AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    For a change of temperature: Q = mc ∆ θ where c is specific heat capacity.

    Full specification wording

    Thermal energy transfer (A-level only): For a change of temperature: Q = mc ∆ θ where c is specific heat capacity.

    When a substance changes temperature without changing state, the energy transferred is found from Q = mc∆θ.

    Checked against the AQA 7408 specification (opens in a new tab) on .

    • Point 5 of 7
    • 3 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    When a substance changes temperature without changing state, the energy transferred is found from Q = mc∆θ. Here Q is the thermal energy transferred in joules, m is the mass in kilograms, c is the specific heat capacity in J kg⁻¹ K⁻¹, and ∆θ is the temperature change in kelvin or degrees Celsius. Because a temperature change of 1 K equals a change of 1 °C, either unit may be used for ∆θ, but the value must be a difference, not a single reading.

    For example: Heating 2.0 kg of water (c = 4200 J kg⁻¹ K⁻¹) from 20 °C to 70 °C gives ∆θ = 50 K and Q = 2.0 × 4200 × 50 = 4.2 × 10⁵ J. Rearranged forms allow c or ∆θ to be found.

    What earns the marks

    • State the equation Q = mc∆θ and identify each symbol with its unit: Q in J, m in kg, c in J kg⁻¹ K⁻¹ and ∆θ in K or °C.
    • Calculate ∆θ as the difference between final and initial temperature, ensuring the sign shows whether energy is gained or lost.
    • Substitute values with consistent SI prefixes, converting grams to kilograms and kJ to J before evaluating.
    • Rearrange the equation correctly to make c or ∆θ the subject when those quantities are required.
    • Interpret the sign of Q as energy transferred to the substance when positive and from it when negative, linking to heating or cooling.

    Common mistakes and how to put them right

    • Using a single temperature reading instead of the change in temperature.

      Put it right by subtracting the initial temperature from the final temperature.

    • Substituting mass in grams while c is quoted per kilogram.

      Put it right by converting the mass to kilograms first.

    • Mixing units such as kJ with J kg⁻¹ K⁻¹.

      Put it right by converting all energy values to joules before substitution.

    Exam tips

    • Write the equation, then the rearranged form, before substituting numbers so the method is clear.
    • Check that ∆θ is a difference and that its unit matches the temperature scale used in c.
    • Estimate the answer first, for example a few hundred kilojoules for heating a few kilograms of water, to catch powers-of-ten errors.

    Try the lesson

    The start of the Thermal energy transfer (A-level only): For a change of temperature: Q = mc ∆ θ where c is specific heat capacity. lesson, made from checked teaching notes for this specification point.

    Have a go first

    A 2.0 kg block of aluminium is heated and its temperature rises by 15 °C. The specific heat capacity of aluminium is 900 J kg⁻¹ K⁻¹. Calculate the thermal energy transferred to the block.

    Listen

    When a substance changes temperature without changing state, the energy transferred is found from Q = mc∆θ. Here Q is the thermal energy transferred in joules, m is the mass in kilograms, c is the specific heat capacity in J kg⁻¹ K⁻¹, and ∆θ is the temperature change in kelvin or degrees Celsius. Because a temperature change of 1 K equals a change of 1 °C, either unit may be used for ∆θ, but the value must be a difference, not a single reading. For example, heating 2.0 kg of water (c = 4200 J kg⁻¹ K⁻¹) from 20 °C to 70 °C gives ∆θ = 50 K and Q = 2.0 × 4200 × 50 = 4.2 × 10⁵ J. Rearranged forms allow c or ∆θ to be found. A strong answer earns marks for these points. State the equation Q = mc∆θ and identify each symbol with its unit: Q in J, m in kg, c in J kg⁻¹ K⁻¹ and ∆θ in K or °C. Calculate ∆θ as the difference between final and initial temperature, ensuring the sign shows whether energy is gained or lost. Substitute values with consistent SI prefixes, converting grams to kilograms and kJ to J before evaluating. Rearrange the equation correctly to make c or ∆θ the subject when those quantities are required. A common slip: Using a single temperature reading instead of the change in temperature. Instead, subtracting the initial temperature from the final temperature. Exam tip: Write the equation, then the rearranged form, before substituting numbers so the method is clear.

    See it

    A top-down flowchart. The top node reads Q = mc∆θ. Five arrows lead from it. One goes to a node reading Q: thermal energy transferred, in J. One goes to m: mass, in kg. One goes to c: specific heat capacity, in J kg⁻¹ K⁻¹. One goes to ∆θ: temperature change, in K or °C, and from that node a further arrow leads down to ∆θ = final temperature − initial temperature. The last arrow from the top node goes to a node reading Rearrange to make c or ∆θ the subject. A separate arrow from the top node leads to a node reading Sign of Q: positive = energy to the substance, negative = energy from it.
    It shows the equation Q = mc∆θ with the meaning and unit of each symbol, how ∆θ is found as a difference, and the rearranged and sign interpretations.

    Key words

    Say what each word means before you turn the card.

    Specific heat capacity

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

    Temperature change

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

    Thermal energy transferred

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

    See every definition
    Specific heat capacity
    A material property denoted by c, measured in J kg⁻¹ K⁻¹, used in the equation Q = mc∆θ for a change of temperature.
    Temperature change
    Denoted by ∆θ, it is the difference between final and initial temperature, in kelvin or degrees Celsius, not a single reading.
    Thermal energy transferred
    Denoted by Q and measured in joules, it is found from Q = mc∆θ when a substance changes temperature without changing state.

    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 top node reads Q = mc∆θ. Five arrows lead from it. One goes to a node reading Q: thermal energy transferred, in J. One goes to m: mass, in kg. One goes to c: specific heat capacity, in J kg⁻¹ K⁻¹. One goes to ∆θ: temperature change, in K or °C, and from that node a further arrow leads down to ∆θ = final temperature − initial temperature. The last arrow from the top node goes to a node reading Rearrange to make c or ∆θ the subject. A separate arrow from the top node leads to a node reading Sign of Q: positive = energy to the substance, negative = energy from it.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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