Real gases are non-hypothetical gases whose molecules occupy space and have interactions; consequently, they adhere to gas laws. To understand the behaviour of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition
For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. On the other hand, real-gas models have to be used near the condensation point of gases, near critical points, at very high pressures, to explain the Joule–Thomson effect and in other less usual cases. The deviation from ideality can be described by the compressibility factor Z.
- 1 Models
- 2 Thermodynamic expansion work
- 3 See also
- 4 References
- 5 Further reading
- 6 External links
Van der Waals model
Real gases are often modeled by taking into account their molar weight and molar volume
Where p is the pressure, T is the temperature, R the ideal gas constant, and Vm the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (Tc) and critical pressure (pc) using these relations:
With the reduced properties the equation can be written in the reduced form:
The Redlich–Kwong equation is another two-parameter equation that is used to model real gases. It is almost always more accurate than the van der Waals equation, and often more accurate than some equations with more than two parameters. The equation is
where a and b two empirical parameters that are not the same parameters as in the van der Waals equation. These parameters can be determined:
Using the equation of state can be written in the reduced form:
Berthelot and modified Berthelot model
The Berthelot equation (named after D. Berthelot) is very rarely used,
but the modified version is somewhat more accurate
This model (named after C. Dieterici) fell out of usage in recent years
with parameters a,b and
The Clausius equation (named after Rudolf Clausius) is a very simple three-parameter equation used to model gases.
where Vc is critical volume.
where A, B, C, A′, B′, and C′ are temperature dependent constants.
The Wohl equation (named after A. Wohl) is formulated in terms of critical values, making it useful when real gas constants are not available, but it cannot be used for high densities, as for example the critical isotherm shows a drastic decrease of pressure when the volume is contracted beyond the critical volume.
- , where are (respectively) the molar volume, the pressure and the temperature at the critical point.
And with the reduced properties one can write the first equation in the reduced form:
This equation is based on five experimentally determined constants. It is expressed as
This equation is known to be reasonably accurate for densities up to about 0.8 ρcr, where ρcr is the density of the substance at its critical point. The constants appearing in the above equation are available in the following table when p is in kPa, v is in , T is in K and R=8.314
|Carbon dioxide, CO2||507.2836||0.07132||0.10476||0.07235||6.60×105|
The BWR equation, sometimes referred to as the BWRS equation,
where d is the molar density and where a, b, c, A, B, C, α, and γ are empirical constants. Note that the γ constant is a derivative of constant α and therefore almost identical to 1.
Thermodynamic expansion work
The expansion work of the real gas is different than that of the ideal gas by the quantity .
- D. Berthelot in Travaux et Mémoires du Bureau international des Poids et Mesures – Tome XIII (Paris: Gauthier-Villars, 1907)
- C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
- Peng, D. Y. & Robinson, D. B. (1976). "A New Two-Constant Equation of State". Industrial and Engineering Chemistry: Fundamentals. 15: 59–64. doi:10.1021/i160057a011.
- A. Wohl (1914). "Investigation of the condition equation". Zeitschrift für Physikalische Chemie. 87: 1–39.
- Yunus A. Cengel and Michael A. Boles, Thermodynamics: An Engineering Approach 7th Edition, McGraw-Hill, 2010, ISBN 007-352932-X
- Gordan J. Van Wylen and Richard E. Sonntage, Fundamental of Classical Thermodynamics, 3rd ed, New York, John Wiley & Sons, 1986 P46 table 3.3
- Kondepudi, D. K.; Prigogine, I. (1998). Modern thermodynamics: From heat engines to dissipative structures. John Wiley & Sons. ISBN 978-0-471-97393-5.
- Hsieh, J. S. (1993). Engineering Thermodynamics. Prentice-Hall. ISBN 978-0-13-275702-7.
- Walas, S. M. (1985). Fazovyje ravnovesija v chimiceskoj technologii v 2 castach. Butterworth Publishers. ISBN 978-0-409-95162-2.
- Aznar, M.; Silva Telles, A. (1997). "A Data Bank of Parameters for the Attractive Coefficient of the Peng-Robinson Equation of State". Brazilian Journal of Chemical Engineering. 14 (1): 19–39. doi:10.1590/S0104-66321997000100003.
- Rao, Y. V. C (2004). An introduction to thermodynamics. Universities Press. ISBN 978-81-7371-461-0.
- Xiang, H. W. (2005). The Corresponding-States Principle and its Practice: Thermodynamic, Transport and Surface Properties of Fluids. Elsevier. ISBN 978-0-08-045904-2.