Density and its units. The methods of Beruni and al-Khazini for finding density
The distances between particles and the masses of particles differ in different substances, so equal volumes of different substances have different masses. The mass per unit volume of a substance is called density: ρ = m : V, where ρ (rho) is density, m mass, V volume. The SI unit of density is kg/m³; g/cm³ is also often used: 1 g/cm³ = 1000 kg/m³. For example, the density of iron is 7800 kg/m³, i.e. an iron cube of volume 1 m³ has mass 7800 kg. Water has 1000 kg/m³ (1 g/cm³), ice 900 kg/m³ (0.9 g/cm³), gold 19 300 kg/m³ (19.3 g/cm³), mercury 13 600 kg/m³ (13.6 g/cm³), air about 1.29 kg/m³. From the formula we also get m = ρ · V and V = m : ρ. If a liquid is given in litres, 1 l = 1 dm³ = 0.001 m³. The volume of an irregular body is found in a measuring cylinder: V = V₂ − V₁. Beruni found the densities of many substances very accurately by immersing a body in a spouted vessel and collecting the displaced water; Abd al-Rahman al-Khazini (12th century) made a special balance for finding densities.
“Density detective”: the teacher gives a mass and a volume (for example 270 g and 100 cm³). Groups calculate the density and find the substance in the table (2.7 g/cm³ — aluminium). The group that identifies most wins.