OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Density and pressure: (a) density; ρ = m/V
Density measures how much mass is packed into each unit of volume, defined by ρ = m/V, where ρ is density in kg m⁻³, m is mass in kg and V is volume in m³.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 1 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Density measures how much mass is packed into each unit of volume, defined by ρ = m/V, where ρ is density in kg m⁻³, m is mass in kg and V is volume in m³. To use it, identify the mass and the volume occupied by the same body, convert to SI units, then divide. For a regular solid, find V from its dimensions; for an irregular solid, use displacement; for a liquid or gas, use the container volume. A 2.0 kg block of volume 5.0 × 10⁻⁴ m³ has ρ = 2.0 ÷ (5.0 × 10⁻⁴) = 4.0 × 10³ kg m⁻³. Rearranged, m = ρV and V = m/ρ. Density is a property of the material, so it can identify a substance, but it changes with temperature for gases and slightly for liquids.
What earns the marks
- States ρ = m/V and identifies ρ as density, m as mass and V as volume.
- Uses SI units: kg m⁻³ for density, kg for mass and m³ for volume, converting cm³ by multiplying by 10⁻⁶.
- Calculates density by dividing mass by volume, or rearranges to m = ρV or V = m/ρ.
- Explains that density is a property of the material and can be used to identify a substance.
- Recognises that gas density depends strongly on temperature and pressure because volume changes.
Common mistakes and how to put them right
Using volume in cm³ without converting.
Put it right: The error is mixing units, and the correction is to convert cm³ to m³ by multiplying by 10⁻⁶ before dividing.
Dividing volume by mass.
Put it right: The error is inverting the formula, and the correction is to divide mass by volume, ρ = m/V.
Treating density as fixed for a gas.
Put it right: The error is ignoring compression, and the correction is to note that gas density rises when the same mass is compressed into a smaller volume.
Exam tips
- Write the equation, substitute values with units, then give the answer with the correct unit and a sensible number of significant figures.
- Convert every length to metres first when a volume is given in cm³ or litres; 1 litre = 1 × 10⁻³ m³.
- Check the rearrangement by substituting a simple case, such as doubling the volume while keeping mass fixed, which should halve the density.
Try the lesson
The start of the Density and pressure: (a) density; ρ = m/V lesson, made from checked teaching notes for this specification point.
Listen
Density measures how much mass is packed into each unit of volume, defined by ρ = m/V, where ρ is density in kg m⁻³, m is mass in kg and V is volume in m³. To use it, identify the mass and the volume occupied by the same body, convert to SI units, then divide. For a regular solid, find V from its dimensions; for an irregular solid, use displacement; for a liquid or gas, use the container volume. A 2.0 kg block of volume 5.0 × 10⁻⁴ m³ has ρ = 2.0 ÷ (5.0 × 10⁻⁴) = 4.0 × 10³ kg m⁻³. Rearranged, m = ρV and V = m/ρ. Density is a property of the material, so it can identify a substance, but it changes with temperature for gases and slightly for liquids. A strong answer earns marks for these points. States ρ = m/V and identifies ρ as density, m as mass and V as volume. Uses SI units: kg m⁻³ for density, kg for mass and m³ for volume, converting cm³ by multiplying by 10⁻⁶. Calculates density by dividing mass by volume, or rearranges to m = ρV or V = m/ρ. Explains that density is a property of the material and can be used to identify a substance. Exam tip: Write the equation, substitute values with units, then give the answer with the correct unit and a sensible number of significant figures.
Key words
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Density
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Rearrangement of ρ = m/V
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SI units and unit conversion for volume
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Density as a material property
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See every definition
- Density
- Measures how much mass is packed into each unit of volume, given by ρ = m/V, where ρ is in kg m⁻³, m in kg and V in m³.
- Rearrangement of ρ = m/V
- The equation can be rearranged to m = ρV and V = m/ρ to find mass or volume.
- SI units and unit conversion for volume
- Density is in kg m⁻³, mass in kg and volume in m³, converting cm³ by multiplying by 10⁻⁶.
- Density as a material property
- Density is a property of the material, so it can identify a substance, but it changes with temperature for gases and slightly for liquids.
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