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Thermophysical properties of moist gases


To support humidity measurements needed for the efficient operation of fuel cells, we have calculated numerous thermophysical properties of water-gas mixtures at elevated pressures (up to 100 MPa) and temperatures (up to 2000 K for some properties). Second virial coefficients, needed to predict departures from ideal behavior, have been calculated for water-air and water-hydrogen mixtures. Using these results absolute humidity of kilograms of water vapor per kilogram of dry hydrogen has been determined as a function of pressure up to 1000 atmospheric pressures for saturation temperatures in the range of –70 °C to 90 °C. A simple presentation in chart form is usually used by industry for fuel cell applications including hydrogen fuel quality specifications.

Intended Impact:

Calculated values of absolute humidity will form a basis for the NIST humidity standard of compressed hydrogen, oxygen and air for calibration of hygrometers used in measuring water vapor content of hydrogen fuel in fuel cell industry.


To establish primary measurement standard of humidity in the range of dew/frost-point temperature between −70 °C and 90 °C and of pressure between 1 bar (101 kPa) and 1000 bars (101 MPa) for fuel cell applications.

Technical Approach:

Reliable measurements and control of water content in hydrogen are required in many applications in the fuel cell industry. Recent efforts at NIST have focused on determining the mixture properties needed to accurately relate hydrogen concentration to the observed dew/frost-point temperature. 

Experimental methods for determining second virial coefficients are prone to relatively large uncertainties. Second virial coefficients for gas-water pairs may be derived from pressure-volume-temperature data, but water adsorption renders this impractical except at high temperatures. More often, the method is indirect, by measuring the water content of the gas equilibrated with ice or with liquid water (or, equivalently, the dew-point conditions for a gas mixture with known water vapor content).

The capabilities of ab initio quantum chemistry have advanced to the point where it is feasible to construct highly accurate pair potentials for H2O with small molecules, which can then be used to calculate the second virial coefficients of interacting molecules. Scaled perturbation theory has been used to construct a potential-energy surfaces for H2O with H2, H2O with H2O and H2 with H2, respectively, and we have used these surfaces to calculate the second virial coefficients. Uncertainties were assigned to the calculated values based on upper and lower bounds for the pair potential produced by ab initio calculations.

The calculated values are in general agreement with the experimental data but have a smaller uncertainty (between 4 cm3/mol and 0.3 cm3/mol) at k = 2 with a 95 % confidence level.

By evaluating the Gibbs function difference of the water vapor between the equilibrium states at a pressure in the mixture and the saturation water vapor pressure at a temperature, the equation of state of a water-hydrogen mixture system can be established to determine accurately the water vapor concentration in the mixture at a given pressure and temperature and its expanded uncertainty. We have calculated the water vapor concentration in kilograms of water vapor per kilogram of dry hydrogen at a given pressure up to 100 atmospheric pressures and its corresponding dew/frost-point temperature in the range of –70 °C to 90 °C.

Major Accomplishments:

  • In 2007, we published: (1) the thermodynamic properties of water-hydrogen and water-air mixtures in fuel cells for absolute pressures of 0.1 MPa, 0.5 MPa, 1 MPa and 2 MPa with water vapor content in the range of dew-point temperatures 60 °C to 200 °C and, (2) a first-principles calculation of the water-air second virial coefficient for the temperature range of 150 K to 2000 K.
  • In 2008, we submitted for publication papers on: (1) the thermodynamic properties of moist air including second virial corrections from 400 K to 1500 K and (2) the humidity of compressed hydrogen.

Selected Publications



Peter Huang
Michael Moldover
Allan Harvey


Thermophysical properties of moist gases:
Peter Huang
301-975-2621 Telephone
301-548-0206 Facsimile

100 Bureau Drive, M/S 8363
Gaithersburg, MD 20899-8363