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Specific heat capacity Why does the same energy heat some things more than others?

Foundation and Higher · AQA · 45 minutes

Students predict whether a kilogram of water or a kilogram of aluminium gets hotter from the same heater, then heat a virtual block themselves, changing the material, the mass and the power. The required practical follows, with why its answer comes out too high. Slides to present, a vote that shows who's stuck, practice and homework.

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The idea in one minute

Heating something puts energy into its thermal store. How far its temperature rises depends on how much energy goes in, its mass and what it is made of. A material's specific heat capacity, c, is the energy needed to raise the temperature of 1 kg of it by 1 °C, in joules per kilogram per degree Celsius (J/kg °C). So the change in thermal energy is ΔE = m c Δθ: the mass in kilograms, the temperature change in °C, the energy in joules. Water's is large, 4200 J/kg °C, nearly five times aluminium's: the same energy warms a kilogram of water far less, which is why water is used to store and carry heat in radiators and hot-water bottles, and why it is slow to cool down.

The lesson starts with a vote before anyone explains: the same heater, for the same time, in a kilogram of water and a kilogram of aluminium; which warms up more? Students then heat a virtual block themselves (a simulation, not a substitute for the practical), rearrange the equation for c, m and Δθ, and work through results from the required practical, seeing why heat lost to the room makes the measured c come out too high. It is for Foundation and Higher; the stretch finds c from a graph.

By the end, students can

  • say what specific heat capacity means, with its unit, J/kg °C
  • work out a change in thermal energy with ΔE = m c Δθ, turning grams into kilograms and kJ into J
  • rearrange ΔE = m c Δθ to find c, m or Δθ, using E = P t for the energy from a heater
  • describe the required practical to find c, and explain why its value comes out too high

Key words

  • specific heat capacity
  • thermal energy store
  • temperature change (Δθ)
  • joule (J)
  • J/kg °C
  • power (W)
  • joulemeter
  • insulation
  • required practical

Before this lesson

Students should know that energy is measured in joules, that power is energy each second (E = P t, t in seconds), and rearrange a formula such as P = E ÷ t.

Taught in Energy stores and transfers.

The lesson, step by step

60 minutes in total. Each step says what changes for this length.

  1. 1 · Think5 min

    Which warms up more?

    The same 60 W heater, for 10 minutes,

    into 1 kg of water, then a 1 kg block of aluminium.

    Both start at 20 °C. Which warms up more?

    A: The water

    B: The aluminium

    C: Both the same

    Vote first. Then say why.

    Write here

    5 min 1 · Hook · students think · the slides say “Think”

    Which warms up more?

    The same heater for the same time in a kilogram of water and a kilogram of aluminium: students vote on which warms up more before anyone explains.

    Say

    “The same 60 W heater runs for 10 minutes, once in 1 kg of water and once in a 1 kg block of aluminium. Both start at 20 °C. Which warms up more, or do they warm up the same?”

    Ask
    • They get the same energy and have the same mass. So what could make a difference?
    • Think of a beach on a hot day: which is hotter, the sand or the sea?
    Watch for

    Saying the same energy and the same mass must give the same rise: keep the votes, the next step needs them.

    For the teacher

    Give a minute of silent thinking, then vote. Many say both the same: the same energy into the same mass. Some say the water, because it is a liquid.

    Don't explain yet. What the block is made of matters: that is the next step. (The aluminium warms by 40 °C, the water by about 8.6 °C: 36 000 J into each.)

    Take a vote with Ask the class: the water, the aluminium, or both the same. Keep the votes on the board for the explain step.

    Shorter: Vote once, no discussion (−2 min).

  2. 2 · Watch14 min

    Specific heat capacity, c

    The energy to warm 1 kg of a material by 1 °C

    Its unit: J/kg °C (joules per kilogram per degree)

    Water 4200 · oil 2000 · aluminium 900

    Iron 450 · copper 385 (all J/kg °C)

    1 kg of water needs 4200 J for each degree

    Large c: slow to warm up, slow to cool down

    Big c: more energy for each degree

    2 · Watch

    The equation: ΔE = m c Δθ

    ΔE: the change in thermal energy, in joules (J)

    m: mass (kg); c: specific heat capacity (J/kg °C)

    Δθ: the temperature change, in °C (end − start)

    The hook: E = P t = 60 × 600 = 36 000 J

    Aluminium: Δθ = 36 000 ÷ (1 × 900) = 40 °C

    Water: Δθ = 36 000 ÷ (1 × 4200) ≈ 8.6 °C

    Δθ is the change, not the end temperature

    2 · Watch

    Try it: heat a block

    60 W into 1 kg of aluminium

    1. Set 2 kg. How fast now?

    2. 1 kg of water: faster or slower?

    3. Aluminium, not wrapped: and now?

    Predict each one before you change it

    HeatingRises 4 °C a minute at first (ΔE = m c Δθ, c = 900 J/kg °C)

    2 · Watch

    Rearranging, and units

    c = ΔE ÷ (m Δθ)

    Δθ = ΔE ÷ (m c)

    m = ΔE ÷ (c Δθ)

    Grams to kilograms: ÷ 1000 (250 g = 0.25 kg)

    kJ to joules: × 1000 (4.5 kJ = 4500 J)

    Minutes to seconds for E = P t: × 60

    Kilograms, joules and seconds first

    2 · Watch

    The required practical

    A 1 kg block, a heater and a thermometer in it

    A joulemeter reads the energy (or E = P t)

    Wrap it in insulation; take the start temperature

    Heat for 10 minutes; record the highest temperature

    Then c = E ÷ (m Δθ)

    Heat lost to the room: Δθ too small, so c too high

    Where else could the heater's energy go?

    14 min 2 · Explain · you explain · the slides say “Watch”

    Specific heat capacity and ΔE = m c Δθ

    What specific heat capacity means; ΔE = m c Δθ answers the hook; students heat a virtual block; rearranging and units; then the required practical and why its c comes out too high.

    Say

    “Every material needs its own amount of energy to warm a kilogram of it by one degree. That amount is its specific heat capacity. Water's is large: it is slow to warm up and slow to cool down.”

    Ask
    • Water's c is 4200 J/kg °C. What does that number tell you?
    • Double the mass, the same energy: what happens to the temperature rise?
    • If heat escapes to the room in the practical, is the block's temperature rise bigger or smaller than it should be?
    Watch for

    Putting the end temperature into the equation: Δθ is the change, end minus start.

    The hook, worked

    Energy in: E = P t = 60 × 600 = 36 000 J

    Aluminium: Δθ = 36 000 ÷ (1 × 900) = 40 °C

    Water: Δθ = 36 000 ÷ (1 × 4200) ≈ 8.6 °C

    Boiling a kettle's water

    1.5 kg of water from 20 °C to 100 °C: Δθ = 80 °C

    ΔE = 1.5 × 4200 × 80 = 504 000 J

    That is 504 kJ

    For the teacher

    Specific heat capacity, c: the energy needed to raise the temperature of 1 kg of a material by 1 °C, in J/kg °C. Water 4200, oil 2000, aluminium 900, iron 450, copper 385.

    The change in thermal energy: ΔE = m c Δθ, ΔE in joules, m in kilograms, Δθ the temperature change in °C (end minus start). Work the hook: 60 W for 600 s is 36 000 J; the aluminium warms by 40 °C, the water by about 8.6 °C. A large c means a small rise for the same energy.

    Try it: 60 W into 1 kg of aluminium rises 4 °C a minute. Twice the mass, half as fast: 2 °C a minute. Water, about 0.86 °C a minute. Not wrapped, it starts at the same rate, but the line bends below the dashed one as the room takes more of the energy.

    Rearranging: c = ΔE ÷ (m Δθ), Δθ = ΔE ÷ (m c), m = ΔE ÷ (c Δθ). Units first: grams ÷ 1000 to kilograms, kJ × 1000 to joules, minutes × 60 to seconds for E = P t.

    The required practical: a 1 kg block with holes for a heater and a thermometer, wrapped in insulation. A joulemeter reads the energy (or E = P t, the power from the heater's rating or from V × I). Take the start temperature, heat for 10 minutes, switch off and record the highest temperature: the block goes on warming as the heat spreads from the heater. Then c = E ÷ (m Δθ). Energy that warms the room, the heater and the thermometer makes Δθ smaller than it should be, so the c worked out comes out too high.

    On the Try it slide, ask for a prediction before each change, then let the class see the simulation's rate. Before the practical slide, ask: where could the heater's energy go besides the block?

    Shorter: On the Try it slide, the first prompt only; say the units in a line (−4 min).

  3. 3 · Your turn13 min

    Mia's results: find c

    A 1.0 kg aluminium block, wrapped

    A 60 W heater for 10 minutes

    Start 20.5 °C; highest 58.0 °C

    1. The energy in? 2. Δθ? 3. c?

    4. Why is it above 900 J/kg °C?

    5. What would bring it closer?

    Open the Lab quiz. Show your working.

    3 · Your turn

    Worked, then yours

    I do: 0.5 kg oil, c = 2000, +30 °C: ΔE = 30 000 J

    You do: 1.5 kg water, c = 4200, +12 °C: ΔE?

    I do: 250 g takes 4.5 kJ for 40 °C: c = 450 J/kg °C

    You do: 500 g takes 7.7 kJ for 40 °C: c?

    I do: 2 kg aluminium gets 36 kJ: Δθ = 20 °C

    You do: 0.4 kg water gets 25.2 kJ: Δθ?

    Kilograms and joules first.

    Write here

    Its answers' slide comes with your copy.

    13 min 3 · Your turn · students write

    Results to c, then yours

    Students turn one set of results from the required practical into a specific heat capacity and say why it is too high, then solve twins of worked examples.

    For this length: Pairs write a ΔE = m c Δθ question with grams and kJ for each other, and swap

    Say

    “Here are Mia's results from the practical. Work out the energy, the temperature change, then c. Then decide why her answer isn't 900.”

    Ask
    • Which number is the temperature change: 58.0 °C, or something else?
    • Is her value higher or lower than the book's? Where did the rest of the energy go?
    Watch for

    Dividing by the highest temperature instead of the temperature change; using 10 minutes as 10 in E = P t.

    Find the energy

    0.5 kg of oil (c = 2000 J/kg °C) warms by 30 °C

    ΔE = 0.5 × 2000 × 30 = 30 000 J

    Then theirs

    1.5 kg of water (c = 4200 J/kg °C) warms by 12 °C. How much energy?

    Find c: grams and kJ first

    250 g of a metal takes 4.5 kJ to warm by 40 °C

    m = 0.25 kg, ΔE = 4500 J

    c = 4500 ÷ (0.25 × 40) = 450 J/kg °C: iron

    Then theirs

    500 g of a metal takes 7.7 kJ to warm by 40 °C. Find c.

    Find the temperature change

    2 kg of aluminium (c = 900 J/kg °C) gets 36 kJ

    Δθ = 36 000 ÷ (2 × 900) = 20 °C

    Then theirs

    0.4 kg of water (c = 4200 J/kg °C) gets 25.2 kJ. By how much does it warm?

    Mia found the specific heat capacity of aluminium in the required practical. Use her results: show your working on paper, and give energies in joules.

    1. Mia heats a 1.0 kg aluminium block, wrapped in insulation, with a 60 W heater for 10 minutes. How much energy does the heater transfer, in joules?
    2. The block starts at 20.5 °C. After the heater goes off, its highest temperature is 58.0 °C. What is its temperature change, in °C?
    3. Use c = ΔE ÷ (m Δθ) to find the specific heat capacity Mia measured, in J/kg °C.
    4. Aluminium's specific heat capacity is 900 J/kg °C. Why is Mia's value higher?
      1. The block warmed more than it should have, because the insulation trapped extra energy
      2. Some of the energy warmed the room, the heater and the thermometer, so the block warmed less than it should have
      3. The heater gave out less energy than 36 000 J
    5. What would bring Mia's value closer to 900 J/kg °C?
      1. Heat the block for longer
      2. Put thicker insulation all round the block
      3. Read the temperature the moment the heater goes off, not the highest one
    6. With no energy lost, 36 000 J would warm the 1.0 kg block (c = 900 J/kg °C) by ___ °C. Mia's block warmed by 37.5 °C, ___ than that, because some energy escaped.
    For the teacher

    Mia's block: 1.0 kg of aluminium, wrapped, a 60 W heater for 10 minutes, from 20.5 °C to a highest 58.0 °C. The energy is 60 × 600 = 36 000 J, the change 37.5 °C, so c = 36 000 ÷ (1.0 × 37.5) = 960 J/kg °C.

    The book value is 900 J/kg °C, and the simulation's wrapped block rose 40 °C on the same energy. Hers rose less because some energy still warmed the room, the heater and the thermometer, so her c is too high. Thicker insulation brings it closer.

    Work the examples aloud while the slower ones finish the quiz; the twins check they turn grams and kJ into kilograms and joules, and rearrange the right way.

    Students open the Lab quiz on their own devices. Open the answers slide once most have done the twins.

    Shorter: The Lab quiz's first four questions and the first pair only (−4 min).

    Longer: Pairs write a ΔE = m c Δθ question with grams and kJ for each other, and swap (+3 min).

  4. 4 · Vote and practise20 min

    Vote first

    500 g of water warms from 20 °C to 30 °C.

    c = 4200 J/kg °C. How much energy did it take?

    A: 21 000 000 J

    B: 21 000 J

    C: 63 000 J

    D: 42 000 J

    Choose on your own, then say why.

    4 · Vote and practise

    Practise: show your working

    1. 2 kg of water warms by 5 °C: ΔE?

    2. c = 385 J/kg °C for copper: what does it mean?

    3. 0.8 kg of aluminium, 15 °C to 40 °C: ΔE?

    4. 200 g of oil gets 12 kJ: Δθ?

    5. A 2100 W kettle, 1.5 kg of water, 2 minutes: Δθ?

    Stuck on 3? Use the change, not the end.

    Write here

    4 · Vote and practise

    Reason it out

    6. Why is water used in radiators?

    7. Same energy: water, aluminium or copper warms most?

    8. A block not wrapped: is c too high or too low?

    9. 1.5 kg, 40 W for 5 minutes, warms 8.0 °C: c?

    10. 3 kW for 7 minutes warms a tank 5 °C: its mass?

    Stretch: c from a graph of temperature and energy

    Seconds in E = P t; kilograms in ΔE = m c Δθ.

    20 min 4 · Who's stuck? · students vote · the slides say “Vote and practise”

    Vote, then practise

    One question shows who uses grams or the end temperature; then practice in levels, and finding c from a graph as the stretch.

    For this length: The stretch: c from a graph of temperature against energy

    Say

    “Choose an answer on your own. Nobody talks until everyone has chosen.”

    Ask
    • What is the mass in kilograms? And by how much did the temperature change?
    Watch for

    Putting 500 into the equation, or 30 °C: ask for the mass in kilograms and the change first.

    Show your working on paper. Use ΔE = m c Δθ; turn grams into kilograms, kJ into joules and minutes into seconds first. Water's specific heat capacity is 4200 J/kg °C. The stretch is optional.

    The question that shows who's stuck

    1. 500 g of water warms from 20 °C to 30 °C. Water's specific heat capacity is 4200 J/kg °C. How much energy did it take?
      1. 21 000 000 J
      2. 21 000 J
      3. 63 000 J
      4. 42 000 J
    In your Classroom, as they answer (an example)
    • A6
    • B11
    • C7
    • D4

    Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.

    1. How much energy does it take to warm 2 kg of water by 5 °C, in joules?
    2. Copper's specific heat capacity is 385 J/kg °C. What does that mean?
      1. It takes 385 J to warm any piece of copper by 1 °C
      2. It takes 385 J to warm 1 kg of copper by 1 °C
      3. 1 kg of copper melts at 385 °C
    3. A 0.8 kg aluminium block (c = 900 J/kg °C) warms from 15 °C to 40 °C. How much energy does it take, in joules?
    4. 200 g of oil (c = 2000 J/kg °C) is given 12 kJ of energy. By how much does its temperature rise, in °C?
    5. A 2100 W kettle heats 1.5 kg of water for 2 minutes. If all of its energy goes into the water, by how much does the water's temperature rise, in °C?
    6. Why is water good for carrying heat round a central-heating system and in hot-water bottles?
      1. Its small specific heat capacity lets it warm up quickly
      2. Its large specific heat capacity means each kilogram holds a lot of energy for each degree, and cools slowly
      3. It doesn't lose any heat to the room
    7. The same energy goes into 1 kg of water (4200 J/kg °C), 1 kg of aluminium (900 J/kg °C) and 1 kg of copper (385 J/kg °C). Which warms up the most?
      1. The water
      2. The aluminium
      3. The copper
      4. All warm up the same
    8. In the required practical, Kian forgets to wrap the block in insulation. How will his value of c compare with the true one?
      1. Too high: more heat escapes, so the block warms less
      2. Too low: energy is lost, so c is smaller
      3. The same: insulation only keeps the block safe to touch
    9. A 1.5 kg block is heated by a 40 W heater for 5 minutes and warms by 8.0 °C. What is its specific heat capacity, in J/kg °C?
    10. A 3 kW heater runs for 7 minutes and warms the water in a tank by 5 °C. If no energy is lost, what is the mass of the water, in kg?
    11. Stretch (Higher): Zara plots the temperature of a 0.5 kg block against the energy put in. Her straight line goes from 20 °C at 0 J to 80 °C at 24 000 J. Its gradient is ___ °C per joule, and the block's specific heat capacity is ___ J/kg °C.

    Support · Write each quantity on its own line with its unit before any multiplying: m = … kg, c = … J/kg °C, Δθ = end − start = … °C, ΔE = … J. Then put them into ΔE = m c Δθ, or its rearranged form.

    For the teacher

    Everyone chooses before anyone explains. Then ask in turn: the mass in kilograms? The temperature change? Times c?

    Questions 1–3 build fluency; 4–5 change the look (grams, kJ, a kettle's power); 6–8 ask for reasons; 9–10 are exam-style. The stretch finds c from a graph of temperature against energy.

    Students show their working on paper or the board; the quiz keeps their final answers.

    If many chose 21 000 000 J or 63 000 J, write m and Δθ on the board for the hinge question together before they practise.

    Shorter: After the vote, questions 1–5 only (−5 min).

    Longer: The stretch: c from a graph of temperature against energy (+8 min).

  5. 5 · Show what you know8 min

    Heat the iron

    A 0.6 kg block of iron, c = 450 J/kg °C

    Heated from 20 °C to 70 °C

    How much energy does it take?

    A 400 g block takes 7.2 kJ to warm by 20 °C

    What is its specific heat capacity?

    Write m, c and Δθ with units first.

    Write here

    8 min 5 · Exit · students show · the slides say “Show what you know”

    Heat the iron

    Energy from a temperature change, then c from grams and kJ, shows who uses the change and the right units.

    For this length: Why does a hot-water bottle stay warm for hours? Answer with specific heat capacity.

    Say

    “Write m, c and Δθ with their units first.”

    Watch for

    Using 70 °C as the change, or 400 and 7.2 in place of kilograms and joules.

    Write m, c and Δθ with their units before you put them into the equation.

    1. A 0.6 kg block of iron (c = 450 J/kg °C) is heated from 20 °C to 70 °C. How much energy does it take, in joules?
    2. A 400 g block takes 7.2 kJ to warm by 20 °C. What is its specific heat capacity, in J/kg °C?
    For the teacher

    A 0.6 kg block of iron (c = 450 J/kg °C) is heated from 20 °C to 70 °C. How much energy does it take?

    A 400 g block takes 7.2 kJ to warm by 20 °C. What is its specific heat capacity?

    Those who used the end temperature or grams need it again next lesson; set the homework.

    Longer: Why does a hot-water bottle stay warm for hours? Answer with specific heat capacity. (+4 min).

One to one: let the student drive the heating simulation while you only ask for a prediction before each change; before any calculation, ask them to say each quantity aloud with its unit, the mass in kilograms and the temperature change, not the end temperature.

Homework: Specific heat capacity

Show your working. Write each quantity with its unit first, in kilograms, joules and seconds. Water's specific heat capacity is 4200 J/kg °C.

  1. Find the energy needed to warm 3.0 kg of water by 15 °C.
  2. A 750 g copper pan (c = 385 J/kg °C) warms from 20 °C to 180 °C. Find the energy it takes, in kJ.
  3. A 2.0 kg block takes 72 kJ to warm by 40 °C. Find its specific heat capacity. Which metal could it be: aluminium (900 J/kg °C), iron (450 J/kg °C) or copper (385 J/kg °C)?
  4. A 1.2 kW heater warms 5.0 kg of oil (c = 2000 J/kg °C) for 4 minutes. If no energy is lost, by how much does the oil's temperature rise?
  5. In the required practical, Ben measures iron's specific heat capacity as 520 J/kg °C. The true value is 450 J/kg °C. Give a reason his value is too high, and one way to improve the experiment.
  6. Dry sand's specific heat capacity is about 800 J/kg °C. Explain why, on a sunny day, the sand on a beach gets much hotter than the sea.

Print the worksheet with working space and homework. Teacher answers come with your Library copy.

Teaching specific heat capacity: common questions

Is specific heat capacity on Foundation and Higher, and in combined science?

Yes. In AQA GCSE Physics (8463) and in AQA's combined science, specific heat capacity and ΔE = m c Δθ are for both tiers, and finding a specific heat capacity is a required practical in both. The whole lesson suits both tiers; the stretch, finding c from a graph's gradient, leans towards Higher.

Do students have to remember ΔE = m c Δθ?

AQA gives it on the equation sheet, so students need to choose it and use it, with its units, rather than recall it. They do need to remember that power is energy transferred each second (P = E ÷ t), which the lesson uses for the energy from a heater.

Why does the practical's value of c come out too high?

c = E ÷ (m Δθ). Some of the energy the joulemeter counts warms the room, the heater and the thermometer instead of the block, so the block's temperature rises less than it would if all of it stayed there. Dividing by a smaller Δθ gives a bigger c. Insulation, good contact between the thermometer and the block, and reading the highest temperature after the heater goes off all bring it closer.

A joulemeter, or a voltmeter and an ammeter?

Either. A joulemeter reads the energy directly. Without one, measure the power (the heater's rating, or the potential difference times the current) and the time in seconds, then E = P t. The lesson's questions use E = P t.

Is the simulation a replacement for the required practical?

No. It is a model: students change the material, the mass, the heater's power and the insulation, and see the temperature–time graph at once, which helps them predict and explain. The required practical still needs to be done with real equipment; the simulation helps students see why heat lost to the room bends the graph and makes the measured c too high.

Can I use the lesson without creating an account?

Yes. Read the lesson, print the worksheet and open its slides without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the quizzes, the answers and the answer slides.

Curriculum reference: AQA GCSE Physics 8463: 4.1.1.3 (energy changes in systems: specific heat capacity, ΔE = m c Δθ, and the required practical to find the specific heat capacity of a material), with 4.1.1.4 (power: P = E ÷ t).

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