Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density (mass divided by volume) of a substance to the density of a given reference material. The relative density of solids and liquids is nearly always measured with respect to water at its densest (at ); for gases, the reference is air at room temperature (). The term "relative density" (abbreviated r.d. or RD) is preferred modern use, for example in ISO, IUPAC, and NIST, while the term "specific gravity" (abbreviated S.G. or SG) is gradually being abandoned.
If a substance's relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.
Temperature and pressure must be specified for both the sample and the reference. The pressure is nearly always atmospheric pressure (), and where it is not, usually the density is specified directly. The reference temperature for water is often , but and are also common standards, depending on the industry (like brewing or petroleum). In British brewing practice, the relative density, as specified above, is multiplied by 1000. Relative density is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, must weight (syrups, juices, honeys, brewers wort, must, etc.) and acids.
Basic calculation Relative density () or specific gravity () is a dimensionless quantity, as it is the ratio of either densities or weights
where is relative density, is the density of the substance being measured, and is the density of the reference. (By convention , the Greek letter rho, denotes density.)
The reference material can be indicated using subscripts: which means "the relative density of substance with respect to reference". If the reference is not explicitly stated then it is normally assumed to be water at 4 °C (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In SI units, the density of water is (approximately) 1000 kg/m3 or 1 g/cm3, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units.
The relative density of gases is often measured with respect to dry air at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m3. Relative density with respect to air can be obtained by
where is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure, i.e., they are both ideal gases. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 L under those same conditions.
Those with SG greater than 1 are denser than water and will, disregarding surface tension effects, sink in it. Those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where relative density finds wide application, often for historical reasons.
True relative density of a liquid can be expressed mathematically as:
where is the density of the sample and is the density of water.
The apparent relative density is simply the ratio of the weights of equal volumes of sample and water in air:
where represents the weight of the sample measured in air and the weight of an equal volume of water measured in air.
It can be shown that true relative density can be computed from different properties:
where g is the local acceleration due to gravity, V is the volume of the sample and of water (the same for both), ρsample is the density of the sample, ρH2O is the density of water, WV represents a weight obtained in vacuum, is the mass of the sample and is the mass of an equal volume of water.
The density of water and of the sample varies with temperature and pressure, so it is necessary to specify the temperatures and pressures at which the densities or weights were determined. Measurements are nearly always made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns), but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure are usually neglected at least where apparent relative density is being measured. For true (in vacuo) relative density calculations, air pressure must be considered (see below). Temperatures are specified by the notation (Ts/Tr), with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, while SGH2O = (20 °C/20 °C), it is also the case that SGH2O = = (20 °C/4 °C). Here, temperature is being specified using the current ITS-90 scale and the densities used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are and respectively, resulting in an SG (20 °C/4 °C) value for water of .
As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, it is extremely important that the analyst enter the table with the correct form of relative density. For example, in the brewing industry, the Plato table lists sucrose concentration by weight against true SG, and was originally (20 °C/4 °C)ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009 i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density, ρH2O equal to 999.972 kg/m3 in SI units ( in cgs units or 62.43 lb/cu ft in United States customary units). The ASBC tableASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer in use today in North America for apparent relative density measurements at (20 °C/20 °C) is derived from the original Plato table using Plato et al.'s value for SG(20 °C/4 °C) = . In the sugar, soft drink, honey, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by A. Brix, which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).
Given the relative density of a substance, its actual density can be calculated by rearranging the above formula:
Temperature dependence See Density for a table of the measured densities of water at various temperatures.
The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa ignoring the variations caused by changing weather patterns) but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are usually neglected at least where apparent relative density is being measured. For true (in vacuo) relative density calculations air pressure must be considered (see below). Temperatures are specified by the notation (Ts/Tr) with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, while SGH2O = 1.000000 (20 °C/20 °C) it is also the case that RDH2O = = 0.9982288 (20 °C/4 °C). Here temperature is being specified using the current ITS-90 scale and the densities used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale the densities at 20 °C and 4 °C are, respectively, 0.9982041 and 0.9999720 resulting in an RD (20 °C/4 °C) value for water of 0.99823205.
The temperatures of the two materials may be explicitly stated in the density symbols; for example: relative density: 8.15 where the superscript indicates the temperature at which the density of the material is measured, and the subscript indicates the temperature of the reference substance to which it is compared.
Uses Relative density can also help to quantify the buoyancy of a substance in a fluid or gas, or determine the density of an unknown substance from the known density of another. Relative density is often used by geologists and mineralogists to help determine the mineral content of a rock or other sample. Gemologists use it as an aid in the identification of gemstones. Water is preferred as the reference because measurements are then easy to carry out in the field (see below for examples of measurement methods).
As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density. For example, in the brewing industry, the Plato table, which lists sucrose concentration by mass against true RD, were originally (20 °C/4 °C) that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of ρ() equal to 0.999972 g/cm3 (or 62.43 lb·ft−3). The ASBC table in use today in North America, while it is derived from the original Plato table is for apparent relative density measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm3. In the sugar, soft drink, honey, fruit juice and related industries sucrose concentration by mass is taken from this workHough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and Brewing Science, Vol. II Hopped Wort and Beer, Chapman and Hall, London, 1997, p. 881 which uses SG (17.5 °C/17.5 °C). As a final example, the British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).
In medicine, relative density is particularly used in the pharmaceutical field. It is used in automated compounders in preparation of multicomponent mixtures for parenteral nutrition, while it is an important factor in urinalysis, relative density is an indicator of both the concentration of particles in the urine and a patient's degree of hydration.
Measurement