Density
densityA measure of compactness and the ratio of mass to volume. It is usually measured in kilograms per metre cubed (kg/m3) or grams per centimetre cubed (g/cm3). is a measure of the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). in a given volumeThe volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml. of a substance. It can be calculated using the equation:
\(density = \frac{mass}{volume}\)
This is when:
- density is measured in kilograms per metre cubed (kg/m³)
- mass is measured in kilograms (kg)
- volume is measured in metres cubed (m³)
Example 1
A piece of aluminium has a mass of 200 kg and a volume of 0.074 m3. Calculate its density in kg/m3, to two significant figures.
\(density = \frac{mass}{volume}\)
\(density = \frac{200}{0.074}\)
\(= 2,700 \: kg/m^3\)
The units for density
The kilogram (kg) is the standard unit for mass. The cubic metre (m3) is the standard unit for volume. However, in many laboratory situations mass will be measured in grams (g) and volume in cubic centimetres (cm3).
Example 2
A piece of iron has a mass of 100 g and a volume of 12.7 cm3. Calculate its density in g/cm3.
\(density = \frac{mass}{volume}\)
\(density = \frac{100}{12.7}\)
\(= 7.87 \: g/cm^3\)
Converting between units
To convert between units:
- kg/m3 to g/cm3, divide by 1,000
- g/cm3 to kg/m3, multiply by 1,000
Example 3
The density of air at 20 °C is 0.00120 g/cm3. Give its density in kg/m3.
density = 0.00120 × 1,000
= 1.20 kg/m3