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

The measurement of the density of a substance is, in principle, extremely simple since from the definition of density, one merely needs to determine the mass of the material contained in a given volume. In practice, the measurement is not so simple, particularly if the thermodynamic state at which the density is required departs significantly from ambient temperature and pressure. The technique employed for measurements also depends upon the phase of the substance.

### Measurements in Liquids

Measurement of the density of a liquid at atmospheric pressure and temperatures near to ambient can readily be conducted with a specific-gravity bottle to an accuracy of better than ±0.1%. The device merely consists of a small glass bottle with an extremely accurately-calibrated volume, which is weighed empty and then filled with the liquid. Obviously, such a device becomes impractical in this form for measurements at high pressures and/or temperatures far removed from ambient.

Measurements of liquid densities at moderate pressures are now most easily performed with the aid of vibrating U-tube densimeters Wood (1989). Such devices are commercially-available for use at pressures up to 40 MPa over a wide temperature range. The principle of the technique is that a thin steel or quartz tube bent into the shape of a 'U' (as shown in Figure 1) is set into oscillation perpendicular to the plane of the U. The frequency of oscillation of the tube is determined by its mass which, in turn, is related to the mass of liquid contained within it. Since the frequency of oscillation is rather easily measured with high precision, accuracies in the measurement of liquid density of 1 part in 105 are claimed.

For operation at higher pressures, these devices are unstable owing to the hydrostatic distortion of the thin-walled tube. Considerably greater efforts must be expended to make measurements of liquid densities under such conditions. It is often necessary to resort to methods that measure the volume of a fixed mass of sample as a function of pressure [Whalley (1975); Dymond and Malhotra (1988)]. Padua et al. (1994) have recently described an alternative method making use of an oscillating body.

### Measurements in Gases

In the gas phase, some of the techniques for measurement of density are quite different owing to the property of a gas to expand and to fill the space made available to it. Thus, at moderate pressures the gas under investigation is contained in a well-defined volume and pressure and temperature are measured and/or controlled. Measurements are then made by varying one quantity and determining the effect on the second. Thus, one may vary the volume and examine the resulting pressure change with the temperature constant throughout. This is the method most often employed for the determination of the second virial coefficient. (See Density of Gases.) If the volume in the quantity is maintained constant and pressure is measured as a function of temperature, one has the so-called isochoric system which is often employed also at higher pressures.

It follows from this general description of the principles of measurements that precise and accurate measurements of a temperature and pressure are required, but modern techniques allow these measurements quite readily. The determination of the volumes of vessels involved in this process is often reduced to a gravimetric measurement armed with the knowledge of the density of a liquid, such as mercury, used to fill the vessels.

Accuracy in direct gas density measurements of one part in 105 are possible, but require extreme care and patience [Saville (1975); Brielles et al. (1975); Malbrunot (1975)].

#### REFERENCES

Wood, R. H. (1989), Flow calorimetry and densitometry at high temperatures, Thermochimica Acta 154, 1.

Whalley, E. (1975) The Compression of Liquids, in Le Neindre, B., Vodar, B., eds., Experimental Thermodynamics of Non-Reacting Fluids, IUPAC, Butterworths, London, Chapter 9.

Dymond, J. H. and Malhotra, R. K. (1988), The Tait equation: 100 years on, Int. J. Themophys. 9, 941.

Padua, A. A. H., Fareleira, J. M. N. A., Calado, J. C. G., and Wakeham, W. A. (1994), A vibrating-wire densimeter for liquids at high pressures: The density of 2,2,4-trimethylpentane from 298.15 to 348.15 K and up to 100 MPa, Int. J. Thermophys. 15, 229.

Saville, G. (1975) Measurements of p-V-T Properties of Gases and Gas Mixtures at Low Pressure, in Le Neindre, B., Vodar, B., eds., Experimental Thermodynamics of Non-Reacting Fluids, IUPAC, Butterworths, London, Chapter 6.

Brielles, J., Dédit, A., Lallemand, M., Le Neindre, B., Leroux, Y, Vemeuse, J., and Vidal, D., ibid., Chapter 7.

Malbrunot, P., ibid., Chapter 8.

#### References

1. Wood, R. H. (1989), Flow calorimetry and densitometry at high temperatures, Thermochimica Acta 154, 1.
2. Whalley, E. (1975) The Compression of Liquids, in Le Neindre, B., Vodar, B., eds., Experimental Thermodynamics of Non-Reacting Fluids, IUPAC, Butterworths, London, Chapter 9.
3. Dymond, J. H. and Malhotra, R. K. (1988), The Tait equation: 100 years on, Int. J. Themophys. 9, 941.
4. Padua, A. A. H., Fareleira, J. M. N. A., Calado, J. C. G., and Wakeham, W. A. (1994), A vibrating-wire densimeter for liquids at high pressures: The density of 2,2,4-trimethylpentane from 298.15 to 348.15 K and up to 100 MPa, Int. J. Thermophys. 15, 229.
5. Saville, G. (1975) Measurements of p-V-T Properties of Gases and Gas Mixtures at Low Pressure, in Le Neindre, B., Vodar, B., eds., Experimental Thermodynamics of Non-Reacting Fluids, IUPAC, Butterworths, London, Chapter 6.
6. Brielles, J., DÃ©dit, A., Lallemand, M., Le Neindre, B., Leroux, Y, Vemeuse, J., and Vidal, D., ibid., Chapter 7.
7. Malbrunot, P., ibid., Chapter 8.