Density

Density is the mass per unit volume of an object
- Objects made from low-density materials typically have a lower mass
- For example, a balloon is less dense than a small bar of lead despite occupying a larger volume
The units of density depend on the units used for mass and volume:
- If the mass is measured in g and volume in cm³, then the density will be in g / cm³
- If the mass is measured in kg and volume in m³, then the density will be in kg / m³

How to calculate density

How to Calculate Density, for IB Physics Revision Notes

Comparison of Molecular Densities, for IB Physics Revision Notes

Gases are less dense than solids due to their molecular arrangements

The volume of an object may not always be given directly but can be calculated using the appropriate formula

Volumes of common 3D shapes

How to Calculate Volume of Regular Shapes, for IB Physics Revisios Notes

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.

Density of a Slab Worked Example, for IB Physics Revisios Notes

Answer:

WE - Density answer image, downloadable AS & A Level Physics revision notes

Worked example

Liquids are about 1000 times denser than gases. Let d be the diameter of a molecule.

Estimate the average intermolecular distance in a gas. Give your answer in terms of d.

Answer:

Step 1: Recall the equation for density

$ρ = \frac{m}{v}$

Step 2: Write down the relationship between the density of a gas ρ_gas and the density of a liquid ρ_liquid

$ρ_{l i q u i d} = 1000 \times ρ_{g a s}$

Step 3: Substitute into the density equation to show the relationship between the masses and volumes of a liquid a gas

$\frac{m_{l i q u i d}}{v_{l i q u i d}} = 1000 \times (\frac{m_{g a s}}{v_{g a s}})$

Step 4: Since the mass stays the same, the relationship between the densities translates into a relationship between volumes as mass cancels out

$\frac{m_{l i q u i d}}{v_{l i q u i d}} = 1000 \times (\frac{m_{g a s}}{v_{g a s}})$

$v_{g a s} = 1000 \times v_{l i q u i d}$

Step 4: Relate the volume to the average distance between the molecules, x

The average distance x between the molecules is related to the cube root of the volume

$x = ∛ 1000 v_{l i q u i d} = 10 \times d$

Exam 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 = 5 / 1000 = 0.005 or 5 × 10^-3 kg

When dealing with squared or cubic conversions, cube or square the conversion factor too

E.g. $1 {mm}^{3} = \frac{1}{1000^{3}} = 1 \times 10^{- 9} m^{3}$
E.g. $1 {cm}^{3} = \frac{1}{100^{3}} = 1 \times 10^{- 6} m^{3}$

Density (HL IB Physics)

Revision Note

Density

How to calculate density

Volumes of common 3D shapes

Worked example

Worked example

Exam Tip

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Author: Katie M