Relative density

Relative density, or specific gravity,[1][2] is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in modern scientific usage.

If a substance's relative density is less than one 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 (or specific gravity) 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. Pressure is nearly always 1 atm equal to 101.325 kPa. Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice the specific gravity as specified above is multiplied by 1000.[3] Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, sugar solutions (syrups, juices, honeys, brewers wortmust, etc.) and acids.

Basic formulas

Relative density (RD) or specific gravity (SG) is a dimensionless quantity, as it is the ratio of either densities or weights

$RD = frac{ ho_mathrm{substance}}{ ho_mathrm{reference}},$

where RD is relative density, ρsubstance is the density of the substance being measured, and ρreference is the density of the reference. (By convention ρ, the Greek letter rho, denotes density.)

The reference material can be indicated using subscripts: RDsubstance/reference, 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

$mbox{RD} = frac{ ho_mathrm{gas}}{ ho_{mathrm{air}}} approx frac{M_mathrm{gas}}{M_{mathrm{air}}}$

Where M 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

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Mining Engineering

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Maijd M. Almotairi

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