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PARTICLE MODEL OF MATTER · CHAPTER 8 OF 10

Heating and cooling curves

Imagine recording the temperature of ice as you heat it. You might expect the temperature to keep rising, but parts of the graph would be flat. Heating and cooling curves reveal when a substance changes temperature and when it changes state.

By the end, you’ll be able to…

  • Read heating and cooling curves and identify the states present.
  • Identify melting, boiling, freezing and condensation on a graph.
  • Explain sloping and flat sections using particle energy.
  • Choose the correct equation for different sections of a curve.
  • Explain what a steeper gradient or longer plateau can tell you when conditions are controlled.

What do the axes show?

A heating or cooling curve usually shows temperature on the vertical axis and time on the horizontal axis. Read it from left to right to follow what happens.

An upward slope means the temperature is rising. A downward slope means it is falling. A horizontal section means the temperature is constant.

A horizontal section is often called a plateau. During a change of state of a pure substance at constant pressure, a plateau appears even though energy is still being transferred.

Follow the heating and cooling curves

These simplified curves show a fixed mass of pure water at normal atmospheric pressure. Choose heating or cooling, then predict what each section represents before opening its explanation.

EXPLORE THE CURVES

Click or tap a pink line section or its label. You can also use the buttons below.

From ice to water vapour

Heating curve for pure water Temperature against time at normal atmospheric pressure. A to B: ice warms. B to C: melting at zero degrees Celsius. C to D: liquid water warms. D to E: boiling at one hundred degrees Celsius. E to F: water vapour warms. Stage durations are illustrative. 0 100 Time Temperature (°C) A B C D E F

From water vapour to ice

Cooling curve for pure water Temperature against time at normal atmospheric pressure. A to B: water vapour cools. B to C: condensation at one hundred degrees Celsius. C to D: liquid water cools. D to E: freezing at zero degrees Celsius. E to F: ice cools. Stage durations are illustrative. 0 100 Time Temperature (°C) A B C D E F

Choose a section to reveal its explanation. Your selected section will turn orange.

A–B · Ice warms

The solid warms towards 0°C. Its particles gain average kinetic energy and vibrate more vigorously about fixed positions.

A–B · Water vapour cools

Energy is transferred out of the gas. Its temperature falls towards 100°C as the molecules’ average kinetic energy decreases.

B–C · Ice melts at 0°C

Solid and liquid are present. Energy transferred in increases particle potential energy as the arrangement changes. Temperature and average kinetic energy stay constant.

B–C · Water vapour condenses at 100°C

Gas and liquid are present. Energy is transferred out and particle potential energy decreases as molecules become closer together. Temperature and average kinetic energy stay constant.

C–D · Liquid water warms

All the ice has melted. Energy transferred in raises the liquid’s temperature towards 100°C and increases the particles’ average kinetic energy.

C–D · Liquid water cools

All the vapour has condensed. Energy transferred out lowers the liquid’s temperature towards 0°C and decreases the particles’ average kinetic energy.

D–E · Water boils at 100°C

Liquid and gas are present. Energy transferred in increases particle potential energy as molecules separate against attractive forces. Temperature and average kinetic energy stay constant; molecules remain intact.

D–E · Water freezes at 0°C

Liquid and solid are present. Energy is transferred out and particle potential energy decreases. Temperature and average kinetic energy stay constant; particles in the solid still vibrate.

E–F · Water vapour warms

All the liquid has become gas. If the vapour is retained and heated further at constant pressure, its temperature and average molecular kinetic energy increase.

E–F · Ice cools

All the water has frozen. Further energy transfer out lowers the ice’s temperature below 0°C. Its particles lose average kinetic energy and vibrate less vigorously.

Pure water at normal atmospheric pressure. Stage lengths are illustrative; do not compare durations.

Surroundings must be cold enough for every stage. Water in a room at 20°C approaches room temperature; it does not freeze.

☆ A flat line does not mean that energy transfer has stopped. During a change of state, internal energy changes while temperature stays constant.

Finding melting and boiling points

Read a plateau’s temperature from the vertical axis. For pure water at normal atmospheric pressure, melting and freezing occur at 0°C; boiling and condensation occur at 100°C.

Other substances have different values. For the same pure substance at the same pressure, melting and freezing share a temperature, as do boiling and condensation.

Temperature alone does not always identify the state. Water at 0°C could be ice, liquid water or both—use the stage of the process to decide.

What else can the graph tell us?

The slopes show how quickly temperature changes. The plateau lengths show how long changes of state take. Explore these comparisons below

What does the gradient tell us?

Gradient tells you how quickly temperature changes. A steeper upward slope means faster warming; a steeper downward slope means faster cooling.

Check the axis scales before comparing graphs. Here, both lines use the same axes.

Which material has the higher specific heat capacity?

Material B. For equal masses receiving the same energy per second, its slower temperature rise shows a higher specific heat capacity.

Equal masses · Same constant energy input per second · Negligible losses · No change of state

Comparing the heating rates of two materials Temperature against time on shared axes. Materials A and B start at the same temperature. The pink line for A rises more steeply than the orange line for B. B warms more slowly. Temperature (°C) Time A B

Compare the plateaus

A plateau’s horizontal length shows how long the change of state takes.

At the same constant energy input per second, a longer plateau means more energy is transferred during the change.

Which material has the higher specific latent heat of fusion?

Material B. Its longer melting plateau means more energy is needed to melt the same mass. The plateau’s height shows melting temperature, not specific latent heat.

Equal masses of pure materials · Same constant energy input per second · Negligible losses · Both melt completely at constant pressure

Comparing melting plateau durations Temperature against time on shared axes. Material A has a higher melting temperature and a shorter plateau. Material B has a lower melting temperature and a longer plateau. B takes longer to melt completely. Temperature (°C) Time A B

☆ These comparisons depend on controlled conditions. Different masses, energy-transfer rates and energy losses can also affect slopes and plateau lengths.

Which equation belongs to each section?

Sloping section

Temperature changes without a change of state.

ΔE = m × c × ΔT

Use the temperature change across that section, rather than the final temperature.

Change-of-state plateau

State changes at constant temperature.

E = m × L

Use the mass that changes state and the specific latent heat for that change.

If a question includes several stages, calculate the energy for each stage separately, then add the amounts. For example, warming ice to 0°C and then melting it involves both equations.

Why might a real graph look different?

These curves show an idealised pattern. Real measurements may produce rounded corners or a less distinct plateau because of energy transfers involving the apparatus and surroundings, uneven temperatures or measurement delays. Mixtures may change state over a range of temperatures.

During ordinary cooling, the rate of energy transfer usually decreases as the sample gets closer to room temperature, so a sloping section may curve and become less steep.

To cool water vapour all the way to ice below 0°C, the surroundings must be cold enough for every stage. Water left in a room at 20°C will approach room temperature; it will not continue cooling until it freezes.

INTERACTIVE QUICK CHECK
1

Pure ice is melting at 0°C while energy is transferred in. Why is this section of its temperature–time graph flat?

Energy is still transferred in. A flat line shows constant temperature, not that energy transfer has stopped. During melting, particle potential energy increases.
Correct. Energy transferred in changes the particle arrangement and increases potential energy. Average kinetic energy and temperature stay constant.
The particles continue moving. During melting, temperature stays constant because their average kinetic energy stays constant, while potential energy increases.
2

A pure liquid cools, then its graph becomes horizontal at 45°C as it freezes. What is its melting point at the same pressure?

Correct. For the same pure substance at the same pressure, melting and freezing occur at the same temperature. This substance melts and freezes at 45°C.
0°C is the melting point of pure water at normal atmospheric pressure. Other substances have different melting points. This substance freezes and melts at 45°C.
The freezing plateau gives the freezing point. For a pure substance at the same pressure, this is also its melting point: 45°C.
3

Equal masses of two liquids receive the same energy per second, with negligible losses and no change of state. Liquid A’s temperature rises more slowly. What does this tell you?

A lower specific heat capacity would give a faster temperature rise under these conditions. A’s slower rise indicates a higher specific heat capacity.
Neither liquid changes state. This comparison tells you about specific heat capacity, rather than specific latent heat.
Correct. For the same mass and energy input, a higher specific heat capacity gives a smaller temperature rise. A’s graph therefore has a shallower upward slope.
CHALLENGE QUESTION

Two identical samples of the same pure solid start at the same temperature below their melting point. Sample A receives energy at twice the constant rate of sample B. All this energy reaches the samples, and both remain at the same constant pressure. How will their heating curves differ before and during melting?

Compare the slopes, plateau temperatures and plateau durations. Assume both graphs use the same axis scales.

Before melting, A’s temperature rises twice as quickly, so its upward slope is twice as steep. The samples have the same mass and specific heat capacity, but A receives twice as much energy each second.

Both plateaus occur at the same temperature because the samples have the same melting point at the same pressure.

Both need the same energy to melt because their masses and specific latent heats are identical. A receives this energy twice as quickly, so its melting plateau lasts half as long.


Chapter 8 summary


Heating and cooling curves

  • Temperature–time graphs show how temperature changes
    as energy is transferred into or out of a sample.
  • Sloping sections show changing temperature and changing
    average particle kinetic energy. A steeper slope means
    a faster temperature change.
  • During a change of state of a pure substance at constant
    pressure, a plateau shows constant temperature while
    particle potential energy and internal energy change.
  • Heating plateaus can represent melting or boiling.
    Cooling plateaus can represent condensation or freezing.
    Both states are present during the change.
  • For the same pure substance at the same pressure,
    melting and freezing share a temperature, as do
    boiling and condensation.
  • Pure water melts and freezes at 0°C, and boils and
    condenses at 100°C, at normal atmospheric pressure.
  • Use ΔE = m × c × ΔT for a temperature change without
    a change of state. Use E = m × L for a change of state
    at constant temperature.
  • Check axis scales and control mass, energy-transfer rate
    and energy losses before using slopes or plateau lengths
    to compare materials.