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

Figure 1 shows a plot of the relationship of the pressure p in a pure substance to its molar volume, , for various temperatures, T, while Figure 2 shows a projection of the same behavior with pressure and temperature as the coordinates and volume as a parameter.

If a pure liquid is contained in a sealed tube in equilibrium with its vapor at a temperature T1 then, in a gravitational field, the top of the liquid is indicated by an interface (meniscus). Such a situation corresponds to the isotherm T1 in Figure 1, where point 2 represents the system at the vapor-pressure of the liquid and corresponds to the liquid molar volume, whereas point 1 corresponds to the larger molar volume of the vapor phase at the same pressure and temperature. In Figure 2, both points 1 and 2 lie on the vapor-pressure curve which separates liquid and vapor phases. If tube temperature is increased to T2 in Figure 1, vapor pressure is increased along 1c of Figure 2. At the same time, the molar volume of the liquid phase is increased and that of the vapor decreased, as shown in Figure 1. If this process is continued, the liquid phase and the vapor phase eventually become indistinguishable at some temperature, which is the situation indicated by point c in Figures 1 and 2. At this temperature, the critical temperature, Tc, the meniscus disappears and the molar volumes of the two phases are equal to . Critical temperature may also be defined as the highest temperature at which the liquid phase of a substance can exist.

As can be seen from Figure 1, along the critical isotherm Tc, the relationship between fluid pressure and its molar volume shows a point of inflection at the molar volume the critical volume, and the corresponding critical pressure pc, so that the conditions

define the critical point. This is the unique thermodynamic state for which, at temperature Tc, molar volume is and pressure, pc It is necessary only to prescribe two of these critical state parameters since the third is then automatically determined.

The critical state parameters Tc, and pc are characteristics of each pure substance and must be determined experimentally. An up-to-date and extensive compilation of the critical state parameters of pure substances is currently being prepared by the Subcommittee on Thermodynamic Data of the IUPAC Commission on Thermodynamics [Young (1995); Ambrose (1995)].

Many of the other physical properties of pure fluids exhibit special behavior near the critical point, which is the subject of current intensive investigation [Sengers and Levelt-Sengers (1986)]. For example, the heat capacity of fluid becomes infinitely large at the critical point as does thermal conductivity, whereas thermal diffusivity becomes zero.

Figure 3 shows experimental results for the thermal conductivity of carbon dioxide near the critical point. Some of these effects, a result of large-sale fluctuations in the density of fluid, extend over a wide range of temperature and density around the critical point. For example, the effect upon isobaric heat capacity and thermal conductivity can be more than 10%, even 50K, above the critical temperature at the critical density.

#### REFERENCES

Ambrose, D. (1995) Article to appear in Pure and Applied Chemistry, citation not yet available.

Bett, K. E., Rowlinson, J. S. and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London.

Sengers, J. V. and Levelt-Sengers, J. M. H. (1986) Ann. Rev. Phys. Chem. 37, 189.

Young, G. J. (1995) Article to appear in Pure and Applied Chemistry, citation not yet available.

#### References

1. Ambrose, D. (1995) Article to appear in Pure and Applied Chemistry, citation not yet available.
2. Bett, K. E., Rowlinson, J. S. and Saville, G. (1975) Thermodynamics for Chemical Engineers, Athlone Press, London.
3. Sengers, J. V. and Levelt-Sengers, J. M. H. (1986) Ann. Rev. Phys. Chem. 37, 189.
4. Young, G. J. (1995) Article to appear in Pure and Applied Chemistry, citation not yet available.