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Relative density

Relative density (also known as specific gravity) is a measure of the density of a material. It is dimensionless, equal to the density of the material divided by the density of water (or, sometimes used for gases, of air).

Since water's density is 1.0 × 103 kg/m3 in SI units, the relative density of a material is approximately the density of the material measured in kg / m3 divided by 1000 (the density of water). There are no units of measurement.

Water's density can also be measured as nearly one gram per cubic centimetre (at maximum density) in metric units. The relative density therefore has nearly the same value as density of the material expressed in grams per cubic centimetre, but without any units of measurement.

Relative density or specific gravity are often ambiguous terms. This quantity is often stated for a certain temperature. Sometimes when this is done, it is a comparison of the density of the commodity being measured at that temperature, with the density of water at the same temperature. But they are also often compared to water at a different temperature.

Relative density is often expressed in forms similar to this:

relative density: 8.15_{\mbox{4 C}}^{\mbox{20 C}} \,\, or specific gravity: 2.432_0^{15}

The superscripts indicate the temperature at which the density of the material is measured, and the subscripts indicate the temperature of the water to which it is compared.

Density of water calculated from formula in 68th CRC Handbook of Chemistry and Physics 1987–1988.

Density of water at 101.325 kPa
(little or no difference at 100 kPa)
Temperature Density
Celsius Fahrenheit kg/m³
0 C 32 F 999.83952
3.98 C 39.16 F 999.9720
15 C 59 F 999.0996
16 2/3 C 62 F 998.8322
20 C 68 F 998.2041
25 C 77 F 997.0449

Water is nearly incompressible. But it does compress a little; it takes pressures over about 400 kPa or 4 atmospheres before water can reach a density of 1000.000 kg/m³ at any temperature.

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. The reason that relative density is measured in terms of the density of water is because that that is the easiest way to measure it in the field. Basically, density is defined as the mass of a sample divided by its volume. With an irregularly shaped rock, the volume can be very difficult to accurately measure. The most accurate way is to put it in a water-filled graduated cylinder and see how much water it displaces. Even this method can be rather inaccurate, though, since it is easy to accidentally spill some water. It is far easier to simply suspend the sample from a spring scale and weigh it under water. Solving Isaac Newton's equations yields the following formula for measuring specific gravity:

G = \frac{W}{W - F}

where G is the relative density, W is the weight of the sample (measured in pounds-force, newtons, or some other unit of force), and F is the force, measured in the same units, while the sample was submerged. Note that with this technique it is difficult to measure relative densities less than one, because in order to do so, the sign of F must change, requiring the measurement of the downward force needed to keep the sample underwater.

Another practical method uses three measurements. The mineral sample is weighed dry. Then a container of water is weighed, and weighed again with the sample immersed. Subtracting the last two readings gives the weight of the displaced water. The relative denisty result is the dry sample weight divided by that of the displaced water. This method works with scales that can't easily accommodate a suspended sample, and also allows for measurement of samples that are less dense than water.

Last updated: 08-31-2005 10:23:11