OCR · GCSE · Physics

    Course version: J249 · Version from Sept 2018

    Apply: for a given mass of gas at a constant temperature: pressure (Pa) ×…

    Full specification wording

    Pressure: apply: for a given mass of gas at a constant temperature: pressure (Pa) × volume (m³) = constant (content found only in the physics separate science qualification)

    For a fixed mass of gas kept at constant temperature, pressure multiplied by volume stays constant.

    Checked against the OCR J249 specification (opens in a new tab) on .

    • Point 1 of 12
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    For a fixed mass of gas kept at constant temperature, pressure multiplied by volume stays constant. This is written p × V = constant, or p₁ × V₁ = p₂ × V₂, where pressure is in pascals (Pa) and volume in cubic metres (m³). If the volume is halved, the pressure doubles, because the same number of particles hits a smaller area more often. To apply it, list the initial pressure and volume, then the final pressure or volume, and solve for the unknown. For example, a gas at 1.0 × 10⁵ Pa in 2.0 m³ compressed to 1.0 m³ gives p₂ = (1.0 × 10⁵ × 2.0) ÷ 1.0 = 2.0 × 10⁵ Pa. Convert volumes to m³ (1 m³ = 1000 dm³) and keep temperature and mass fixed. This content appears only in the physics separate science qualification.

    What earns the marks

    • States that pressure multiplied by volume is constant for a fixed mass of gas at constant temperature.
    • Uses p₁ × V₁ = p₂ × V₂ to find an unknown pressure or volume.
    • Recognises that halving the volume doubles the pressure when temperature and mass are unchanged.
    • Converts volumes to cubic metres before substituting into the relationship.
    • Keeps pressure in pascals and volume in cubic metres so the constant has consistent units.

    Common mistakes and how to put them right

    • Uses the relationship when temperature or mass changes.

      Put it right: Apply it only when both are held constant.

    • Leaves volume in cubic decimetres or litres.

      Put it right: Convert to cubic metres first so units match.

    • Adds pressures or volumes instead of multiplying.

      Put it right: Multiply pressure by volume to obtain the constant.

    • Inverts the ratio so pressure falls as volume falls.

      Put it right: Expect pressure to rise when volume decreases.

    Exam tips

    • Write p₁ × V₁ = p₂ × V₂ and fill in the three known values before rearranging.
    • Convert every volume to m³ and every pressure to Pa so the units are consistent.
    • Check the direction of change: a smaller volume should give a larger pressure.

    Try the lesson

    The start of the Pressure: apply: for a given mass of gas at a constant temperature: pressure (Pa) × volume (m³) = constant (content found only in the physics separate science qualification) lesson, made from checked teaching notes for this specification point.

    Have a go first

    A fixed mass of gas at constant temperature has a pressure of 100 000 Pa and a volume of 0.20 m³. The gas is compressed until its volume is 0.10 m³. Calculate the new pressure.

    Listen

    For a fixed mass of gas kept at constant temperature, pressure multiplied by volume stays constant. This is written p × V = constant, or p₁ × V₁ = p₂ × V₂, where pressure is in pascals (Pa) and volume in cubic metres (m³). If the volume is halved, the pressure doubles, because the same number of particles hits a smaller area more often. To apply it, list the initial pressure and volume, then the final pressure or volume, and solve for the unknown. For example, a gas at 1.0 × 10⁵ Pa in 2.0 m³ compressed to 1.0 m³ gives p₂ = (1.0 × 10⁵ × 2.0) ÷ 1.0 = 2.0 × 10⁵ Pa. Convert volumes to m³ (1 m³ = 1000 dm³) and keep temperature and mass fixed. This content appears only in the physics separate science qualification. A strong answer earns marks for these points. States that pressure multiplied by volume is constant for a fixed mass of gas at constant temperature. Uses p₁ × V₁ = p₂ × V₂ to find an unknown pressure or volume. Recognises that halving the volume doubles the pressure when temperature and mass are unchanged. Converts volumes to cubic metres before substituting into the relationship. Exam tip: Write p₁ × V₁ = p₂ × V₂ and fill in the three known values before rearranging.

    See it

    A top-down flowchart. The first box reads 'Fixed mass of gas at constant temperature' and points to 'Pressure × volume = constant', which points to 'p₁ × V₁ = p₂ × V₂'. That points to 'List initial pressure and volume', then to 'List final pressure or volume', then to 'Convert volumes to m³ and pressures to Pa', then to 'Solve for the unknown', and finally to 'Check direction: smaller volume gives larger pressure'.
    The sequence for applying p₁ × V₁ = p₂ × V₂ to find an unknown pressure or volume for a fixed mass of gas at constant temperature.

    Put it in order

    Put these steps in the order they happen.

    1. 1. List final pressure or volume
    2. 2. Check direction: smaller volume gives larger pressure
    3. 3. Convert volumes to m³ and pressures to Pa
    4. 4. Fixed mass of gas at constant temperature
    5. 5. Pressure × volume = constant
    6. 6. Solve for the unknown
    7. 7. p₁ × V₁ = p₂ × V₂
    8. 8. List initial pressure and volume

    Key words

    Say what each word means before you turn the card.

    Gas pressure and volume

    Try answering aloud or in your head before turning the card.

    Constant temperature and fixed mass

    Try answering aloud or in your head before turning the card.

    Inverse relationship between pressure and volume

    Try answering aloud or in your head before turning the card.

    Unit consistency in gas calculations

    Try answering aloud or in your head before turning the card.

    See every definition
    Gas pressure and volume
    For a fixed mass of gas at constant temperature, pressure multiplied by volume stays constant, written p × V = constant.
    Constant temperature and fixed mass
    The relationship applies only when both temperature and mass are held constant.
    Inverse relationship between pressure and volume
    If the volume is halved, the pressure doubles, because the same number of particles hits a smaller area more often.
    Unit consistency in gas calculations
    Pressure is kept in pascals and volume in cubic metres, converting volumes to m³ first, so the constant has consistent units.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The first box reads 'Fixed mass of gas at constant temperature' and points to 'Pressure × volume = constant', which points to 'p₁ × V₁ = p₂ × V₂'. That points to 'List initial pressure and volume', then to 'List final pressure or volume', then to 'Convert volumes to m³ and pressures to Pa', then to 'Solve for the unknown', and finally to 'Check direction: smaller volume gives larger pressure'.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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