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B.1 Thermal energy transfers · SL + HL · Part 1 of 3 · student investigation · 80 minutes

Particles, temperature and heating

Predict what happens to the molecules when a gas gets a little warmer, which warms more with the same energy (water or aluminium), whether a bath or a cup of tea has more internal energy, and where the temperature ends up when a hot metal is dropped into water. Then test each prediction with a simulation.

1 Predict · 7
2 Temperature · 14
3 Internal energy · 14
4 Specific heat capacity · 16
5 Mixing · 19
6 Show + reflect · 10

Learning goals: by the end you can…

change between °C and K, and explain why a temperature change is the same on both scales.
use Ē_k = (3/2)k_BT to link the kelvin temperature to the average kinetic energy of the particles.
define internal energy word for word, and tell it apart from temperature and heat.
use Q = mcΔT, and explain what a large specific heat capacity means.
solve a mixing problem with “energy lost = energy gained”.

How to work in this lesson

How to work. Pairs discuss and agree, but each of you writes. Pairs → individual discuss the method, then write your own answer. Individual no discussion until your teacher says so. Your typed answers are saved on this device only.

Everything you need is on this page. Each simulation uses the same numbers as the questions next to it, and stays locked until you have made your prediction. Type powers of ten like 1.9×10^24 or 1.9e24. Give answers in the unit shown next to the box.

📘 From the data booklet (B.1)

T(K) = θ(°C) + 273Ē_k = (3/2)k_BTQ = mcΔTρ = m/V

k_B = 1.38 × 10⁻²³ J K⁻¹. Specific heat capacities (J kg⁻¹ K⁻¹): water 4200, aluminium 900, iron 440, copper 385, lead 130. A temperature change in K equals the change in °C.

2. Temperature: test prediction 1.1

14 minPairs → individual

ATL Self-management: change to kelvin every time. Thinking: link the large scale (temperature) to the particles.

Simulation A · Temperature and the molecules the arrows show how fast the molecules move; Ē_k = (3/2)k_BT

temperature 20 °C

T in kelvin—

average kinetic energy—

compared with 20 °C—

Learn it word for word

Temperature in kelvin is a measure of the average kinetic energy of the particles: Ē_k = (3/2)k_BT.
T(K) = θ(°C) + 273. A temperature change is the same number in K and in °C.

2.1Set 20 °C. The average kinetic energy of a molecule =

2.2Set 40 °C. Ē_k(40 °C)/Ē_k(20 °C) =

2.3At what Celsius temperature is Ē_k twice its value at 20 °C?

°C

Find the mistake

A student answers question 2.3:

“Ē_k doubles when the temperature doubles, so 2 × 20 = 40 °C.”

What is wrong?

Ē_k is proportional to the kelvin temperature: double 293 K, which is 313 °C. The answer should be 10 °C. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Set the slider to −273 °C. What does absolute zero mean?

A. the particles have their lowest possible kinetic energy; nothing can be colder B. water freezes C. the gas has turned into a liquid

Back check

2.bBack check: set 100 °C. Ē_k =

2.4Was prediction 1.1 right? Explain with the kelvin scale.

What a good answer looks like

B, about 7 %. Ē_k is proportional to the kelvin temperature. 20 °C = 293 K and 40 °C = 313 K, so Ē_k rises by 313/293 = 1.068. Doubling the Celsius number does not double the energy, because 0 °C is not the zero of energy.

3. Internal energy: test prediction 1.3

14 minPairs

ATL Communication: use the exact words (total, random, intermolecular, molecules). Thinking: average against total.

Simulation B · Average or total? the same substance (water); bars show the average and the total random kinetic energy of the molecules

average Ē_k: tea ÷ bath—

total random KE: bath ÷ tea—

more internal energy—

Learn it word for word

Internal energy: the total intermolecular potential energy arising from the forces between the molecules plus the total random kinetic energy of the molecules arising from their random motion.
Thermal energy (heat): energy transferred because of a temperature difference.

3.1Average kinetic energy per molecule: tea (80 °C) ÷ bath (40 °C) =

3.2Total random kinetic energy: bath ÷ tea (same substance, so the number of molecules ∝ mass) =

3.3Temperature tells us about…

the average kinetic energy of one molecule the total internal energy the amount of heat in the body

Find the mistake

A student writes a definition:

“Internal energy is kinetic energy plus potential energy.”

Why would this score 0?

It does not say whose energy: the molecules’ total random kinetic energy and total intermolecular potential energy. Internal energy is only kinetic energy. It should say heat.

Hinge question

Choose your answer. You will see at once if it is right, and why.

A sealed box of gas is carried on a fast train. Compared with the same box at rest, its internal energy is…

A. the same: only the random motion of the molecules counts B. larger, because the molecules move faster C. smaller

3.4Was prediction 1.3 right? Explain the difference between temperature and internal energy.

What a good answer looks like

A, the bath. The tea is hotter, so each of its molecules has a slightly larger average kinetic energy (1.13 times). But the bath has 600 times as many molecules, so its total random kinetic energy is 532 times larger (and its potential energy too). Temperature is about the average; internal energy is the total.

4. Specific heat capacity: test prediction 1.2

16 minIndividual

ATL Self-management: ΔT is a change. Thinking: what a large c means in everyday life.

Simulation C · Same energy, different materials Q = mcΔT; the grey bar is water with the same mass and energy

mass 0.50 kgenergy supplied 9000 J

c of the material—

temperature rise—

water: temperature rise—

Learn it word for word

Specific heat capacity c: the energy required to raise the temperature of 1 kg of a substance by 1 K.

Q = mcΔT · c in J kg⁻¹ K⁻¹ · ΔT is the change (in K or °C, the same number)

4.1Aluminium, 0.50 kg, 9000 J. Temperature rise =

4.2Water, 0.50 kg, 9000 J. Temperature rise =

4.3Energy needed to heat 2.0 kg of water in a kettle from 15 °C to 100 °C =

Find the mistake

A student answers 4.3:

“Q = 2.0 × 4200 × 100 = 8.4 × 10⁵ J.”

What is wrong?

ΔT is the change, 100 − 15 = 85 K, not the final temperature. The temperature should be in kelvin, 373 K. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Why is water used in central-heating radiators?

A. its large c means each kilogram carries a lot of energy for each degree it cools B. it warms up quickly C. it is a good conductor

Back check

4.bBack check: choose lead (c = 130). Temperature rise for 0.50 kg and 9000 J =

4.4Was prediction 1.2 right? Explain with c.

What a good answer looks like

B, the aluminium, about 4.7 times more (20 K against 4.3 K). With the same Q and m, ΔT ∝ 1/c, and c(water)/c(aluminium) = 4200/900 = 4.7. Water needs much more energy for each degree.

5. Mixing: test prediction 1.4

19 minPairs → individual

ATL Self-management: follow the 4 steps. Thinking: which body changes temperature more, and why.

Simulation D · Mixing a hot block is dropped into water at 20 °C; nothing escapes, so energy lost = energy gained

block mass 0.20 kgblock temperature 100 °Cwater mass 0.20 kg

final temperature—

energy gained by water—

energy lost by block—

Every mixing problem in 4 steps

Write energy lost = energy gained.
For each body write mcΔT with ΔT = (higher − lower), so every term is positive.
Solve for the unknown (often the final temperature θ).
Check: θ lies between the two starting temperatures.

5.1Copper 0.20 kg at 100 °C into 0.20 kg of water at 20 °C. Final temperature =

°C

5.2Energy gained by the water =

5.3Method of mixtures: a 0.30 kg metal block at 90 °C goes into 0.40 kg of water at 20 °C; the final temperature is 25 °C. c of the metal =

J kg⁻¹ K⁻¹

Find the mistake

A student writes for 5.1:

“0.20 × 385 × (θ − 100) = 0.20 × 4200 × (θ − 20)”

What is wrong?

For the copper, ΔT must be (100 − θ): otherwise the left side is negative and the equation gives a wrong θ. The masses should be added. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

In 5.3 some energy escaped to the air while the block was moved. The true c of the metal is…

A. larger than 431: the block was really cooler than 90 °C when it reached the water B. smaller than 431 C. exactly 431

What if? · stretch

5.w0.50 kg of water at 80 °C is mixed with 0.50 kg of water at 20 °C. Final temperature =

°C

5.4Was prediction 1.4 right? Explain why the final temperature is close to the water’s.

What a good answer looks like

B, about 27 °C. The water has mc = 0.20 × 4200 = 840 J K⁻¹, the copper only 0.20 × 385 = 77 J K⁻¹. The energy the copper loses in falling 73 K warms the water by only 6.7 K. The body with the larger mc changes temperature the least.

6. Show it, then reflect

10 minIndividual

ATL Communication + Self-management: choose how to show your understanding, retrieve without notes, plan your next step.

Success criteria: your answer must…

use kelvin when you link temperature to kinetic energy;
define internal energy word for word;
use Q = mcΔT with ΔT as a change;
use one number from a simulation today.

Option A · Written

One paragraph: “Temperature, internal energy and heat are three different things.” Use the bath and the tea.

Option B · Worked example

Make up your own mixing problem (a hot metal into water), solve it with the 4 steps, and check it with Simulation D.

Option C · Spoken

Explain to your partner in 1 minute why the copper in 5.1 ends up close to 27 °C. Your partner ticks the success criteria.

6.1Write your paragraph, your worked example or your notes.

What a good answer looks like

Model answer (Option A): Temperature measures the average kinetic energy of the molecules: the tea at 80 °C (353 K) has molecules with 1.13 times the average kinetic energy of those in the bath at 40 °C (313 K). Internal energy is the total random kinetic energy plus the total intermolecular potential energy of all the molecules, so the bath, with 600 times as many molecules, has about 530 times as much random kinetic energy. Heat is neither: it is the energy transferred because of a temperature difference, and it always flows from the hotter body to the colder one until they reach the same temperature.

Exit ticket (no notes)

1Average kinetic energy of a gas molecule at 60 °C (in J, k_B = 1.38 × 10⁻²³ J K⁻¹) =

2A temperature rise of 15 °C is a rise of…

15 K 288 K 258 K

3Energy to warm 0.80 kg of water by 15 K (in J) =

4Internal energy is…

the total random kinetic energy plus total intermolecular potential energy of the molecules the average kinetic energy of the molecules the heat stored in a body

50.50 kg of water at 80 °C is mixed with 0.50 kg of water at 20 °C. Final temperature (°C) =

6Which idea from today is still the least clear to you?

What a good answer looks like

There is no single right answer. A good answer names one idea exactly, for example: “I am not sure which temperature goes into ΔT in a mixing problem.”

7Feedforward: Next time I will check ________ before I ________.

What a good answer looks like

A good feedforward names an action: “Next time I will write “energy lost = energy gained” first and use (higher − lower) on both sides.”

TOK · 2 minutes

Theory of knowledge: how do we know? There is no single right answer. Write two or three sentences.

TOKFor a long time heat was thought to be a fluid, “caloric”, that flowed from hot bodies to cold ones. The caloric model explained mixing problems well. How can a model that is wrong still give correct answers, and what finally shows that it is wrong?

Points you could make

A model can be useful in a limited range: caloric explained energy lost = energy gained in mixing, just like our model.
It failed elsewhere: rubbing hands together produces “heat” without taking it from anywhere (Rumford’s cannon boring).
Scientific knowledge is provisional: a model is kept while it works and replaced when it cannot explain new evidence.

Read the notes Part 2 Back to B.1