Density
Density is the mass per unit volume. It can be measured in several ways.
The most accurate way to calculate the density of any solid, liquid or gas is to divide its mass in
kilograms by its volume (length × width × height) in cubic metres.
Density can be found using the equation:
Density = \frac{mass}{volume}
\rho = \frac{m}{v}
The unit for density is kg/m3. The density of water is approximately 1000 kg/m3 and the density of air is
approximately 1.2 kg/m3.
If solid objects are placed in water and they sink, they have a density greater than water (1000 kg/m3).
The reverse is also true.
If several liquids that don’t mix (immiscible) are placed in the same container, the least dense one will
rise to the top and the densest one will sink to the bottom. This is also true of gases, but they are often
harder to see because gases tend to mix with each other very easily.
Take a look at this practical demonstration of the relative densities of liquids:
Not all objects have regular volumes that are easy to measure. A ‘eureka can’ can be used in these
cases.
Eureka can filled with water to just below overflow hole. Object lowered into can and displaces own
volume of water. Water passes through overflow, down spout and collected in measuring cylinder.
Calculating volume of a solid using a Eureka can
A eureka can is a container large enough to hold the object with a spout positioned near the top. The
can is filled to the top with water and the object placed in it. The volume of the object is equal to the
volume of the water that is forced through the spout.
Eureka cans are named after a scientist called Archimedes who first recorded this idea. They are
sometimes also called displacement vessels.
Densities of solids, liquids and gases
For most substances, the change from a solid to a liquid state does not mean a big change in volume.
This is because the particles stay approximately the same distance apart. This means that the density of
a substance, for example iron, does not change by much when it melts.
Solid cube: side length 1 unit, 64 particles in tightly packed lattice. Liquid cube: 1 unit, contains approx
30 particles. Gas cube: side length 10 units contains 15 scattered particles.
Relative particle density for a solid, liquid and gas
When a liquid changes into a gas, the spacing between the particles increases significantly. This means
that the gas takes up a lot more space than the liquid, so its volume increases dramatically.
When a gas condenses to form a liquid, its volume decreases significantly.
Question
A block of copper has a volume of 0.005 m3. The density of copper is 8.96 × 103 kg/m3.
Calculate the mass of the copper block.