The shape of the lesson
By the end of the lesson, learners can
- Energy runs down the temperature gradient: Bring a hot object and a cold one together and energy crosses the boundary from hot to cold.
- Equal temperature means no net flow: Two bodies are in thermal equilibrium when there is no net transfer of energy between them, which happens precisely when they are at the same temperature.
- Warming without a state change: Q = mcΔθ.
- Changing state at constant temperature: Q = mL.
- Scales: T / K = θ / °C + 273.15; absolute zero is 0 K = −273.15 °C.
One picture every idea returns to
Thermal energy flows from regions of higher temperature to regions of lower temperature. Two bodies at the same temperature are in thermal equilibrium, with no net flow between them.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Hot to cold, until equal.. Thermal energy flows from hot to cold, and stops when temperatures match. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Energy runs down the temperature gradient | Bring a hot object and a cold one together and energy crosses the boundary from hot to cold. Project tab 1 of the lab (Thermal equilibrium) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Equal temperature means no net flow | Two bodies are in thermal equilibrium when there is no net transfer of energy between them, which happens precisely when they are at the same temperature. | Anticipation / Reaction Guide |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 43 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Equal temperature means no net flow, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
No examiner trap is recorded for this lesson. Use the quiz key below to spot the distractor most of the class picks.
Thermal equilibrium: topic worksheet
4 questions, 43 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
Two metal blocks A and B are placed in thermal contact and isolated from their surroundings, as shown in Fig. 1.1. Block A starts at 85 °C and block B starts at 25 °C.
(a) State what is meant by thermal equilibrium between two bodies. [2]
(b) For the two blocks in contact:
(i) state the direction of the net transfer of thermal energy and explain your answer, [3]
(ii) state what is true of the two temperatures once thermal equilibrium is reached. [1]
(c) Using T / K = θ / °C + 273.15:
(i) express the starting temperature of block A in kelvin, [1]
(ii) a block later has a thermodynamic temperature of 300 K; state this in °C. [1]
(d) State the Celsius value of absolute zero, and state what is special about it in terms of the energy of the particles. [2]
(e) State one reason the thermodynamic temperature scale is preferred to a scale defined by the expansion of a particular liquid. [2]
Two blocks at different temperatures are placed in contact inside a thermally isolated container, as shown in Fig. 4.1.
(a) State what is meant by thermal equilibrium. [2]
(b) State the direction of the net flow of thermal energy before equilibrium. [1]
(c) Explain, in terms of energy, why the hot block cools while the cold block warms. [2]
(d) State the quantity that determines the direction of net thermal energy flow. [1]
(e) At equilibrium, state whether the two blocks are at the same temperature and whether they hold the same internal energy. [2]
(f) Explain why two objects with equal internal energies need not be at the same temperature. [2]
Thermometers measure temperature through a physical property that varies with it.
(a) State two physical properties that can be used to measure temperature. [2]
(b) Explain what is meant by calibrating a thermometer using two fixed points. [2]
(c) Explain why two different thermometers may disagree at temperatures between the fixed points. [2]
(d) State one advantage of the thermodynamic scale over an empirical scale. [2]
(e) A resistance thermometer reads 100 Ω at 0 °C and 138 Ω at 100 °C. Assuming a linear response, find the temperature when its resistance is 119 Ω. [2]
A 0.50 kg copper block at 200 °C is dropped into 0.40 kg of water at 20 °C in an insulated container. This question links thermal equilibrium with specific heat capacity. Take c(copper) = 390 J kg⁻¹ K⁻¹ and c(water) = 4200 J kg⁻¹ K⁻¹.
(a) State the principle used to find the final temperature. [2]
(b) Write the energy-balance equation for the block and the water. [2]
(c) Calculate the final equilibrium temperature. [3]
(d) State the assumption made in this calculation. [1]
(e) Explain, in terms of thermal equilibrium, why the block and water end at the same temperature. [2]
(f) State whether the block and the water hold equal internal energies at equilibrium. [1]
Answer key and marking notes
- (a)Two bodies are in thermal equilibrium when there is no net transfer of thermal energy between them ✓, which happens when they are at the same temperature ✓
- (b)(i)Net energy is transferred from A to B ✓, because A is at the higher temperature ✓; net flow is always from higher to lower temperature ✓
- (b)(ii)The two temperatures become equal ✓
- (c)(i)T = 85 + 273.15 = 358 K ✓
- (c)(ii)θ = 300 − 273.15 = 27 °C ✓
- (d)Absolute zero is −273 °C (−273.15 °C) ✓; it is the temperature at which the particles have their minimum (least) kinetic energy ✓
- (e)The thermodynamic scale does not depend on the property or substance used ✓; different liquids would not agree at points between the fixed points, whereas the thermodynamic scale gives one substance-independent value ✓
- (a)A state in which there is no net flow of thermal energy between the objects ✓, because they are at the same temperature ✓
- (b)From the hotter block to the cooler block ✓
- (c)There is a net transfer of energy from the hot block to the cold block ✓, lowering the internal energy of one and raising the other until temperatures are equal ✓
- (d)The temperature (difference), not the amount of internal energy ✓
- (e)They reach the same temperature ✓; their internal energies are generally not equal ✓
- (f)Internal energy depends on the mass and material as well as the temperature ✓✓
- (a)Any two of: the volume of a liquid, electrical resistance, the e.m.f. of a thermocouple, the pressure of a fixed-volume gas ✓✓
- (b)Marking the readings at two known temperatures (such as the ice and steam points) ✓ and dividing the scale evenly between them ✓
- (c)Their chosen properties vary differently (non-linearly) with temperature ✓, so the empirical scales agree only at the fixed points ✓
- (d)It is independent of the substance and agrees everywhere ✓✓
- (e)θ = (119 − 100)/(138 − 100) × 100 = 19/38 × 100 ✓ = 50 °C ✓
- (a)Conservation of energy: the thermal energy lost by the copper equals that gained by the water ✓✓
- (b)m(Cu)c(Cu)(200 − T) = m(w)c(w)(T − 20) ✓✓
- (c)0.50 × 390 × (200 − T) = 0.40 × 4200 × (T − 20) ✓; 195(200 − T) = 1680(T − 20) ✓; T = 39 °C ✓
- (d)No energy is lost to the container or surroundings ✓
- (e)Energy flows from the hotter copper to the cooler water until their temperatures are equal, when there is no net flow ✓✓
- (f)No: they share a temperature, not an internal energy ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
When two objects at different temperatures are placed in contact, the net flow of thermal energy is:
- Afrom the hotter object to the colder object
- Bfrom the colder object to the hotter object
- Cequal in both directions, so nothing changes
- Dalways from the larger object to the smaller
Two bodies are in thermal equilibrium when:
- Athey are at the same temperature, with no net energy flow
- Bthey have the same internal energy
- Cthey have the same mass
- Done has stopped losing energy to the air
A cup of tea and a swimming pool are at the same temperature. Compared with the tea, the pool has:
- Amore internal energy, because it has far more particles
- Bless internal energy
- Cthe same internal energy
- Da higher temperature
The temperature of an object determines:
- Athe direction of net energy flow when it touches another object
- Bthe total thermal energy it contains
- Cits mass
- Dits specific heat capacity
Quiz key
Net energy always flows from higher to lower temperature, and continues until the temperatures are equal.
Thermal equilibrium is defined by equal temperature and therefore no net transfer of energy between the bodies.
Temperature can be equal while internal energy differs hugely; the pool stores much more energy because it has vastly more particles.
Temperature sets the direction of net flow between objects in contact; the amount of energy stored also depends on mass and material.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.