Physics Report: Density, Measurement, and Dependence

This report provides a comprehensive overview of density, a fundamental concept in physics, defining it as the ratio of mass to volume. It explores the measurement of density for both homogeneous and inhomogeneous objects, detailing the use of scales, balances, and fluid displacement methods. The report highlights the dependence of density on temperature and pressure, especially in gases, where increased temperature leads to decreased density and increased pressure leads to increased density. It also discusses the significance of relative density and specific volume, and concludes by emphasizing the importance of density in various applications such as trade and healthcare. The report includes relevant equations, examples, and a table of densities for common materials, supported by references to academic sources.

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

solids and liquids. For instance, for a typical solid or a liquid, the compressibility factor is about
10-6/bar which is very small.
For gases, changes in temperature and pressure have a significant effect on density. For an ideal
gas, the density is given by the following relation:
ρ = MP
RT
M is the molar mass
P is the pressure
R is the gas constant
T is the absolute temperature (K)
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The equation clearly displays the dependence of density on both temperature and pressure. We
observe that,
ρ ∝ 1
T

This means that as the temperature of the gas is increased, its density decreases. This is because
an increase in temperature increases the kinetic energy of the gas molecules making them move
faster and further apart hence the volume of the gas increases with a corresponding decrease in
density.
ρ ∝ p
This means that the density of the gas is directly proportional to the pressure of the gas. As the
pressure on the gas is increased, its volume decreases and consequently the density increases.
Conclusion
Density is such a crucial physical quantity in our everyday lives. It is needed in trade and
healthcare for the protection of consumers, for instance in determining the concentration of sugar
in beverages and the concentration of alcohol in alcoholic drinks.

References
Abildskov J, M EllegaardJ O’Connell, 'Correlation Of Phase Equilibria And Liquid Densities
For Gases With Ionic Liquids' (2009) 286 Fluid Phase Equilibria
English NJ Tse, 'Density Fluctuations In Liquid Water' (2011) 106 Physical Review Letters
Gillum D, Industrial Pressure, Level, And Density Measurement (International Society of
Automation 2009)
Gupta S, Practical Density Measurement And Hydrometry (Inst of Physics Publ 2002)
Hu S, 'Monte Carlo Simulations On The Thermodynamic Properties Of High-Density Gases'
(2012) 71 International Journal for Numerical Methods in Fluids
Kolker A, V KorolevD Batov, 'Relationship Between The Internal Pressure And Cohesive
Energy Density Of Liquids' (2005) 46 Journal of Structural Chemistry