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B.1 Thermal energy transfers · SL + HL · Part 2 of 3 · student investigation · 80 minutes

Phase changes and latent heat

Predict what the thermometer does while ice melts, how much longer it takes to boil water away than to melt the same mass of ice, where the temperature ends when ice is dropped into water, and why a wet cloth feels cold. Then test each prediction with a simulation.

1 Predict · 7
2 The heating curve · 16
3 Latent heat · 14
4 Ice in water · 18
5 Evaporation · 15
6 Show + reflect · 10

Learning goals: by the end you can…

read a heating curve: sloping parts use Q = mcΔT, flat parts use Q = mL, and Q = Pt on every part.
explain, in terms of molecules, why a phase change happens at constant temperature.
define specific latent heat word for word and use Q = mL.
solve an ice-in-water problem, and check first whether all the ice melts.
explain why evaporation cools a liquid, and why steam burns are worse than burns from boiling water.

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)

Q = mcΔTQ = mLQ = Pt

Water: c = 4200, ice: c = 2100 J kg⁻¹ K⁻¹. L_f(ice) = 3.34 × 10⁵ J kg⁻¹, L_v(water) = 2.26 × 10⁶ J kg⁻¹. Energy lost = energy gained when nothing escapes.

2. The heating curve: test prediction 1.1

16 minPairs → individual

ATL Thinking: read each part of a graph with its own equation. Communication: explain with molecules.

Simulation A · The heating curve ice at −20 °C, heated at constant power until all the water has boiled away

heater power 500 Wmass 0.50 kg

time to reach 0 °C—

time to melt—

time to boil away—

Learn it word for word

During a phase change the temperature is constant. The energy supplied increases the intermolecular potential energy (the molecules move apart, bonds are broken); the average random kinetic energy of the molecules does not change.

Reading a heating curve

Every part: energy = P × (time of that part).
Sloping part: one phase warms, Q = mcΔT.
Flat part: a phase change, Q = mL.
Gradient of a sloping part = P/(mc): steeper means smaller c.

2.1Time for the ice to warm from −20 °C to 0 °C =

2.2Time for all the ice to melt =

2.3Gradient of the ice line ÷ gradient of the water line =

Find the mistake

A student writes about the flat part at 0 °C:

“The temperature does not change, so no energy is going into the ice.”

What is wrong?

Energy is still supplied (Pt); it increases the potential energy of the molecules, not their kinetic energy. The temperature does change slowly. Nothing is wrong.

Hinge question

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

During melting, what happens to the internal energy of the ice–water mixture?

A. it increases B. it stays the same C. it decreases

Back check

2.bBack check: set 250 W. Time to reach 0 °C =

2.4Was prediction 1.1 right? Explain in terms of molecules.

What a good answer looks like

B, it stays at 0 °C. During melting the energy from the heater separates the molecules: their intermolecular potential energy increases, but their average random kinetic energy does not change. Temperature measures the average kinetic energy, so it stays at 0 °C until all the ice has melted.

3. Latent heat: test prediction 1.2

14 minIndividual

ATL Self-management: choose mcΔT or mL. Thinking: why boiling needs more energy than melting.

Simulation B · Boiling water on a balance a heater of power P keeps water boiling; the balance shows the mass left

heater power 800 Wtime 5.0 min

energy supplied—

mass boiled away—

balance reading—

Learn it word for word

Specific latent heat L: the energy required to change the phase of 1 kg of a substance at constant temperature. Q = mL. L_f: fusion (melting/freezing); L_v: vaporization (boiling/condensing).

3.1Energy to melt 0.50 kg of ice at 0 °C =

3.2Energy to boil away 0.50 kg of water at 100 °C =

3.3Simulation: 800 W for 5.0 min. Mass boiled away =

Find the mistake

A student finds the energy to boil away 0.50 kg of water at 100 °C:

“Q = mcΔT = 0.50 × 4200 × 0 = 0 J.”

What is wrong?

At a phase change the temperature does not change; use Q = mL, not mcΔT. ΔT should be 100 K. Nothing is wrong: boiling needs no energy.

Hinge question

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

Why is L_v of water about 7 times bigger than L_f?

A. in boiling the molecules are pulled completely apart, so much more work is done against the forces between them B. water is hotter when it boils C. steam has a larger c

Back check

3.bBack check: set 600 W. Time to boil away 0.10 kg =

3.4Was prediction 1.2 right? Explain with L_f and L_v.

What a good answer looks like

B, about 7 times longer. With the same heater the time is proportional to the energy: melting needs 0.50 × 3.34 × 10⁵ = 1.67 × 10⁵ J, boiling away needs 0.50 × 2.26 × 10⁶ = 1.13 × 10⁶ J, which is 6.8 times more. On the heating curve, the boiling plateau is about 7 times longer than the melting plateau.

4. Ice in water: test prediction 1.3

18 minPairs → individual

ATL Self-management: do the check before the equation. Thinking: when a calculation gives an impossible answer.

Simulation C · Ice dropped into water ice at 0 °C into water; nothing escapes; the bars compare what the water can give with what the ice needs

mass of ice 60 gmass of water 200 gwater temperature 20 °C

water can give (to 0 °C)—

melting all the ice needs—

result—

Ice in water: check first

Energy the water can give by cooling to 0 °C: m_wc_w(θ_w − 0).
Energy needed to melt all the ice: m_iceL_f (plus m_icec_iceΔT if the ice is below 0 °C).
If the water can give MORE: all the ice melts; use lost = gained to find θ.
If the water can give LESS: θ = 0 °C and some ice is left; mass melted = (energy available)/L_f.

4.1Energy the 200 g of water at 20 °C can give by cooling to 0 °C =

4.2Energy needed to melt all 60 g of ice =

4.3Mass of ice that melts =

Find the mistake

A student skips the check and uses lost = gained for 60 g of ice:

“0.20 × 4200 × (20 − θ) = 20 040 + 0.060 × 4200 × θ → θ = −1.4 °C.”

What does the negative answer tell you?

Not all the ice melts: the final temperature is 0 °C, with ice left over. The mixture freezes below 0 °C. The calculation is right.

Hinge question

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

At the end of question 4.3, the ice and the water are at the same temperature. What is it?

A. 0 °C: ice and water can only be together at the melting point B. 10 °C C. between 0 °C and 20 °C, depending on the masses

Back check

4.bBack check: set 40 g of ice. Final temperature =

°C

4.4Was prediction 1.3 right? Explain with the two energies.

What a good answer looks like

B, 0 °C with some ice left. Cooling the water to 0 °C gives only 16 800 J, but melting 60 g of ice needs 20 040 J. So only 16 800/334 000 = 50 g melts; the rest stays as ice and the mixture sits at 0 °C.

5. Evaporation: test prediction 1.4

15 minPairs

ATL Communication: explain with the average kinetic energy. Thinking: link to sweating and to steam burns.

Simulation D · Evaporation the bars show how many molecules of the liquid have each kinetic energy; only the fastest can escape from the surface

molecules escaped—

average KE of those left—

so the liquid…—

Learn it word for word

Evaporation cools a liquid: the fastest (most energetic) molecules escape from the surface, so the average kinetic energy of the molecules left behind decreases, and so does the temperature. Evaporation happens at the surface, at any temperature.

5.1Which change makes a puddle evaporate faster?

a larger surface area, a higher temperature or wind a deeper puddle colder air with no wind

5.2During exercise 20 g of sweat evaporates from the skin (L = 2.4 × 10⁶ J kg⁻¹ at skin temperature). Energy taken from the body =

5.3For a 70 kg body (c = 3500 J kg⁻¹ K⁻¹), the temperature drop this causes =

Find the mistake

A student writes:

“Evaporation only happens when water reaches 100 °C.”

What is wrong?

That is boiling. Evaporation happens at the surface at any temperature (a puddle dries at 20 °C). Evaporation only happens at 0 °C. Nothing is wrong.

Hinge question

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

Why is a burn from 10 g of steam at 100 °C much worse than from 10 g of boiling water?

A. the steam first condenses on the skin and gives out its latent heat B. steam is hotter than 100 °C C. steam molecules have more kinetic energy at the same temperature

What if? · stretch

5.w10 g of steam at 100 °C condenses on skin and cools to 37 °C; 10 g of water at 100 °C cools to 37 °C. Energy from the steam ÷ energy from the water =

5.4Was prediction 1.4 right? Explain with molecules.

What a good answer looks like

B, cool. Water molecules with the most kinetic energy escape from the cloth. The average kinetic energy of the molecules left behind falls, so the water gets colder than your arm, and thermal energy flows from your arm into the cloth. The energy for evaporation (mL) is taken from your skin.

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…

say what happens to the potential and kinetic energy of the molecules during a phase change;
use Q = mL and Q = Pt correctly;
check whether all the ice melts before using lost = gained;
use one number from a simulation today.

Option A · Written

One paragraph: “Why the thermometer stops rising while ice melts.” Use molecules and energy.

Option B · Worked example

Make up your own ice-in-water problem where NOT all the ice melts, solve it, and check it with Simulation C.

Option C · Spoken

Explain to your partner in 1 minute how to read a heating curve (flat and sloping parts). 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): While ice melts, the heater still supplies energy (Pt), but the temperature stays at 0 °C. The energy increases the intermolecular potential energy of the molecules: they move further apart and the bonds of the solid break. Their average random kinetic energy does not change, and temperature is a measure of the average kinetic energy, so the thermometer stays at 0 °C. The internal energy still increases. With 500 W, melting 0.50 kg of ice takes 0.50 × 334 000/500 = 334 s, and only then does the temperature start to rise again.

Exit ticket (no notes)

1Energy to melt 0.25 kg of ice at 0 °C (L_f = 3.34 × 10⁵ J kg⁻¹), in J =

2During boiling, the average kinetic energy of the water molecules…

stays the same increases decreases

3A 600 W heater keeps water boiling. Time to boil away 0.10 kg (L_v = 2.26 × 10⁶ J kg⁻¹), in s =

4Ice and water are left together in an insulated flask. Their temperature is…

0 °C room temperature below 0 °C

5Evaporation cools a liquid because…

the fastest molecules escape, so the average kinetic energy of the rest falls the liquid loses potential energy the air above it is cold

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 how to tell whether all the ice melts.”

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

What a good answer looks like

A good feedforward names an action: “Next time I will compare the energy the water can give with the energy the ice needs before I write lost = gained.”

Read the notes Part 3 Back to B.1