A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering

If the gas or vapor represented by the point X in the phase for a pure fluid shown in Figure 1 is compressed slowly and isothermally, the pressure rises until the vapor becomes saturated and the first drop of liquid appears at conditions corresponding to point 1. If the compression is continued, condensation takes place at a constant pressure known as the saturation pressure for the given temperature. For a pure substance, the relationship between the saturation pressures and temperatures is given by measurements of this vapor pressure. At any point on the line between point 1 and point 2, saturated liquid and saturated vapor are in equilibrium. At point 2 the vapor phase disappears and only saturated liquid remains. Although the specific volume of a two-phase system changes continuously as the relative amounts of the two phases change, the specific volumes of the saturated vapor and liquid in equilibrium along the line 1-2 are those of points 1 and points 2, respectively. The specific volume of a liquid-vapor mixture with a quality, x, is given by

which is known as the Lever Rule.

The most important saturation property is therefore the vapor pressure, which can be determined experimentally by a number of techniques [Ambrose (1973)]. Once the saturation line is defined, it is possible to consider the properties of both coexisting phases at saturation, including the density and heat capacity. The density of the vapor at saturation is seldom measured directly owing to the difficulties involved so that it is frequently obtained indirectly. On the other hand, the liquid phase density at saturation is more easily measured. Heat capacity measurements in both liquid and vapor phases are possible [Marsh and O'Hare (1994)]. It is noteworthy that in the liquid phase it is possible to define three specific heat capacities: cp, the change in enthalpy with temperature at constant pressure; cσ, the change in enthalpy with temperature for the saturated liquid and csat, the energy required to effect a temperature change while maintaining the liquid in a saturated state. The three heat capacities do not generally differ by very much. Estimation methods for saturated densities and heat capacities at saturation are available [Reid et al. (1977)].

#### REFERENCES

Ambrose, D. (1973) in Experimental Thermodynamics of Non-Reacting Fluids, Le Neindre, B., Vodar, B., Eds., IUPAC, Butterworths, London.

Marsh, K. N. and O'Hare, P. A. G. (1994) Experimental Thermodynamics IV: Solution Calorimetry, Blackwell, Oxford.

Reid, R. C, Prausnitz, J. M., and Sherwood, T. K. (1977) The Properties of Gases and Liquids, McGraw-Hill, New York.

#### References

1. Ambrose, D. (1973) in Experimental Thermodynamics of Non-Reacting Fluids, Le Neindre, B., Vodar, B., Eds., IUPAC, Butterworths, London.
2. Marsh, K. N. and O'Hare, P. A. G. (1994) Experimental Thermodynamics IV: Solution Calorimetry, Blackwell, Oxford.
3. Reid, R. C, Prausnitz, J. M., and Sherwood, T. K. (1977) The Properties of Gases and Liquids, McGraw-Hill, New York.