DENSITY AND SPECIFIC GRAVITY

Density is defined as mass per unit volume (Fig. 2–3). That is,
Density: (2–1) The reciprocal of density is the specific volume v, which is defined as volume
per unit mass. That is, v ! V/m ! 1/r. For a differential volume element
of mass dm and volume dV, density can be expressed as r ! dm/dV.
The density of a substance, in general, depends on temperature and pressure.
The density of most gases is proportional to pressure and inversely
proportional to temperature. Liquids and solids, on the other hand, are
essentially incompressible substances, and the variation of their density with
pressure is usually negligible. At 20°C, for example, the density of water
changes from 998 kg/m3 at 1 atm to 1003 kg/m3 at 100 atm, a change of
just 0.5 percent. The density of liquids and solids depends more strongly on
temperature than it does on pressure. At 1 atm, for example, the density of
water changes from 998 kg/m3 at 20°C to 975 kg/m3 at 75°C, a change of
2.3 percent, which can still be neglected in many engineering analyses.
Sometimes the density of a substance is given relative to the density of a
well-known substance. Then it is called specific gravity, or relative density,
and is defined as the ratio of the density of a substance to the density of
some standard substance at a specified temperature (usually water at 4°C,
for which rH2O ! 1000 kg/m3). That is,