Chemistry for Everyone
Letters Steam Tables below 0 ⬚C A common misconception about water substance is that only ice exists if the temperature is below 0 ⬚C. Regrettably, this misconception is enhanced by the fact that many “steam tables” only list properties for water substance at and above 0 ⬚C. However, a recent review by Glasser (1) gives a phase diagram for pressures up to 4 × 106 MPa for temperatures from ᎑150 to 200 ⬚C and another review (2) mentions thirteen phases of ice and gives a phase diagram from ᎑200 to 80 ⬚C up to 2.5 MPa. As stated in ref 1, thermodynamic properties can be calculated from the Helmholtz function but since the function cited there has sixty-eight terms this is not regarded as practical. While Glasser’s article (1) provides useful equations for vapor pressure and density, no information is given for other properties. Apparently the most useful source for these properties is the review by Grigull and Marek (3), which gives tables for ten properties for 25 temperatures down to ᎑9 ⬚C and 1 MPa. Another publication (4) presents extensive information on enthalpy and entropy but only in graphical form for temperatures from ᎑22 to 420 ⬚C and pressures up to 2900 MPa. Only one table, for the subcooled liquid, is given for temperatures below 0 °C. The present work is an attempt to tabulate values in the range ᎑22 to 0 ⬚C for the liquid and also for the ices for pressures up to about 630 MPa. Analysis
tively. Note that if Tables 3 and 4 are used to extrapolate values to the ice points, results that differ moderately from those in Table 1 may be obtained. For the solid–liquid equilibrium at normal pressures below 0 ⬚C, the tables of Jones and Dugan (9) are apparently the most recent available. However, their vapor pressures differ from the calculations of Wagner et al. (10). Table 5 gives values of the vapor pressures calculated from the Wagner formulation and also the ideal gas enthalpies and entropies. These were calculated from the tables of Woolley (11) and were adjusted to match the saturated vapor values of Harvey (12) at 0 ⬚C. Simple equation fits for the properties of water substance at and above 0 ⬚C have been given elsewhere (13) and a more elaborate fitting has also appeared (14). W
Supplemental Material
Tables 1–5 and Figure 1 are available in this issue of JCE Online. Literature Cited 1. 2. 3. 4. 5.
Table 1 gives properties for the solid–liquid equilibrium (see the Supplemental MaterialW for all tables). The pressures were calculated from equations given by Glasser (1) for ice I from 273.16 to 251.17 K, for ice III from 251.17 to 256.16 K, and for ice V from 256.16 to 273.31 K. The minimum temperature at which water can exist in the liquid form under pressure is 251.17 K or ᎑21.99 ⬚C, that is, approximately ᎑22 ⬚C. Note that liquid water at atmospheric pressure can be cooled to temperatures as low as ᎑40 ⬚C (5) under special conditions (see also ref 6 ). The enthalpy and entropy values were interpolated from values at 0, ᎑5, ᎑10, and ᎑15 ⬚C kindly supplied by Harvey (7) for ices I and V. The values for ice III were estimated from the limiting values for ices I and V and from the graphs given by Grigull et al. (4). No attempt was made to give volume data for the ices. The reader is referred to the work of Archer (8) for information on the composition of ice. Values of thermodynamic properties for the liquid for temperatures at and below 0 ⬚C were based on values at 0, ᎑5, ᎑10, and ᎑15 ⬚C (7). A modified Tait equation was found to excellently represent the volume values, and coefficients for this equation are given in Table 2. Similar tables for the enthalpy and entropy are given in Tables 3 and 4, respec-
www.JCE.DivCHED.org
•
6. 7. 8. 9. 10. 11.
12.
13. 14.
Glasser, L. J. Chem. Educ. 2004, 81, 414–418. Klug, D. D. Physics World 2005, 18, 25. Grigull, U.; Marek, R. Warme U. Staff. 1994, 30, 1. Grigull, U.; Straub, J.; Schiebener, P. Steam Tables in SI Units, 3rd ed.; Springer-Verlag: Berlin, 1950; p 137. Bigg, E. K. Sci. J. Roy. Coll. Sci. (London, U.K.), 1953, 23, 107–114. Mason, B. J. Adv. Phys. 1958, 7, 221. Harvey, A. H. National Institute of Standards and Technology, Boulder, CO. Private communication, 2005. Archer, D. G.; Carter, R. W. J. Phys. Chem. B 2000, 104, 8563–8584. Jones, J. B.; Dugan, R. E. Engineering Thermodynamics; Prentice Hall: Englewood Cliffs, NJ, 1996; p 912. Wagner, W.; Saul, A.; Pruss, A. J. Phys. Chem. Ref. Data 1994, 23, 515–521. Woolley, H. W. Water and Steam, Their Properties and Current Industrial Applications; Straub, J., Scheffler, K., Eds.; Pergamon: New York, 1980; pp 166–175. Harvey, A. H. Thermodynamic Properties of Water, NISTIR 5078; National Institute of Standards and Technology: Boulder, CO, 1998; p 93. Liley, P. E. Int. J. Mech. Eng. Educ. 1999, 27, 317–323. Fernandes, J. L. M. Int. J. Energy Res. 1995, 19, 507–514. Peter E. Liley 3608 Mulberry Drive Lafayette, IN 47905-3937
[email protected] Vol. 83 No. 11 November 2006
•
Journal of Chemical Education
1601
