OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Apply the relationship between density, mass and volume to changes where…
Full specification wording
The particle model: apply the relationship between density, mass and volume to changes where mass is conserved
Density links mass and volume through ρ = m ÷ V, so a fixed mass squeezed into a smaller volume has a higher density and the same mass spread through a larger volume has a lower density.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 7 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Density links mass and volume through ρ = m ÷ V, so a fixed mass squeezed into a smaller volume has a higher density and the same mass spread through a larger volume has a lower density. Because mass is conserved, only volume changes in these situations: heating a gas in a sealed rigid container raises pressure but keeps both mass and volume, while compressing a gas in a syringe keeps mass constant and reduces volume, raising density. Worked method: a 0.60 kg sample occupies 200 cm³, so ρ = 0.60 kg ÷ 0.000200 m³ = 3000 kg/m³; halving the volume to 100 cm³ doubles density to 6000 kg/m³ with mass still 0.60 kg. Convert cm³ to m³ by dividing by 1 000 000, and check that the mass value you use is the same before and after the change.
What earns the marks
- Selects the form ρ = m ÷ V and substitutes a mass that stays unchanged across the change.
- Converts a volume in cm³ to m³ by dividing by 1 000 000 before substituting.
- States that halving the volume of a fixed mass doubles the density.
- Explains that a change in density arises from a change in volume because mass is conserved.
- Rejects an option that treats mass as changing when only the volume changes.
Common mistakes and how to put them right
Uses a changed mass value after the volume change.
Put it right: Keep the mass identical and alter only the volume.
Forgets to convert cm³ to m³ and divides kilograms by cubic centimetres.
Put it right: Divide the volume by 1 000 000 first.
Assumes density stays the same when a gas is compressed.
Put it right: Recognise that reduced volume at constant mass raises density.
Inverts the relationship and multiplies mass by volume.
Put it right: Divide mass by volume instead.
Exam tips
- Write the equation, then list the known mass and both volumes before touching the options.
- Convert every volume to m³ in one step and note the conversion factor beside your working.
- Use ratio reasoning as a check: quarter the volume and density should rise fourfold at constant mass.
Try the lesson
The start of the The particle model: apply the relationship between density, mass and volume to changes where mass is conserved lesson, made from checked teaching notes for this specification point.
Have a go first
A sample of gas is compressed so that its volume halves while no gas escapes. The original density was 1.6 kg/m³. What is the new density?
Listen
Density links mass and volume through ρ = m ÷ V, so a fixed mass squeezed into a smaller volume has a higher density and the same mass spread through a larger volume has a lower density. Because mass is conserved, only volume changes in these situations: heating a gas in a sealed rigid container raises pressure but keeps both mass and volume, while compressing a gas in a syringe keeps mass constant and reduces volume, raising density. Worked method: a 0.60 kg sample occupies 200 cm³, so ρ = 0.60 kg ÷ 0.000200 m³ = 3000 kg/m³; halving the volume to 100 cm³ doubles density to 6000 kg/m³ with mass still 0.60 kg. Convert cm³ to m³ by dividing by 1 000 000, and check that the mass value you use is the same before and after the change. A strong answer earns marks for these points. Selects the form ρ = m ÷ V and substitutes a mass that stays unchanged across the change. Converts a volume in cm³ to m³ by dividing by 1 000 000 before substituting. States that halving the volume of a fixed mass doubles the density. Explains that a change in density arises from a change in volume because mass is conserved. Exam tip: Write the equation, then list the known mass and both volumes before touching the options.
See it
Key words
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Density
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Conservation of mass
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Unit conversion between cm³ and m³
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Proportional reasoning with inverse relationships
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See every definition
- Density
- A quantity found by dividing mass by volume, so a fixed mass squeezed into a smaller volume has a higher density.
- Conservation of mass
- Mass stays the same across a change, so only volume changes and a change in density arises from a change in volume.
- Unit conversion between cm³ and m³
- Converting a volume in cm³ to m³ by dividing by 1 000 000 before substituting into the density equation.
- Proportional reasoning with inverse relationships
- Halving the volume of a fixed mass doubles the density, and quartering the volume raises density fourfold at constant mass.
Label the diagram
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1Box 1
2Box 2
3Box 3
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