In most treatments of heat and mass transfer in engineering, it is usual to treat fluids as continua. Thus, it becomes possible to introduce the concept of a fluid (liquid or gas) density at a point. On this basis, the mass density of a gas, ρ, is simply the mass of a gas contained in a macroscopic volume whereas the amount-of-substance density, , is the amount (number of moles) of a gas in the same volume. The density of a gas is a strong function of temperature and pressure. For very low pressures, every gas conforms to the Perfect Gas equation
where R is the universal gas constant and T, the absolute temperature. But there are significant deviations from this simple behavior as the pressure is increased.
One of the simplest means of representation of the behavior of real gases qualitatively is the Van der Waals' Equation of State, expressed as:
in which a and b are constant characteristics of a particular substance which account for the attractive forces between molecules and their finite size. Since the van der Waals' equation reveals a critical point, the constants a and b can be related to the critical state parameters
and
These relationships do, in fact, provide a very crude means of estimating the density of a gas from the van der Waals' equation of state if the critical state variables are known for the substance. More accurate equations of state, such as that of Redlich and Kwong or Benedict, Webb and Rubin, have been developed which may be used in a similar manner for the estimation of the density of gases. However, none of these simple equations of state represent the behavior of any real substances over a wide range of conditions so that one must always have recourse to measurements, at least to define the parameters in an equation of state.
For some fluids, very accurate equations of state exist which describe the density, as well as other thermodynamic properties of a gas, over a wide range of conditions. These equations are based on a set of critically-evaluated experimental data. Equations used to describe these data are often quite complicated [e.g., de Reuck and Craven (1993)].
The density of a gas is sometimes expressed in terms of a virial expansion, which emerges from a statistical mechanical treatment of the gas. Here,
where B, C... are known as virial coefficients which have a known relationship to the forces between molecules. For moderately low densities, equations of this form can be used to calculate gas densities if B and C are available, which is sometimes the case [Dymond and Smith (1980)].
Other means of estimating the density of gases are available, such as those based upon Corresponding States procedures (Reid et al.).
REFERENCES
Bett, K. E., Rowlinson, J. S., and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London. DOI: 10.1016/0300-9467(76)80049-4
de Reuck, K. M. and Craven, R. J. B. (1993) International Thermodynamic Tables of the Fluid State—12. Methanol (Blackwell Scientific, London).
Dymond, J. H. and Smith, E. B. (1980) The Virial Coefficients of Pure Gases and Mixtures. A Critical Compilation (Clarendon Press, Oxford).
Reid, R. C., Prausnitz, J. M., and Sherwood, T. K. (1977) The Properties of Gases and Liquids, 3rd ed. (McGraw-Hill, New York).
References
- Bett, K. E., Rowlinson, J. S., and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London. DOI: 10.1016/0300-9467(76)80049-4
- de Reuck, K. M. and Craven, R. J. B. (1993) International Thermodynamic Tables of the Fluid Stateâ€”12. Methanol (Blackwell Scientific, London).
- Dymond, J. H. and Smith, E. B. (1980) The Virial Coefficients of Pure Gases and Mixtures. A Critical Compilation (Clarendon Press, Oxford).
- Reid, R. C., Prausnitz, J. M., and Sherwood, T. K. (1977) The Properties of Gases and Liquids, 3rd ed. (McGraw-Hill, New York).