Editing Relative density (section)

==Basic calculation==
Relative density (<math>RD</math>) or specific gravity (<math>SG</math>) is a [[dimensionless quantity]], as it is the ratio of either densities or weights
<math display="block">\mathit{RD} = \frac{\rho_\mathrm{substance}}{\rho_\mathrm{reference}},</math>
where <math>RD</math> is relative density, <math>\rho_\mathrm{substance}</math> is the density of the substance being measured, and <math>\rho_\mathrm{reference}</math> is the density of the reference. (By convention <math>\rho</math>, the Greek letter [[rho]], denotes density.)

The reference material can be indicated using subscripts: <math>RD_\mathrm{substance/reference}</math> 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&nbsp;°[[Celsius|C]] (or, more precisely, 3.98&nbsp;°C, which is the temperature at which water reaches its maximum density). In [[International System of Units|SI]] units, the density of water is (approximately) 1000&nbsp;[[Kilogram|kg]]/[[Cubic metre|m<sup>3</sup>]] or 1&nbsp;[[Gram|g]]/[[Cubic centimetre|cm<sup>3</sup>]], 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&nbsp;°C and a pressure of 101.325 kPa absolute, which has a density of 1.205&nbsp;kg/m<sup>3</sup>. Relative density with respect to air can be obtained by
<math display="block">\mathit{RD} = \frac{\rho_\mathrm{gas}}{\rho_\mathrm{air}} \approx \frac{M_\mathrm{gas}}{M_\mathrm{air}},</math>
where <math>M</math> is the [[molar mass]] and the approximately equal sign is used because equality pertains only if 1 [[Mole (unit)|mol]] of the gas and 1&nbsp;mol of air occupy the same volume at a given temperature and pressure, i.e., they are both [[ideal gas]]es. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0&nbsp;°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 specific gravity finds wide application, often for historical reasons.

True specific gravity of a liquid can be expressed mathematically as:
<math display="block"> SG_\mathrm{true} = \frac {\rho_\mathrm{sample}}{\rho_\mathrm{H_2O}},</math>
where <math>\rho_\mathrm{sample}</math> is the density of the sample and <math>\rho_\mathrm{H_2O}</math> is the density of water.

The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:
<math display="block"> SG_\mathrm{apparent} = \frac {W_{\mathrm{A},\text{sample}}}{W_{\mathrm{A},\mathrm{H_2O}}},</math>
where <math>W_{A,\text{sample}}</math> represents the weight of the sample measured in air and <math>{W_{\mathrm{A},\mathrm{H_2O}}}</math> the weight of an equal volume of water measured in air.

It can be shown that true specific gravity can be computed from different properties:
<math display="block"> SG_\mathrm{true} = \frac {\rho_\mathrm{sample}}{\rho_\mathrm{H_2O}} = \frac {\frac{m_\mathrm{sample}}{V}}{\frac{m_\mathrm{H_2O}}{V}} = \frac {m_\mathrm{sample}}{m_\mathrm{H_2O}} \frac{g}{g} = \frac {W_{\mathrm{V},\text{sample}}}{W_{\mathrm{V},\mathrm{H_2O}}},</math>

where ''g'' is the local acceleration due to gravity, ''V'' is the volume of the sample and of water (the same for both), ''ρ''<sub>sample</sub> is the density of the sample, ''ρ''<sub>H<sub>2</sub>O</sub> is the density of water, ''W''<sub>V</sub> represents a weight obtained in vacuum, <math>\mathit{m}_\mathrm{sample}</math> is the mass of the sample and <math>\mathit{m}_\mathrm{H_2 O}</math> 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&nbsp;kPa ± variations from changing weather patterns), but as specific gravity 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 specific gravity is being measured. For true (''in vacuo'') specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation (''T''<sub>s</sub>/''T''<sub>r</sub>), with ''T''<sub>s</sub> representing the temperature at which the sample's density was determined and ''T''<sub>r</sub> the temperature at which the reference (water) density is specified. For example, SG (20&nbsp;°C/4&nbsp;°C) would be understood to mean that the density of the sample was determined at 20&nbsp;°C and of the water at 4&nbsp;°C. Taking into account different sample and reference temperatures, while ''SG''<sub>H<sub>2</sub>O</sub> = {{val|1.000000}} (20&nbsp;°C/20&nbsp;°C), it is also the case that ''SG''<sub>H<sub>2</sub>O</sub> = {{frac|{{val|0.9982008}}|{{val|0.9999720}}}} = {{val|0.9982288}} (20&nbsp;°C/4&nbsp;°C). Here, temperature is being specified using the current [[ITS-90]] scale and the densities <ref name="PTB-Mitteilungen" /> used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20&nbsp;°C and 4&nbsp;°C are {{val|0.9982041}} and {{val|0.9999720}} respectively,<ref name="„kell">{{cite journal |last1=Kell |first1=George S. |title=Density, Thermal Expansivity, and Compressibility of Liquid Water from 0 to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale |journal=Journal of Chemical and Engineering Data |volume=20 |pages=97–105 |doi=10.1021/je60064a005 |url=https://doi.org/10.1021/je60064a005|url-access=subscription }}</ref> resulting in an SG (20&nbsp;°C/4&nbsp;°C) value for water of {{val|0.998232}}.

As the principal use of specific gravity 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 specific gravity. For example, in the brewing industry, the [[Plato scale|Plato table]] lists sucrose concentration by weight against true SG, and was originally (20&nbsp;°C/4&nbsp;°C)<ref name="ReferenceA">ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009</ref> i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20&nbsp;°C) but referenced to the density of water at 4&nbsp;°C which is very close to the temperature at which water has its maximum density, ''ρ''<sub>H<sub>2</sub>O</sub> equal to 999.972&nbsp;kg/m<sup>3</sup> in SI units ({{val|0.999972|u=g/cm<sup>3</sup>}} in [[CGS system|cgs units]] or 62.43&nbsp;lb/cu&nbsp;ft in [[United States customary units]]). The [[American Society of Brewing Chemists|ASBC]] table<ref name="ReferenceB">ASBC Methods of Analysis ''op. cit.'' Table 1: Extract in Wort and Beer</ref> in use today in North America for apparent specific gravity measurements at (20&nbsp;°C/20&nbsp;°C) is derived from the original Plato table using Plato et al.‘s value for SG(20&nbsp;°C/4&nbsp;°C) = {{val|0.9982343}}. In the sugar, soft drink, honey, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by [[Brix|A. Brix]], which uses SG (17.5&nbsp;°C/17.5&nbsp;°C). As a final example, the British SG units are based on reference and sample temperatures of 60&nbsp;°F and are thus (15.56&nbsp;°C/15.56&nbsp;°C).

Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula:
<math display="block">\rho_\mathrm{substance} = SG \times \rho_\mathrm{H_2O}.</math>

Occasionally a reference substance other than water is specified (for example, air), in which case specific gravity means density relative to that reference.