04 1.3 Relative density
Relative density of a material = (density of the material at a given temperature) ÷ (density of water at 4 °C).
relative density = ρmaterial / ρwater(4 °C)
Since the density of water at 4 °C is 1000 kg/m³ (1 g/cm³),
relative density = mass of a certain volume of the material ÷ mass of the same volume of water at 4 °C.
- It is a ratio of two quantities of the same kind → it has no unit (and no dimensions).
- Its numerical value equals the density in g/cm³.
Example 1. A liquid of volume 250 cm³ has a mass of 200 g. ρ = 200/250 = 0.8 g/cm³ = 800 kg/m³; relative density = 0.8.
Example 2. Find the mass of 3 litres of mercury (ρ = 13 600 kg/m³). Vol = 3 L = 3 × 10⁻³ m³; m = ρVol = 13 600 × 3 × 10⁻³ = 40.8 kg.
Example 3. An iron block has dimensions 10 cm × 5 cm × 4 cm and mass 1.56 kg. Vol = 200 cm³ = 2 × 10⁻⁴ m³; ρ = 1.56/(2 × 10⁻⁴) = 7800 kg/m³; relative density = 7.8.
Example 4. The relative density of a certain oil is 0.9. Its density is 0.9 × 1000 = 900 kg/m³, and 2 m³ of it has mass 1800 kg.