ITS-90 Density of Water Formulation for Volumetric Standards Calibration

A new formulation of the density of air-saturated water as a function of temperature on the 1990 International Temperature Scale (ITS-90) is presented. Also, a new equation for calculating isothermal compressibility as a function of temperature on ITS-90 was developed. The equations are to be used to calculate the density of water, in the temperature range 5 to 40 °C on ITS-90, used in the gravimetric determination of the volume of volumetric standards.


Introduction
In the gravimetric determination of the volume (calibration) of volumetric standards, water is used as the calibrating fluid. The volume is calculated from the mass and density of the water. In many quarters, the formulation of Wagenbreth and Blanke [1] is used to calculate the density of water. In this paper, a new formulation of the density of water (based primarily on the work of Kell [2]) as a function of temperature on the 1990 International Temperature Scale is presented.
In contrast with the Kell equation, a term in r* is not necessary due at least in part to the fact that the 0 to 4 °C region, in which p increases with increasing temperature, has been excluded. Equation (3) applies to air-free water.
Values of the density of air-free water were calculated for temperatures (ITS-90, t^) between 4.999 and 39.990 "C using Eq. (3) and compared with corresponding Kell values. The estimate of the standard deviation (SD) of the difference was 0.00034 kg m-^ The ratio of SD to the mean value of density was 3.4 x IQ-^ which is negligible.

Conversion of IPTS-68 to ITS-90
A very simple equation relating ITS-90 temperature, ^90, to IPTS-68 temperature, ^68, has been used in the present work to generate values of/» for the development of Eq. (3). The equation for the temperature range 0 to 40 °C is In the temperature range 0 to 100 °C the equation is /«, = 0.0005+ 0.9997333/68 . (4b)

Change in Density of Water with Air Saturation
Bignell [4] measured the change in the density of water with air saturation for 80 points in the range of 4 to 20 °C. He fitted the points to develop the equation where Ap is in kg m"^. There is no need to adjust for temperature scale. Bignell concluded that "there is probably not much need to extend the work to higher temperatures because the effect diminishes and the accuracy of density metrology at these temperatures would not warrant a more accurately known correction."

Density of Air-Saturated Water on ITS-90
Equation (5) was added to Eq. (3) to produce an equation to be used to calculate the density, pas, of air-saturated water in the temperature range 5 to 40 °C on ITS-90: Pas = 999.84847 + 6.337563 x 10 -^ / -8.523829x10-^/^ + 6.943248x10-'/ = -3.821216x10-'/" The uncertainty in the density of air-saturated water for an uncertainty in temperature of 1 °C is approximately 210 ppm or 0.21 kg m"^ at 20 °C.
The value of the isothermal compressibility of water is approximately 46.5 parts per million (ppm)/atmosphere at 20 °C. At locations where the atmospheric pressure is significantly different from 1 atmosphere (101.325 kPa), a correction for compressibility calculated using Eq. (7) should be made. For example, at Boulder, CO, the correction for compressibility is approximately -8 ppm at 20 °C.

Compressibility-Corrected Water Density Equation
The expression for the density of air-saturated water, pasc, at an ambient pressure of P kPa is where pas is calculated using Eq. (6) and KT is calculated using Eq. (7). Table 1 is a tabulation of values of the density of air-saturated water using Eq. (6). Table 2 is a tabulation of the values of the density of air-free water calculated using Eq. (3). Table 3 is a tabulation of values of air-free water calculated using the formulation of Wagenbreth and Blanke [1], this table has been included in this paper for purposes of comparison.

Tables
The units for water density in these tables are g/cm^, as a convenience to those who routinely use these units. Table 1. Density of air-saturated water (g/cm')from Eq. (6) using Kell [2] data