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Cooling Curve (Temperature–Time Graph)

Key idea: Learn how to sketch and interpret a cooling curve and explain flat sections using latent heat for O Level Physics.

  • 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

A. Cooling curve

A cooling curve is a graph of temperature against time as a substance cools.

For a pure substance, flat sections mean a change of state at constant temperature (latent heat).

2. Key Ideas

  • For a pure substance, the temperature:
    • falls while it cools in a single state (solid / liquid / gas)
    • stays constant during a change of state (because of latent heat)
  • Sloping section: temperature changes → average kinetic energy of particles changes.
  • Flat section (plateau): temperature constant → energy transfer changes the particles’ arrangement and potential energy.
  • The temperature of a plateau gives the boiling point (condensation) or melting point (freezing) for a pure substance.

3. Detailed Explanations

A. Typical cooling curve (shape only)

What you need for this course

You should be able to sketch and interpret a cooling curve, including its constant-temperature changes of state.

Cooling curve for a pure substance

Schematic temperature–time graph falling from gas to solid. A plateau at 80 degrees Celsius marks condensation and a plateau at 20 degrees Celsius marks freezing. The temperatures and time intervals are illustrative and not to scale.

Schematic temperature–time graph falling from gas to solid. A plateau at 80 degrees Celsius marks condensation and a plateau at 20 degrees Celsius marks freezing. The temperatures and time intervals are illustrative and not to scale.Schematic temperature–time graph falling from gas to solid. A plateau at 80 degrees Celsius marks condensation and a plateau at 20 degrees Celsius marks freezing. The temperatures and time intervals are illustrative and not to scale.
Illustrative, not-to-scale cooling curve: a pure substance cools within one state on each slope and changes state at constant temperature on each plateau.
View figure data
Values for Cooling curve for a pure substance
Illustrative time (min)Temperature
0120
280
480
620
820
100

B. How to interpret each part of a cooling curve

When the substance is cooling:

  • Gas cooling (slope down): particles lose kinetic energy → temperature falls.
  • Condensation (flat): gas changes to liquid at constant temperature → latent heat is released.
  • Liquid cooling (slope down): temperature falls as kinetic energy decreases.
  • Freezing/solidification (flat): liquid changes to solid at constant temperature → latent heat of fusion is released.
  • Solid cooling (slope down): temperature falls further.

C. Why is the temperature constant during the flat sections?

During a change of state, energy transfer does not change the average kinetic energy of the particles, so the temperature stays constant. Instead, it changes the particles’ arrangement and potential energy as attractive forces are overcome or re-form.

This links directly to:

4. Common Mistakes

  • Thinking the temperature keeps changing during a change of state (for a pure substance, it stays constant).
  • Mixing up freezing (liquid → solid) with condensation (gas → liquid).

5. Exam Tips

  • Always label axes: temperature on the y-axis, time on the x-axis.
  • Plateaus happen at fixed temperatures for a pure substance (melting point / boiling point).
  • Use the curve to state what state(s) are present at a given time interval (e.g. “liquid + solid during freezing”).

6. Worked Examples

Modelled example 1

Reading a cooling curve

Core

Problem

A pure substance cooling from a gas has a flat temperature–time section at 78°C. Interpret this temperature and process.
Study the worked solution

  1. Use the graph shape

    Method

    Identify the flat section as a constant-temperature change of state.

    Reason

    Energy leaves while particle potential energy changes rather than average kinetic energy.

    Working

    Plateau → state change at 78°C.

  2. Use the cooling direction and initial state

    Method

    Identify condensation from gas to liquid.

    Reason

    A gas cooling through its gas–liquid transition condenses.

    Working

    78°C is the boiling/condensation temperature at the stated pressure.

Guided practice 2

States present during a plateau

About 4 min

Problem

A substance cooling from a liquid has a flat section at 0°C. Identify the process and states present.

Combine direction with the plateau

Process and states

Hints

Hint 1: follow the cooling direction
Liquid changes toward solid.
Hint 2: use coexistence
At a plateau, the old and new states are both present.
View solution step by step

  1. Identify the change

    Method

    State freezing or solidification.

    Reason

    The substance begins as liquid and is cooling at a fixed temperature.

    Working

    Liquid → solid.

  2. State the phases

    Method

    State that liquid and solid coexist.

    Reason

    Only part of the sample has solidified before the plateau ends.

    Working

    States: liquid + solid.

Common misconception 3

Pure vs impure substance

Find and correct the mistake

Learner response

A sample forms solid while its temperature continues to fall slowly. A student says every pure substance has a sloping freezing section. Diagnose the claim.

Use the pure-substance benchmark

Likely reason

View solution step by step

  1. Recall the pure-substance pattern

    Method

    Expect a fixed-temperature plateau during freezing.

    Reason

    A pure substance changes state at one freezing point at fixed pressure.

    Working

    Pure sample: horizontal freezing section.

  2. Interpret the observed range

    Method

    Suggest that the sample is a mixture or contains impurities.

    Reason

    Such a sample can solidify over a range of temperatures.

    Working

    Sloping freezing region → possible impurity/mixture.

Examiner practice 4

Identify the stages

3 marks

Examination question

A cooling graph slopes from 120°C to 78°C, is flat at 78°C, then slopes to 10°C. Identify the state or process in each section. [3 marks]

Label each graph section in sequence

View solution step by step

  1. Label the first slope

    1 mark

    Method

    State that gas cools.

    Reason

    The temperature falls in one state before the upper transition.

    Working

    120°C to 78°C: gas cooling.

  2. Label the plateau

    1 mark

    Method

    State condensation from gas to liquid.

    Reason

    The flat section is a constant-temperature state change during cooling.

    Working

    At 78°C: condensation.

  3. Label the final slope

    1 mark

    Method

    State that liquid cools.

    Reason

    The gas has fully condensed by the end of the plateau.

    Working

    78°C to 10°C: liquid cooling.

Challenge 5

Sketching from data

Minimal support

Data-to-graph transfer

A pure substance has boiling point 60°C and freezing point -20°C. It starts as hot gas and cools into a solid. Describe the required cooling-curve features in order.

Translate transition temperatures into graph segments

Hints

Hint 1: place the two plateaux
Use horizontal sections at 60°C and -20°C.
Hint 2: connect single-state regions
Add downward slopes for gas, liquid and solid cooling.
View solution step by step

  1. Build the gas-to-liquid region

    Method

    Draw gas cooling to 60°C, then a condensation plateau.

    Reason

    The boiling point is also the condensation temperature for the pure substance.

    Working

    Downward gas slope → flat at 60°C.

  2. Build the liquid-to-solid region

    Method

    Draw liquid cooling to -20°C, a freezing plateau, then solid cooling.

    Reason

    The freezing point sets the second constant-temperature transition.

    Working

    Liquid slope → flat at -20°C → solid slope.

7. Mind Stretchers

Mind stretcher 1: “Two states at once”Extension

During the flat section for freezing, what states are present, and where does the energy go?

Show Answer

Both liquid and solid are present. Energy is transferred out as latent heat of fusion, which decreases the potential energy between particles as they form a solid lattice. The temperature stays constant.

Mind stretcher 2: Why a plateau might not be perfectly flatExtension

In a real cooling curve experiment, the “flat” section can slope slightly. Suggest two reasons.

Show Answer

Possible reasons include:

  • the substance is not perfectly pure, so the change of state happens over a small temperature range,
  • the sample has temperature gradients or the thermometer has not reached thermal equilibrium with the part being measured.

8. Practice and next step

Sketch a cooling curve from a blank set of axes, label every state and plateau, and explain where kinetic and potential energy change. Then complete the structured Thermal Physics questions and return to the Thermal Physics hub for the full checklist.

Continue with the next resource in this course.

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