Thermal insulation

1 Plan and risk assessment

Hot water transfers energy to its cooler surroundings, faster the hotter it is. An insulator, with a low thermal conductivity and trapped air, lowers the rate of energy transfer, so the water cools more slowly. The drop in temperature in the same time compares how well each material insulates.

ΔE = m c Δθ

Prediction

2 Apparatus

• ✓Kettle Boils the water.
• ✓Beakers: 100 ml, 250 ml and 800 ml Hold the hot water; the 800 ml beaker holds the insulation around the 100 ml one.
• ✓Measuring cylinders (100 ml and 250 ml) (resolution 1 ml (100 ml), 2 ml (250 ml)) Measure the same volume of water for every beaker: 80 ml in the 100 ml cylinder, 200 ml in the 250 ml one.
• ✓Two thermometers (digital or liquid-in-glass) (resolution 0.1 °C or 1 °C) Measure the temperature of the water in each beaker.
• ✓Two stopwatches (resolution 0.01 s) Time the 5-minute readings for each beaker.
• ✓Cardboard lids with a hole Cover the beakers; the thermometer goes through the hole.
• ✓Insulating materials and rubber bands Bubble wrap, polystyrene granules, sawdust, corrugated card and newspaper.
• ✓Heatproof mats and a tray Protect the bench; catch spilt granules.

3 Method: your choices

• Check the thermometers: DoneA thermometer that reads high or low adds the same error to every reading it takes (a zero error).
• Choose your investigation: Different materials (Part 1)80 ml of hot water in a 100 ml beaker, inside an 800 ml beaker. You pack the space between them with one material and leave the other beaker empty.
• Choose your material: Bubble wrapYou pack bubble wrap around one beaker. The class results show the other materials.
• Choose your thermometers: Digital thermometers (0.1 °C)Resolution 0.1 °C, and the display is read directly: no parallax error.
• Stand the beakers on heatproof matsSafety: DoneNear-boiling water scalds. A beaker held in the hand can tip or slip while you pour.
• Measure the water: DoneMore water stores more energy, so it cools more slowly. Both beakers (and every group) must use the same volume for a fair test.
• Pack the insulation: DoneGaps full of air let convection currents carry energy away. Every group must pack its material the same way.
• Put on the lids: DoneHot water loses a lot of energy from its surface by evaporation. A lid on every beaker keeps that the same for each one.
• When will you start the stopwatch?: When its thermometer reads 80 °CEvery beaker starts at the same temperature, so their drops can be compared fairly. You wait a few minutes first.

• 0.0 Ringed: the anomaly, left out of your results.

Anomaly: Bubble wrap, 10 min, left out of your results. Likely cause: most likely the thermometer was lifted out of the water to read it (or its bulb was not fully in the water), so it read the cooler air.

6 Analysis

1. Drop in temperature: beaker A

   drop in temperature = temperature at 0 min − temperature at 20 min

   Calculate the drop in temperature of the water in beaker A (no insulation) over the 20 minutes.

   21.4 °C Right first time

2. Drop in temperature: beaker B

   drop in temperature = temperature at 0 min − temperature at 20 min

   Calculate the drop in temperature of the water in beaker B (bubble wrap) over the 20 minutes.

   13.2 °C Right first time

3. Shape of the graph

   Describe the shape of your cooling curve.

   The temperature falls quickly at first, then more and more slowly. Right first time

4. Energy transferred from beaker B

   ΔE = m c Δθ (c of water = 4200 J/kg °C)

   The water in beaker B had a mass of 0.080 kg (80 ml). Its temperature fell by 13.2 °C. Calculate the energy it transferred to the surroundings.

   4440 J Right first time

5. Where the energy goes

   3 of 3 right first time Right first time

6. The class’s results

   The rest of the class is simulated for you: each group tested one material against a beaker with no insulation, and your result is included. The mean drop in temperature in 20 minutes for each material is shown. Which material was the best insulator?

   Bubble wrap: mean drop 13.7 °C (4 groups) Right first time

7 Conclusion and evaluation

Conclusion

Sources of error

Improvement

Repeatable or reproducible

9 Exam questions on your data

On your own readings, self-marked against the mark scheme, with error carried forward where it applies. Total 30/30.

1. 01.1[2 marks]

   Another student compared four insulating materials. The student wrapped each material around a beaker of hot water and timed how long the water took to cool from 80 °C to 60 °C.

   Give the independent variable and the dependent variable in this investigation.

   Your answer

   Independent variable: the type of insulating material. Dependent variable: the time taken for the water to cool from 80 °C to 60 °C.

   2/2 self-marked

   • Independent variable: (type of) insulation / material (do not accept thickness of material)
   • Dependent variable: time (taken to cool from 80 °C to 60 °C)

   Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

   Model answer: Independent variable: the type of insulating material. Dependent variable: the time taken for the water to cool from 80 °C to 60 °C.

2. 01.2[1 mark]

   In your investigation you compared a beaker of hot water packed with insulation with one that had none.

   Give one control variable in your investigation.

   Your answer

   The volume of water in each beaker

   1/1 self-marked

   • Any one of: volume (or mass) of water; starting temperature; lid (or no lid); size or type of beaker; room temperature; time between readings

   Self-marked: 1 of 1 mark. This is your own judgement against the mark scheme.

   Model answer: The volume of water in each beaker.

3. 01.3[1 mark]

   Another student used a digital thermometer. At one point its display showed 74.1 °C.

   What is the resolution of the digital thermometer?

   Your answer

   0.1

   1/1

   • 0.1 (°C)

   Full marks. Well done.

   Model answer: 0.1 °C

4. 01.4[1 mark]

   Another student used a liquid-in-glass thermometer.

   Give one source of error when reading a liquid-in-glass thermometer.

   Your answer

   Parallax error: the reading depends on the viewing angle if your eye is not level with the top of the liquid.

   1/1 self-marked

   • Viewing angle affects the measurement (parallax error); also credit: you have to judge where the top of the liquid is (not enough: “human error”, “hard to read”)

   Self-marked: 1 of 1 mark. This is your own judgement against the mark scheme.

   Model answer: The reading depends on the angle you view it from (parallax error), so your eye must be level with the top of the liquid.

5. 01.5[2 marks]

   Another student measured the temperature with a digital thermometer (resolution 0.1 °C) every 5 minutes.

   A teacher said a temperature probe and data logger (resolution 0.1 °C) would be no better for this investigation.

   Explain why the digital thermometer is just as suitable as the data logger.

   Your answer

   They have the same resolution of 0.1 °C. You only need a reading every 5 minutes, so you do not need continuous readings from a data logger.

   2/2 self-marked

   • The digital thermometer and the data logger have the same resolution
   • Only a few readings are needed (every 5 minutes, or only the start and end temperatures), not continuous readings

   Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

   Model answer: The digital thermometer has the same resolution as the data logger (0.1 °C), and only one reading is needed every 5 minutes, so continuous readings are not needed.

6. 01.6[1 mark]

   In an insulation investigation, hot water from a kettle is poured into a glass beaker. A thermometer or temperature probe and a lid are used, and the kettle is plugged into the mains.

   Give one hazard in this investigation and the harm it could cause.

   Your answer

   Near-boiling water from the kettle could scald your skin.

   1/1 self-marked

   • A hazard with its harm: hot water or a hot beaker could scald or burn the skin; broken glass could cut; the kettle lead could give an electric shock (ignore "the water is hot" alone)

   Self-marked: 1 of 1 mark. This is your own judgement against the mark scheme.

   Model answer: Near-boiling water from the kettle could scald your skin.

7. 02.1[1 mark]

   Table 1 shows your readings for the beaker with bubble wrap.

   Which reading is anomalous?

   Select one row.

   Table 1

   Time in min	Temperature in °C
   0	80.0
   5	76.4
   10	67.7
   15	69.9
   20	66.8

   Your answer

   the reading at 10 minutes

   1/1

   • The reading at 10 minutes: it is much lower than the smooth curve through the others

   Full marks. That is exactly what the mark scheme is looking for. At 10 minutes (67.7 °C) the temperature drops much more than the pattern of the readings either side.

   Model answer: The reading at 10 minutes: it does not fit the smooth curve of the others.

8. 02.2[2 marks]

   Table 2 shows your readings for the beaker with no insulation.

   Table 2

   Time in min	Temperature in °C
   0	80.0
   5	73.5
   10	67.9
   15	63.1
   20	58.6

   Calculate the mean rate of cooling of the water in the first 10 minutes.

   Your answer

   1.21

   Working: Fall in temperature = 80.0 − 67.9 = 12.1 °C Rate = 12.1 ÷ 10 = 1.21 °C/min

   2/2

   • Fall in temperature = 80.0 − 67.9 = 12.1 °C
   • Rate = 1.21 °C/min

   Full marks. Well done.

   Model answer: Fall in temperature = 80.0 − 67.9 = 12.1 °C Rate = 12.1 ÷ 10 = 1.21 °C/min

9. 02.3[2 marks]

   In your beaker with no insulation, the temperature fell by 6.5 °C in the first 5 minutes but only 4.5 °C in the last 5 minutes.

   Explain why the water cooled fastest at the start.

   Your answer

   At the start the temperature difference between the water and the surroundings was greatest, so the rate of energy transfer to the surroundings was highest.

   2/2 self-marked

   • The temperature difference between the hot water and the surroundings was greatest at the start (allow the water was hottest)
   • So the rate of energy transfer (to the surroundings) was greatest

   Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

   Model answer: At the start the temperature difference between the hot water and the surroundings was greatest, so the rate of energy transfer to the surroundings was greatest.

10. 02.4[2 marks]

    You put a cardboard lid on each beaker. Another group left their lids off, and their water cooled much faster.

    Explain why the water cools faster when the beaker has no lid.

    Your answer

    Without a lid, energy is transferred from the surface of the water by evaporation, so the rate of energy transfer to the surroundings is higher.

    2/2 self-marked

    • Energy is transferred from the surface of the water by evaporation (allow convection above the water; steam escaping)
    • So the rate of energy transfer (to the surroundings) is higher

    Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

    Model answer: Without a lid, energy is transferred from the surface of the hot water by evaporation, so the rate of energy transfer to the surroundings is higher.

11. 02.5[2 marks]

    Two other groups also tested bubble wrap. Table 3 shows their results.

    Table 3

    Group	Temperature at start in °C	Temperature after 20 min in °C	Drop in temperature in °C
    A	91.2	75.8	15.4
    B	80.0	67.7	12.3

    Suggest two reasons why the two groups got different drops in temperature.

    Your answer

    Group A started at a higher temperature, so its water cooled faster. They may also have used different volumes of water.

    2/2 self-marked

    • Different starting temperatures (group A started hotter, so its water cooled faster)
    • Different volumes (or masses) of water
    • The material was packed differently (different thickness or air gaps)
    • A lid used by one group but not the other, or a different room temperature or draughts
    • Thermometer errors (a zero error, or reading the thermometer differently)

    Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

    Model answer: Group A started at a higher temperature, so its water cooled faster. The groups may also have used different volumes of water.

12. 02.6[2 marks]

    Table 4 shows the class’s results. Each material was tested by three or four groups.

    Table 4

    Material	Mean drop in temperature in 20 min in °C
    Bubble wrap	13.7
    Polystyrene granules	14.2
    Sawdust	22.2
    Corrugated card	17.5
    Newspaper	19.0

    Which material was the best insulator? Give a reason for your answer.

    Your answer

    Bubble wrap, because its water had the smallest mean drop in temperature.

    2/2 self-marked

    • Bubble wrap
    • Its water had the smallest (mean) drop in temperature (it cooled least or most slowly)

    Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

    Model answer: Bubble wrap: its water had the smallest mean drop in temperature in 20 minutes.

13. 02.7[3 marks]

    Another student’s beaker of water cooled by 16 °C.

    The energy transferred from the water to the surroundings was 16.8 kJ.

    Specific heat capacity of water = 4200 J/kg °C

    change in thermal energy = mass × specific heat capacity × temperature change ΔE = m c Δθ

    Calculate the mass of water in the beaker.

    Use the Physics Equations Sheet.

    Your answer

    0.25

    Working: ΔE = 16.8 kJ = 16800 J 16800 = m × 4200 × 16 m = 16800 ÷ (4200 × 16) m = 0.25 kg

    3/3

    • Substitution: 16 800 = m × 4200 × 16 (allow 16.8 not converted)
    • Rearrangement: m = 16 800 ÷ (4200 × 16) (allow 16.8 not converted)
    • m = 0.25 kg

    Full marks. Well done.

    Model answer: ΔE = 16.8 kJ = 16 800 J 16 800 = m × 4200 × 16 m = 16 800 ÷ (4200 × 16) m = 0.25 kg

14. 02.8[2 marks]

    Another student timed how long the water took to cool from 80 °C to 60 °C with each of four materials, A, B, C and D. Each material was the same thickness.

    Table 5

    Material	Time to cool from 80 °C to 60 °C in min
    A	15.0
    B	9.0
    C	14.0
    D	12.0

    Explain what the results show about the thermal conductivity of material B.

    Your answer

    B has the highest thermal conductivity. The water cooled by the same amount in the shortest time, so the rate of energy transfer through B was highest.

    2/2 self-marked

    • B has the highest thermal conductivity (of the four)
    • B let the water cool by the same amount in the least time, so energy passed through B at the highest rate

    Self-marked: 2 of 2 marks. This is your own judgement against the mark scheme.

    Model answer: B has the highest thermal conductivity: its water cooled by the same amount in the shortest time, so the rate of energy transfer through B was highest.

15. 03[6 marks]

    A student wants to investigate how the number of layers of newspaper wrapped around a metal can affects how quickly hot water in the can cools.

    The student has: a metal can, sheets of newspaper, rubber bands, a kettle, a measuring cylinder, a digital thermometer and a stopwatch.

    Plan an investigation the student could do.

    Your answer

    1. Wrap one layer of newspaper around the metal can and hold it with rubber bands. 2. Measure 200 ml of hot water from the kettle with a measuring cylinder and pour it into the can. 3. Put the digital thermometer in the water. When it reads 80 °C, start the stopwatch. 4. Record the temperature after 10 minutes. 5. Calculate the drop in temperature. 6. Repeat with 2, 3, 4 and 5 layers of newspaper. 7. Keep the volume of water, the starting temperature and the time the same each time, and put a lid on the can. 8. The more layers, the smaller the drop: compare the drops for each number of layers.

    6/6 self-marked

    • Wrap a number of layers of newspaper around the metal can (held with rubber bands)
    • Pour a measured volume of hot water into the can
    • Measure the initial temperature with the digital thermometer (and start the stopwatch)
    • Measure the temperature after a set time (e.g. 10 minutes), or every few minutes
    • Repeat with different numbers of layers
    • Keep a control variable the same: volume of water, starting temperature, time, lid, room temperature, same type of newspaper
    • Calculate the drop in temperature and compare it for each number of layers

    Self-marked: Level 3, 6 of 6 marks. You ticked 7 of 7 indicative points. This is your own judgement against the mark scheme.

    Model answer: 1. Wrap one layer of newspaper around the metal can and hold it with rubber bands. 2. Measure 200 ml of hot water from the kettle with a measuring cylinder and pour it into the can. 3. Put the digital thermometer in the water. When it reads 80 °C, start the stopwatch. 4. Record the temperature after 10 minutes. 5. Calculate the drop in temperature. 6. Repeat with 2, 3, 4 and 5 layers of newspaper. 7. Keep the volume of water, the starting temperature and the time the same each time, and put a lid on the can. 8. The more layers, the smaller the drop: compare the drops for each number of layers.

Unseen data: the same skills, new apparatus

1. 01[3 marks]

   A student pours 0.46 kg of hot soup into a flask with the lid off and reads its temperature every 4 minutes.

   Temperature of the soup

   Time in min	Temperature in °C
   0	86.5
   4	82.6
   8	79.1
   12	75.1
   16	72.1
   20	68.8

   Calculate the mean rate of cooling of the soup between 4 minutes and 16 minutes, in °C per minute. Give your answer to 2 significant figures.

   Your answer

   0.88

   Working: 82.6 - 72.1 = 10.5 16 - 4 = 12 10.5 / 12

   3/3

   • Fall = 82.6 − 72.1 = 10.5 °C.
   • Time taken = 16 − 4 = 12 min.
   • Mean rate = fall ÷ time taken, in °C per minute.

   Full marks. That is exactly what the mark scheme is looking for.

   Model answer: Fall = 82.6 − 72.1 = 10.5 °C in 16 − 4 = 12 minutes. Mean rate of cooling = 10.5 ÷ 12 = 0.88 °C per minute.

2. 02[2 marks]

   A student puts the same mass of hot water into three identical cups. Each cup has a sleeve of a different material, of the same thickness. They time how long the water in each cup takes to cool from 70 °C to 60 °C.

   Time to cool from 70 °C to 60 °C

   Sleeve	Time
   Felt	7 min 10 s
   Wool	5 min 15 s
   Foam	3 min 20 s

   Which TWO conclusions are correct? Tick (✓) two boxes.

   • ✓ The foam sleeve has the highest thermal conductivity. (your choice)
   • ✓ The rate of energy transfer through the foam sleeve was the highest. (your choice)
   • The foam sleeve is the best insulator, because its water reached 60 °C first.
   • The felt sleeve has the highest thermal conductivity, because it kept the water hot for longest.
   • The water in the felt cup transferred more energy in total than the others.

   Your answer

   The foam sleeve has the highest thermal conductivity.; The rate of energy transfer through the foam sleeve was the highest.

   2/2

   • The foam sleeve has the highest thermal conductivity.
   • The rate of energy transfer through the foam sleeve was the highest.

   Full marks. Clear and precise.

   Model answer: The water in the foam cup fell by the same 10 °C in the shortest time, so energy was transferred through that sleeve at the highest rate: it has the highest thermal conductivity. Every cup lost the same energy (same mass, same fall), only at different rates.

3. 03[2 marks]

   Two students compare takeaway cups. The water in the paper cup starts at 90 °C and falls 18.1 °C in 10 minutes. The water in the plastic cup starts at 69 °C and falls 11.3 °C in 10 minutes. The room and the volume of water are the same. They conclude that the plastic cup is the better insulator.

   Which TWO statements about their conclusion are correct? Tick (✓) two boxes.

   • ✓ The conclusion is not valid: the starting temperature should have been the same for both cups. (your choice)
   • ✓ Water that starts hotter cools faster, because its temperature difference with the room is bigger. (your choice)
   • The conclusion is valid: the water in the plastic cup fell by less.
   • Repeating each test three times and taking a mean would make the comparison valid.
   • Water always falls by the same number of degrees in 10 minutes, whatever temperature it starts at.

   Your answer

   The conclusion is not valid: the starting temperature should have been the same for both cups.; Water that starts hotter cools faster, because its temperature difference with the room is bigger.

   2/2

   • The conclusion is not valid: the starting temperature should have been the same for both cups.
   • Water that starts hotter cools faster, because its temperature difference with the room is bigger.

   Full marks. Your answer meets all the points for this question.

   Model answer: The paper cup started 21 °C hotter, so its water was further above room temperature and cooled faster whatever the cup. The starting temperature is a control variable: start both at the same temperature (say 80 °C). Repeats with the same unfair start would not fix it.