A Gas-Vapor (GV) System is an idealized model of a class of fluid mixture for which a liquid phase may condense from a gaseous phase, and this liquid phase consists entirely of only one of the mixture substances. This substance is called the condensable substance, and is denoted in the following as substance A. A real fluid mixture can be accurately modeled as a GV system when the following condition holds:
This typically is the case in practise when:
The term gas-vapor refers to the fact that, since T < TcA, the gas phase of the pure condensable substance (A) is a vapor at the system T. Since the remaining substances are above their critical temperatures, in their pure state they can only exist in the gas phase.
A familiar example of a system that can be modeled as a GV system is a mixture of dry air1 and water vapor, referred to as moist air. For the primary constituents of moist air, Tc(H2O) = 647K, Tc(N2) = 126K, and Tc(O2) = 155K. Conditions of interest for moist air systems typically range from about 273K up to the critical temperature of water, at moderate (near-atmospheric) pressures. Under such conditions, moist air can be accurately modeled as a GV system. The most-air system is so important in practice that the special term psychrometry (or psychrometrics) is used to refer to the measurement and analysis of moist atmospheric air. Although moist air is important, in part due to air-conditioning applications, there are many other GV systems to which the same fundamental thermodynamic considerations apply, examples of which we give in Section 9.
For GV systems, a principal interest lies in determining the relationships among the variables temperature (T), pressure (P), and gaseous composition (mole fraction, y, of the condensable substance) under which a liquid phase can exist in equilibrium with the gas phase. (Other thermodynamic properties of the system are also of interest, but these are not considered in this tutorial.) For given values of P and y, the T at which a liquid phase may form is called the dew-point temperature of the mixture, Tdp. Similarly, for given values of T and y, the P at which a liquid phase may form is called the dew-point pressure of the mixture, Pdp.
In this tutorial, we present the general characteristics of
GV systems, and describe the calculation of
Finally, we emphasize that the particular forms of the relationships given herein do not directly extrapolate to more general types of vapor-liquid equilibria. These are the subject of a future tutorial.
2. Review of Vapor-Liquid Equilibrium in Pure-Component Systems
The conditions in GV systems under which condensation occurs are related to the conditions for condensation for the pure condensable substance, A. The following facts are relevant (you might like to review them in a thermodynamics textbook of your choice):
Although the thermodynamic analysis given in what follows provides
the governing equations, in order to perform numerical calculations,
knowledge of p*(T ) for the pure
condensable substance is prerequisite information (and may be
referred to as a constitutive relation for the problem).
This may be available by means of tables or in the form of an
analytical equation for the particular substance of interest.
3. The GV Saturation Conditions: Simplest Approximations
In addition to the vapor-pressure curve of the condensable substance, an additional constitutive relation generally required is the equation of state (EOS) of the gaseous and liquid phases. The assumptions that:
considerably simplify the calculations for GV systems. In Section 8, we discuss how the calculations are modified when these ideality assumptions are relaxed.
The (saturation) condition for the simultaneous existence of
the liquid and gas phases is, in general, a consequence of the
equality of the chemical potentials of the condensable
substance in each phase (or equivalently in this case, the equality
of their fugacities). Under the approximations here, the
condition that governs the condensation of liquid A is the same
as that for pure A (Section 2), but with the total pressure P
replaced by its partial pressure, pA, defined
where y is the mole fraction of substance A in
the gas phase. Thus, the condition under which the liquid phase
is present (the saturation condition) is
Equation  is the key equation for SSC systems, relating the 3 variables (y, P, T) when both phases are present. This condition is a natural consequence of the ideal-gas EOS assumption, since gaseous A behaves as if the other substances are not present, but at a pressure pA, rather than the total pressure P.
Since the gas phase is always present for a GV system, the conditions determining the phase behavior are thus Equation  for the 2-phase case, and
in the single(gas)-phase case. A measure of the undersaturation
of the gas can be defined as the relative saturation
RS varies between 0 and 1 and is often expressed as a percentage. When RS < 1, the gas is undersaturated, and when RS = 1, it is saturated, and a liquid phase is also present in the system.
At saturation conditions (RS = 1), combining Equations 
and  yields the condition
Equation  relates the 3 variables Tdp,
RS, and T. Note that Equation  has no explicit dependence
on P. This is a consequence of the assumption of the ideal-gas
EOS (in Section 8, we show how the P dependence arises
when this assumption is improved).
4. Special Case of Moist-Air System
Although Tdp, Pdp, and RS are defined for all GV systems, the following definitions are used only in the context of moist-air systems:
5. Calculations of Pdp and Tdp for GV Systems
Equation  gives
This may be expressed in terms of RS using equation , to
For given pA, Equation  is a nonlinear equation for Tdp. For given RH and T, Equation  is a nonlinear equation for Tdp. (Note that the constitutive relation p*(T ) is required in all cases except for the determination of Pdp via Equation ).
For a given value of RS, the value of Tdp obtained from Equation  can be plotted against the value of T. For moist-air systems, this type of plot is called a psychrometric chart and such charts appear in many textbooks. The plots relate the 2 values of T with RH as a parameter, and also contain other thermodynamic information concerning the moist-air system.
Although charts are useful, they are a carry-over from the
pre-computer era, and Tdp can be directly calculated
from Equation . Knowledge of the basis for implementing such
a procedure also allows calculations to be performed in the absence
of charts (which may not be available for other GV systems). Although
many constitutive relations for p*(T )
of water are available, of varying degrees of accuracy, for illustrative
purposes we will use the following correlation3:
where p* is in Pa, T is in K, and A=73.649, B=-7258.2, C=-7.3037, D=4.1653E-06.
Equation  can be solved using any of the popular computer
algebra systems4 (Maple, Mathematica, Mathcad). For
illustation, the following simple Maple commands calculate Tdp
in a moist-air system for a dry-bulb temperature T=30°and
a relative humidity of 50%.
7. GV Calculations Using EQS4WIN Lite
The Lite version of EQS4WIN can be used to perform the calculation of Tdp and Pdp. For example, Tdp cab be calculated as follows (using the case RH = 0.5, T = 30°for illustration):
First, find the vapor pressure, p*(T):
Second, find Tdp:
The value of Tdp can be refined by calculating
more precise values of p*(30), and then by refining
the calculation of Tdp in the final step.
8. Improving the Simplest Approximations for GV Systems
If the solubilities of the other gases in the condensed liquid are significant, then more general phase equilibrium approaches must be used. This occurs, for example, if the critical temperatures of the remaining substances are below the system T, but not substantially so. We consider here only the relaxation of the approximations of Section 3.
In general, at saturation, we must equate the chemical potentials
of the condensable component in each phase. This is equivalent
to equating their fugacities. Thus we have, at saturation (2-phase)
where T refers to Tdp, f is
the fugacity, g denotes the gas phase, liq denotes
the liquid phase and y is the mole fraction of the condensable
component, A, in the gas. Using the fugacity coefficient Ø,
we may re-write this as
The bracketed terms can be calculated from an EOS for pure
condensed A and for the gas mixture, respectively, and Equation
 may be re-written as
where PC is the Poynting correction for the fugacity of pure
liquid A and Ø* is the second bracketed
term. PC is given by integrating
from p* (where PC = 1) to P at the
mixture T, where vm is the molar volume
of condensed A and R is the universal gas constant. Calculation
of Ø* requires an EOS for the mixture.
For example, if we assume the mixture obeys the virial equation
of state up to and including the second virial coefficient6
where B2 is the second virial coefficient
of pure A, and
where 1 refers to the second component of the mixture, B1
is its second virial coefficient, and B12 is
the mixture second virial coefficient cross term.
9. Other GV Systems
A binary mixture of n-hexane and nitrogen is another example
of a GV system. The Tc values are respectively
507.43 K and 126.10 K. A situation that is analogous to a "dehumidification
of moist air via cooling" is the following:
A mixture of n-hexane and nitrogen can be separated by passing it through a "cooler-condenser", in which the entering gas stream is cooled to condense the n-hexane. Assuming that the exit gas stream is in equilibrium with the condensed (n-hexane) liquid stream, the n-hexane partial pressure in the exit stream is the saturation pressure corresponding to the exit temperature.
Other GV systems are mixtures of water with each of the gases
nitrogen, oxygen, methane, hydrogen, helium, neon, argon, krypton,
xenon, carbon dioxide, and ethane. Properties of these mixtures
are given in reference 5 given below. However, users of this reference
should also have reference 6 available, which shows how errors
in Reference 5 must be corrected.