Density
- Density is the mass per unit volume of an object
- Where:
- ρ (the Greek letter rho) = density in kilograms per metre cubed (kg m-3)
- m = mass in kilograms (kg)
- V = volume in metres cubed (m3)
- Gases are less dense than liquids, which are less dense than solids
- This is because there are fewer particles, and therefore less mass, per unit volume
Relative density of a gas and a solid
Gases are less dense than solids because they have fewer particles, and therefore less mass, per unit volume
- The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape
Calculating the volumes of different shapes
Expressions for calculating the volume of a sphere, a cube and a cylinder
Worked example
A paving slab has a mass of 73 kg and dimensions 40 mm × 500 mm × 850 mm.
Calculate the density, in kg m-3 of the material from which the paving slab is made.
Answer:
Step 1: List the known quantities and convert to SI units
- Mass, m = 73 kg
- Length, = 0.850 m
- Width, w = 0.500 m
- Height, h = 0.040 m
Step 2: State the equation for density
Step 3: Calculate the volume
Step 4: Substitute the known values to calculate
Examiner Tip
- When converting a larger unit to a smaller one, you multiply (×)
- E.g. 125 m = 125 × 100 = 12 500 cm
- When you convert a smaller unit to a larger one, you divide (÷)
- E.g. 5 g = = 0.005 or 5 × 10-3 kg
- When dealing with squared or cubic conversions, cube or square the conversion factor too
- E.g. 1 mm3 = = 1 × 10-9 m3
- E.g. 1 cm3 = = 1 × 10-6 m3