A single-component system containing two phases (gas and liquid) in equilibrium has one degree of freedom. It is thus completely specified by a single independent variable, usually the temperature. The remaining equilibrium state variables, *vapor pressure* p_{s}, and the molar volumes of the two coexisting phases and follow from the combination of thermodynamic equilibrium criteria and the equation of state applied to the two coexisting planes. The latent heat of vaporization ΔH corresponds to the amount of energy that must be supplied to the system to convert a unit amount of substance from the liquid to the vapor phase under conditions of equilibrium between the two phases. This transition thus always occurs at constant temperature and the corresponding vapor pressure, p_{s}. The second law of thermodynamics yields the relationship between the *heat of vaporization* and the *entropy of vaporization* as:

The *enthalpy of vaporization* is equal to the heat of vaporization since the pressure is constant along the phase transition, so that

where the subscript s denotes saturation conditions.

The latent heat of vaporization may be related to other thermodynamic quantities [Majer et al. (1989)]; for example, the equation

relates it to the (pT) behavior of the fluid. A further relationship of some significance is the *Clapeyron equation*

since integration with it yields an exact relationship expressing the dependence of the vapor pressure on temperature. From this result, an approximate relationship — valid in the limit of vanishing vapor pressure — can be derived

which is known as the Clausius-Clapeyron Equation and provides a means for estimating latent heat of vaporization from vapor pressure data.

Heats of vaporization of fluid mixtures are much more difficult to discuss simply because in a two-phase, multicomponent system, the number of degrees of freedom is equal to the number of components in the system. Vaporization can occur in an infinite number of ways, characterized by the amount of mixture evaporated and changes in temperature and/or pressure. The various definitions are discussed in detail by Majer et al. (1989)

Methods for the determination of heats of vaporization have been critically evaluated by Majer et al. (1989) who have also summarized methods for estimating quantity. Majer and Svoboda (1985) have given an extensive critical review and data compilation for the heats of vaporization of organic compounds.

#### REFERENCES

Majer, V., Svoboda, V., and Pick, J. (1989) *Heats of Vaporisation of Fluids*. Elsevier. Amsterdam.

Majer, V. and Svoboda, V. (1985) Enthalpies of vaporisation of organic compounds. A critical review and data compilation. *IUPAC Chemical Data Series No. 32.* Blackwell. Oxford.

#### References

- Majer, V., Svoboda, V., and Pick, J. (1989)
*Heats of Vaporisation of Fluids*. Elsevier. Amsterdam. - Majer, V. and Svoboda, V. (1985) Enthalpies of vaporisation of organic compounds. A critical review and data compilation.
*IUPAC Chemical Data Series No. 32.* Blackwell. Oxford.