UNITED STATES DEPARTMENT OF COMMERCE • Charles Sawyer, Secretary NATIONAL BUREAU OF STANDARDS • E. U. Condon, Director Density of Solids and Liquids by Peter Hidnert and Elmer L. Peffer National Bureau of Standards Circular 487 Issued March 15, 1950 For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington 25, D. C. Price 20 cents Preface Density is one of the significant physical properties of materials that is important in science and industry. This Circular is issued to supply a demand for information about various methods for determinations of the densities of solids and liquids. The Circular also indicates that density determinations may be used to identify materials, and to obtain relationships between density, chemical composition, thermal and mechanical treatments, etc. This Bureau has published during the past- four decades the results of investigations on the densities of various materials. A list of these publications will be sent upon request to anyone interested. E. U. Condon, Director. Contents Page Preface II I. Introduction 1 1. Definitions and terms 1 II. Types of apparatus for density determinations 3 1. Hydrostatic weighing method _ _ 3 (a) Solids 3 9. (b) Liquids 3 2. Pienometer method. 8 (a) Liquids 8 (b) Solids 14 3. Flotation method. 15 4. Hydrometer method 18 5. Falling-drop method- . ... 22 6. Balanced-column method- __ 24 7. Method based on Boyle’s law - 24 S. Electromagnetic method 25 Elastic helix method 26 10. Ice calorimeter method __ 27 11. Volumetric method 27 III. References 28 in \ Density of Solids and Liquids by Peter Hidnert and Elmer L. Peffer* Density data may be used for obtaining relationships between density, chemical com- position, thermal and mechanical treatments of materials, etc. This circular defines density and specific gravity, describes 11 methods (hydrostatic weighing, picnometer, flotation, hydrometer, falling drop, balanced column, Boyle’s law, electromagnetic, elastic helix, ice calorimeter, and volumetric) for determinations of the densities of solids and liquids, and indicates the accuracy of various methods. 1 I. Introduction 1. Definitions and Terms stance. Care must lie taken, however, to state the units employed and the temperatures in- Density is a significant physical property of volved, otherwise there is danger of confusion and materials, and is important in science and in- misinterpretation of results. dustry. The extensive literature on density Specific gravity may be determined at any shows that determinations of the density of ma- convenient temperature and referred to water terials is a constant and recurrent problem. at any desired temperature. For example, spe- For example, density determinations may be used cific gravity may be determined at 20° C and to identify materials, and to obtain relationships referred to water at 20°, 15°, 4° C, or any other between density, chemical composition, thermal temperature. It is then expressed as specific and mechanical treatments of materials, etc. gravity at 20°/20° C, 20°/15° C, or 20°/4° C. In any list of the physical properties of a sub- If determined at 25° C, the specific gravity is stance, its density or specific gravity is usually expressed as 25°/20° C, 25°/15° C, or 25°/4° C. included. If the values of the density of a sub- Specific gravity is often expressed in terms of stance are to be relied upon when obtained by water at the same temperature a.s that at which different observers or by different methods, it is the substance is weighed; for example, 15°/15° C, important that they be both accurate and com- 20°/20° C, or 25°/25° C. It is preferable, how- parable. ever, especially in the case of liquids, to express Density is the mass per unit volume and is all specific gravities in terms of water at 4° C. usually expressed in grams per cubic centimeter The values are then directly comparable, since (or per milliliter) at some definite temperature. they are measured in terms of the same unit, and Specific gravity is an abstract number expressing if the change of specific gravity per degree change the ratio of the weight of a certain volume of the of temperature is known they may all be easily material in question to the weight of the same reduced to the same temperature. There is also volume of some other substance taken as standard the additional advantage that specific gravities at a stated temperature. Water is usually used when so expressed are numerically the same as as the standard substance. Both the temperature densities in grams per milliliter. For example, of the material and the temperature of the standard specific gravity at 20°/4° C is numerically the substance should be indicated. same as density at 20° C expressed in grams per Density and specific gravity, while funda- milliliter. This is obvious, since, by definition, mentally different, are nevertheless determined 1 milliliter of water at 4° C weighs 1 gram. in the same way and may have the same numerical In making specific gravity determinations on a values. The two terms are often used synony- series of samples of the same kind, it is likely that mously as expressing the “heaviness” of a sub- the temperatures of the various samples will differ unless a constant temperature bath is * Deceased. somewhat 1 The cubic centimeter (that is, the volume of a cube 1 cm on a side) is not used. Suppose the temperatures range as follows: equal to the milliliter, but the difference is so slight as to be negligible in all 26.2° ordinary determinations. The milliliter is equal to 1.000028 cubic centi- 23.5°, 24.4°, 25.0°, 25.6°, and C. The meters. In volumetric measurements the unit of volume usually employed specific gravities may then be calculated at 23.5°/4°, is the milliliter (ml), though it is sometimes erroneously referred to as the cubic centimeter (ec). When the cubic centimeter is actually intended it 24.4°/4°, 25.074°, 25.674°, and 26,2°/4° C, and, should be written "cm 3 ” and not as "cc”. The cubic centimeter is usually employed to express volumes calculated from linear measurements. if the change of specific gravity per degree centi- l . 0 Table 1 . Corrections, to be applied to apparent specific grade is known, I lie values can at once be reduced gravities in order to obtain true specific gravities a, to 25°/4° C by multiplying the change per degree 25°125° C ( V. S. Pharmacopoeia) centigrade by the difference between the tempera- ture of observation and 25° C. For example, if Apparent Apparent oil, of the change in the samples are linseed which specific Correction specific Correction specific gravity is 0.00068 per degree centigrade, gravity gravity the specific gravities can be reduced to 25°/4° C by subtracting from the observed values of the 0. 6 0. 00047 2.0 —.00118 . 7 . 00035 8.0 -.00236 successive samples 0.00068 times 1.5, 0.6, 0.0, . 8 .00024 4.0 -.00353 . 9 .00012 5. -.00471 — 0.6, and —1.2. 1.0 .00000 6.0 -.00589 1.1 -.00012 If the above specific gravities had been expressed 7. 0 -.00706 1.2 -.00024 8.0 - . 00824 in terms of water at the temperature of observa- 13 -.00035 9.0 —.00942 1 4 -.00047 10.0 —.01060 tion, they would have been at 23.5°/23.5°, 24.4°/ 1.5 —.00059 11.0 -.01177 24.4°, 25.6725.6°, and 26.2°/26.2° C, 1.6 —.00071 12.0 -.01295 25.0725.0°, 1.7 -.00082 13.0 -.01413 and would not then have been directly comparable 1.8 —.00094 14.0 -.01530 1.9 —.00106 15.0 -.01648 or easily reducible to the same basis, since the correction to be applied in each case would then involve both the expansion of the sample itself in vacuum, is calculated by multiplying the air and the change of the unit of measurement, that density by the difference in volume between the is, the density of water. body weighed and the weights required to balancej For purposes of comparison, specific gravities it on an even arm balance, or are sometimes shown in parallel columns at 15°/15° 25°/25° and at C. This method does not B—p(V—Vw), ( 1 ) make possible a real comparison since the values given in the two columns are measured in different where B is the air buoyancy, p the air density,! 1 units. It shows only the difference between the ' the volume of body weighed, and Yw the volume expansion of the sample in question and that of of weights. water over the same temperature range. If it The numerical values of V and Yw can be ar-| should happen that the sample in question had rived at by an approximat ion which may be carried the same rate of expansion as water then the to any desired degree of accuracy. The value of specific gravities of the sample at 15°/15° and at Y may be obtained from the relation 25°/25° C would be identical, that is, it would appear that the specific gravity of the sample did in V= 2 not change with change of temperature. T ( ) In all determinations one should distinguish between apparent and true specific gravity. In where m is the mass, and d is the density of the case the true specific gravity is desired, this can be body. For a first approximation m may be taken obtained either by correcting all weighings for as the uncorrected weight, and d as the apparent! air buoyancy before determining the ratio of the density.