constant, 6.02214076 × 10²³ per mole, both fixed exactly by definition, so R itself carries no measurement uncertainty. Dividing by molar mass switches the counting unit from moles to kilograms, since 1/M is the number of moles in one kilogram of the gas. The result is inversely proportional to M, so a 1% error in molar mass produces a 1% error in the opposite direction. That makes molar mass the only input needing care, especially for mixtures, where a mass-weighted average in place of a mole-weighted one gives the wrong answer. Nothing in the formula corrects for intermolecular forces, which matter at high pressure.

A worked example.

Frequently asked questions.

References& sources.

1. [1]BIPM, SI Brochure, 9th ed., molar gas constant from exact k and N_A.
2. [2]NASA Glenn Research Center, Equation of State.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.