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Thermal Equilibrium

Key idea: Learn what thermal equilibrium means and why energy transfers from a hotter object to a cooler one until their temperatures become equal.

  • SEC G3 Physics 2027
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Learning objectives

  • Compare physical properties of solids, liquids and gases
  • Explain state properties using particle arrangement, motion, forces and separation
  • Infer random molecular motion from a Brownian-motion experiment
  • Relate temperature rise to increased average kinetic energy of particles
  • Explain gas pressure using particle collisions with container walls
  • Explain heating from higher to lower temperature until thermal equilibrium
  • Describe conduction in solids through particle vibration and mobile electrons
  • Describe convection in fluids through density changes and bulk motion
  • Explain that energy transfer by electromagnetic radiation needs no material medium
  • Explain how surface colour, texture, temperature and area affect radiation transfer rate
  • Apply conduction, convection and radiation in everyday systems
  • describe internal energy as an energy store that is made up of the total kinetic energy associated with the random motion of the particles and the total potential energy between the particles in the system
  • Define heat capacity and specific heat capacity
  • Apply energy transferred = mass × specific heat capacity × temperature change
  • describe melting/solidification and boiling/condensation as processes of energy transfer without a change in temperature
  • Explain the difference between boiling and evaporation
  • Define latent heat and specific latent heat
  • Apply energy transferred for a change of state = mass × specific latent heat
  • Explain latent heat using particle behaviour
  • Sketch and interpret a cooling curve

1. Definition

Two objects (or regions) are in thermal equilibrium when they are at the same temperature, so there is no net energy transfer between them by heating.

What you need for this course

You should be able to explain that energy is transferred by heating from a region at higher temperature to one at lower temperature until thermal equilibrium is reached.

2. Key Ideas

  • Heating transfers energy from hot → cold because of a temperature difference.
  • Thermal equilibrium means:
    • same temperature, and
    • no net energy transfer between them by heating.
  • Thermal contact means energy can be exchanged (it does not mean temperatures are already equal).
  • A thermometer gives the correct reading only after it reaches thermal equilibrium with the object.

3. Detailed Explanations

A. Thermal contact vs thermal equilibrium

  • Thermal contact: energy can be transferred between the objects.
  • Thermal equilibrium: there is no net energy transfer by heating between them because their temperatures are equal.

B. What happens when a hot object touches a cold one?

  1. Energy is transferred by heating from the hotter object to the colder object.
  2. The hotter object cools down; the colder object warms up.
  3. In an isolated two-object system, both eventually reach the same temperature (thermal equilibrium). In an open system, the surroundings may also exchange energy with them.

C. Using thermal equilibrium in temperature measurement

When you place a thermometer in a liquid:

  • energy is transferred by heating between them,
  • the thermometer reading changes,
  • the reading becomes steady when thermometer and liquid are in thermal equilibrium.

4. Common Mistakes

  • Saying objects in thermal equilibrium have the same internal energy (not necessarily; internal energy depends on mass and material too).
  • Saying heat is “stored” in an object (heat is energy in transfer; the stored energy is internal energy).
  • Saying that all microscopic energy exchange stops. Energy can still be exchanged in both directions, but the net transfer is zero at equilibrium.

5. Exam Tips

  • If asked for the direction of energy transfer, answer “from higher temperature to lower temperature”.
  • If the question says “when equilibrium is reached”, state “same temperature” and “no net energy transfer by heating”.
  • Use mark-scheme phrasing: “Energy is transferred (by heating) from a region of higher temperature to a region of lower temperature until thermal equilibrium is reached.”

6. Worked Examples

Modelled example 1

Mixing

Core

Problem

Hot water is mixed with cooler water. Describe the energy transfer and the final equilibrium condition.
Study the worked solution

  1. Use the initial temperature difference

    Method

    Transfer energy by heating from the hotter water to the cooler water.

    Reason

    A temperature difference causes net thermal-energy transfer from higher to lower temperature.

    Working

    Hotter region → cooler region.

  2. Identify equilibrium

    Method

    Reach one common temperature with no net energy transfer by heating.

    Reason

    The driving temperature difference has disappeared.

    Working

    Same temperature → thermal equilibrium.

Guided practice 2

Thermometer reading

About 4 min

Problem

A room-temperature thermometer is placed in hot water. Explain why its reading rises and when the reading becomes valid and steady.

Identify the steady-reading condition

Steady reading condition

Hints

Hint 1: compare initial temperatures
The water is initially hotter than the thermometer.
Hint 2: use equilibrium
A valid reading requires the thermometer to reach the liquid’s temperature.
View solution step by step

  1. Explain the rising reading

    Method

    Transfer energy from hot water to the cooler thermometer.

    Reason

    The thermometer warms because of the initial temperature difference.

    Working

    Thermometer temperature rises.

  2. Explain the steady reading

    Method

    Wait until both have the same temperature and no net energy transfer by heating.

    Reason

    That thermal-equilibrium temperature is what the thermometer reports.

    Working

    Steady reading → thermal equilibrium.

Common misconception 3

Same temperature, still in contact

Find and correct the mistake

Learner response

Two touching metal blocks are both at 30°C. A student says thermal equilibrium means all microscopic energy exchange stops. Diagnose the statement.

Use the word net precisely

Net energy transfer

View solution step by step

  1. Apply equal temperature

    Method

    State that the blocks are in thermal equilibrium.

    Reason

    They are in contact at the same temperature.

    Working

    T_A = T_B = 30°C

  2. Correct the absolute claim

    Method

    State that net energy transfer is zero, not that microscopic exchange must cease.

    Reason

    Energy exchanged in opposite directions balances on average.

    Working

    Net transfer = 0.

Examiner practice 4

Spoon in hot tea

3 marks

Examination question

A room-temperature metal spoon is placed in hot tea. Explain why it becomes hot and state the eventual equilibrium condition. [3 marks]

State direction, mechanism and endpoint

View solution step by step

  1. Explain the warming

    2 marks

    Method

    Transfer energy from hotter tea to cooler spoon, mainly by conduction.

    Reason

    The initial temperature difference drives net transfer into the metal.

    Working

    Tea → spoon; spoon temperature rises.

  2. State the endpoint

    1 mark

    Method

    Reach the same temperature with no net energy transfer by heating.

    Reason

    This is thermal equilibrium.

    Working

    Tₛₚₒₒₙ = Tₜₑₐ

Challenge 5

What the final temperature must be

Minimal support

Insulated-system transfer

Two objects at different temperatures touch inside a well-insulated box until equilibrium. State where the final temperature lies relative to the two initial temperatures and explain.

Use energy conservation to bound the result

Hints

Hint 1: follow transfer direction
The hot object loses energy while the cold object gains energy.
Hint 2: use insulation
No energy is transferred outside the two-object system.
View solution step by step

  1. Track both temperature changes

    Method

    Cool the hotter object and warm the cooler object.

    Reason

    Energy transfers from higher to lower temperature.

    Working

    Tₕₒₜ decreases; T_cold increases.

  2. Bound the equilibrium temperature

    Method

    Place the final common temperature between the initial values.

    Reason

    In the insulated box, energy lost by the hot object equals energy gained by the cold object.

    Working

    T_(cold,initial) < T_final < T_(hot,initial)

7. Mind Stretchers

Mind stretcher 1: Thermal contact but not equilibriumExtension

A cold metal spoon is placed in hot tea. Is the spoon and tea in thermal contact? Are they in thermal equilibrium immediately? Explain.

Show Answer

They are in thermal contact (energy can be exchanged).

They are not in thermal equilibrium immediately because their temperatures are different at first, so there is net energy transfer from the hot tea to the cold spoon until they reach the same temperature.

Mind stretcher 2: Why stirring helpsExtension

When a thermometer is placed in water, stirring the water often makes the thermometer reach a steady reading faster. Suggest why.

Show Answer

Stirring helps mix the warmer and cooler parts of the water, making the temperature more uniform. This increases the rate of energy transfer to/from the thermometer, so it reaches thermal equilibrium faster.

8. Practice and next step

Explain why a room-temperature thermometer should not be read immediately after it is placed in hot water. Check your answer against this lesson, then study the three transfer mechanisms in order: conduction, convection, and radiation.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027