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2.2  Mechanical properties of materials

2.2.1 Densities

Density of water (unit 1 kg m⁻³)

Pure air-free water under a pressure of 101 325 Pa.

Values based on the following expression (Kell, 1975, 97–105, recalculated for ITS-90 by Bettin and Spieweck, 1990, 195–196):

  density at t/°C = (999.839 52 + 16.952 577t − 7.990 512 7 × 10⁻³t² − 46.241 757 × 10⁻⁶t³

                    + 105.846 01 × 10⁻⁹t⁴ − 281.030 06 × 10⁻¹²t⁵)/(1 + 16.887 236 × 10⁻³t)

A new formula with lower uncertainty is available for the temperature range 0 °C to 40 °C, see Tanaka et al., 2001, 301-309. This new formula is valid for SMOW (standard mean ocean water) and it predicts density values that are about 3 ppm higher than those given by the above formula. Taking this into account, the deviations from the above formula are less than 1 ppm.

In the range 0 to 25 °C, the correction (/kg m ⁻³) for air-saturated water at temperature t (Bignell 1983, 57−59) is

     −(4.612 − 0.106t) × 10⁻³

The temperature (t_m/°C) of maximum density at different pressures (p/Pa) is given by

     t_m = 3.98 − 0.222 × 10⁻⁶(p − 101 325)

Information on the preparation of water as a reference material, together with the dependence of its density upon isotopic abundance can be found in Marsh (1987, 13–16).

Density of heavy water

Originally calculated by Kell (1967), from measurements by Chang and Tung (1949), Shrader and Wirtz (1951) and Steckel and Szapiro (1963).

Under a pressure of 101 325 Pa.

Density of mercury (unit 1 kg m^-3)

Under a pressure of 101 325 Pa.

Based on:

   Density at 0 °C = 13 595.08 kg m⁻³

and the expression

   ρ = ρ₀/(1 + αt)

where ρ is the density at t °C and

   10⁸α = 18 158.68 + 0.545 83t + 3.4980 × 10⁻³t² + 1.5558 × 10⁻⁶t³

The formula for α relates to temperatures expressed in terms of the ITS-90 temperature scale. The formula for α, together with the density at 0°C, was derived by Ambrose (1990, 245–247) from the density at 20 °C determined by Cook (1961) and Cook and Stone (1957) and the expansion formula of Beattie et al. (1941), both of which were related to the IPTS-48 scale.

Other reference materials

A number of other materials (most notably single crystal silicon) are recommended by the International Union of Pure and Applied Chemistry as reference materials for density determination. Details of these, including their preparation, reliability and stability, can be found in Marsh (1987, 30–37).

Approximate densities of commonly used materials*

  * For densities of the elements and chemical compounds, see under the Chemistry Section of this book.
  † Tungsten with metallic additives.

References

D. Ambrose (1990) Metrologia, 27, 245–247.
J. A. Beattie et al. (1941) Proc. Am. Acad. Arts Sci., 71, 771.
H. Bettin and F. Spieweck (1990) PTB-Mitteilungen, 100, 195–196.
N. Bignell (1983) Metrologia, 19, 57–59.
A. H. Cook (1961) Philos. Trans. R. Soc. London Ser. A, 254, 125–154.
A. H. Cook and N. W. B. Stone (1957) Philos. Trans. R. Soc. London Ser. A, 250, 279–323.
G. S. Kell (1967) J. Chem. Engng Data, 12(1), 66–69.
G. S. Kell (1975) J. Chem. Engng Data, 20(1), 97–105.
K. N. Marsh, Ed. (1987) Recommended Reference Materials for the Realization of Physicochemical Properties (Blackwell Scientific Publications, Oxford).
M. Tanaka et al. (2001) Metrologia, 38, 301 - 309.

Sylvia L. Peggs, Horst Bettin

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