Density: Definition, Measurement, and Dependence on Pressure and Temperature

Density
Introduction
The density of a material or a substance can be defined as the ratio of its mass to its volume. It is
represented by the symbol rho (ρ). It has also been defined as the ratio of the weight of a
substance to its volume (especially in the US and in the oil and gas industries). However, this
definition is more suited as the definition of the specific weight of the substance. Many
substances or materials have different values of gravity. For instance, different metals have
different densities. The density of copper is different from the density of aluminum. At standard
temperature and pressure, the densest substance known is Osmium. Density is a very useful
concept which can be used to explain the behaviour of substances and objects such as floating or
buoyancy.
The fact that a fluid whose density is less than the density of another fluid in a mixture floats on
the denser fluid is applied in the separation of some substances in industry. The same concept
can be applied to solids as long as we take some. For example an object whose density is less
than that of a liquid such as water will float on it where as an object whose density is higher than
that of water will sink below the water surface.
Density can also be used to determine the purity of substances. Since the densities of most
standard substances such as the elements are known, this can be applied to determine whether an
object or substance is pure or not. If a substance contains impurities, its density will deviate from
the standard known values hence it is possible to rule out impure substances from pure ones.
There are some cases in which density is given as a quantity without dimensions such as relative
density. The relative density of a substance is the density of that substance computed with
respect to another standard substance. Water is the most used substance for the determination of
relative densities. For instance, an object or substance with a relative density below one is
considered to float in water. Another commonly encountered quantity in the study of gravity is
called specific volume. This is defined as the reciprocal of the density of a substance. It is mostly
used in thermodynamics.
Discussion
In equation form, density is defined as:
ρ = m
v
Where;
M is the mass of the material or substance and v is its volume.
The SI unit for gravity is kg/m3 and in the centimeter-gram-second system, the unit is g/cm3

For example: consider an object with a mass of 25kg and a volume of 2m3, the density of this
object is calculated as follows:
ρ = m
v = 25
2 =12.5 kg/m3
Material/substance Density (kg/m3)-at STP
Salty water 1030
Fresh water 1000
Iron 7870
Lead 11340
Table 1: Densities of common materials/substances
Density measurement
For an homogeneous object, the density at a given point of the object is simply the ratio of the
mass of the object to its volume. To measure the mass, a scale or a balance is used and the
volume may be obtained fluid displacement for an irregular object or calculated from the
dimensions for a regular object. For an inhomogeneous body, the density is more complex since
it becomes dependent on position1. In this case the density for a small volume of the body is
measured and in the limit of this volume the density of the inhomogeneous body at a given point
is then expressed as:
ρ(x) = dm
dV
The mass of the object is then given by:
m = ∫ ρ( x)dV
The density of a substance made up of granules is not well defined because its volume can be
estimated using various ways. For example, if sand is placed in a container without any
compression, its density will be low because the volume will be high. On the other hand if the
sand is compressed, its volume will decrease and its density will increase. The reason for this is
because substances made up of granules are mostly composed of empty space between the
particles thus the density of the substance takes into account the density of the air between the
granules.
Density dependence on pressure and temperature
Density is highly dependent on factors such as the temperature of the object or fluid or the
pressure on it. Generally, an increase in temperature increases the volume of an object or a fluid
and since the density is a ratio of mass to volume and the mass is constant, the density reduces.
However, the effect of changes in temperature and pressure on the density of solids and liquids is
considered to be very small. This is due to the low typical compressibility and expansivity of