D3.7 Explain phase-change energy transfer with kinetic molecular theory

Ontario Grade 11 Physics

Energy and Society

Using kinetic molecular theory to explain melting, freezing, boiling, and condensation

A substance can absorb or release energy while its temperature stays the same. This happens during a phase change, such as melting or boiling. Kinetic molecular theory helps explain why. It describes matter as particles that are always moving and that attract one another. In this lesson, energy transferred into the chosen substance is positive. Energy transferred out is negative. Heat is energy transferred because of a temperature difference; it is not a material stored inside an object.

What you will learn

Describe particles in terms of motion and attractions between them.
Explain why energy transfer can change a substance's phase without changing its temperature.
Use the latent heat relationship to calculate energy transferred during a phase change.
Explain the direction of energy transfer during melting, freezing, boiling, and condensation.

1. Particle motion, temperature, and phase

Start with two familiar ideas. Matter is made of particles, and temperature tells us about the particles' average kinetic energy. Kinetic energy is energy of motion. When a substance's temperature rises, its particles have greater average kinetic energy. When its temperature falls, their average kinetic energy decreases.

Particles also attract one another. In a solid, particles stay in fixed positions but vibrate. In a liquid, particles remain close together but can move past one another. In a gas, particles are much farther apart and move freely. A phase is a form of matter, such as solid, liquid, or gas.

A phase change occurs when a substance changes from one phase to another. Melting changes a solid to a liquid. Freezing changes a liquid to a solid. Boiling changes a liquid to a gas. Condensation changes a gas to a liquid. For a pure substance at a given pressure, each phase change occurs at a particular temperature.

The system in this lesson is the substance undergoing the phase change. The surroundings are everything outside that substance. Use a simple sign convention: energy transferred into the system is positive, and energy transferred out is negative. Energy is a scalar, so it has magnitude but no direction in space. Its transfer has a direction: into or out of the system.

Q>0 into the system, Q<0 out of the system

Temperature relates to average particle kinetic energy.
Attractions between particles help hold solids and liquids together.
Energy-transfer direction is described as into or out of the system.

2. What energy does during a phase change

When a substance is heated but does not change phase, its temperature usually rises. The added energy increases the particles' average kinetic energy. During a phase change, the energy transfer has a different main effect. It changes how strongly the particles are held together or how far apart they are, rather than increasing or decreasing their average kinetic energy.

During melting, energy enters the substance. The particles gain energy that helps them move out of their fixed solid positions, despite the attractions between them. During boiling, energy enters again. Particles separate enough to form a gas. In both cases, the temperature stays constant while the phase change is taking place, so average particle kinetic energy stays constant during that interval.

The reverse changes release energy. During freezing, particles settle into fixed positions and attractions hold them in the solid arrangement. During condensation, gas particles come closer together to form a liquid. Energy leaves the substance and transfers to the surroundings. The temperature remains constant while the phase change proceeds.

A useful mental picture is an energy ledger. For melting and boiling, energy goes into changing particle arrangement against attractions. For freezing and condensation, energy leaves as particles move into a more closely held arrangement. This description does not mean particles stop moving. They continue to move or vibrate in every phase.

For a phase change, the energy transferred depends on the mass and the substance's latent heat. Latent heat is the energy needed per kilogram for a particular phase change at its phase-change temperature. It is given in joules per kilogram. Use the latent heat of fusion for melting or freezing, and the latent heat of vaporization for boiling or condensation. The relationship gives the magnitude of energy; apply the sign convention separately.

|Q|=mL

During a phase change, energy transfer changes particle arrangement and attractions; temperature stays constant.
Melting and boiling absorb energy. Freezing and condensation release energy.
Latent heat is measured in joules per kilogram.

3. Applying the phase-change model

In the relationship,

Q

is the energy transferred, measured in joules (J). The symbol

m

is the mass in kilograms (kg). The symbol

L

is the appropriate latent heat, in joules per kilogram (J/kg). Since a phase change absorbs or releases energy, use the phase and the stated direction of transfer to decide whether

Q

is positive or negative.

Before calculating, identify the system, the phase change, the mass, and the latent heat. Then decide whether energy enters or leaves. Substitute values with units. Report a sensible number of significant figures, include the sign and unit, and check that the result makes sense. For example, melting should give positive

Q

under this convention, while freezing should give negative

Q

.

The model applies to the energy transferred during the phase change itself. If a question also describes warming or cooling before or after the phase change, treat that as a separate temperature change. Do not use latent heat to represent a temperature rise or fall. The key distinction is whether energy changes average particle motion or changes the arrangement of particles during a phase change.

Q=\pm mL

Use the latent heat for the specific change of phase.
The equation gives energy magnitude; the sign shows transfer direction.
Keep phase-change energy separate from energy that changes temperature.

Worked example

Melting ice

A

0.250\text{ kg}

sample of ice melts at its melting point. Use a latent heat of fusion of

3.34\times10^5\text{ J/kg}

. Find the energy transferred to the ice.

Define the system and direction
The system is the ice. Energy enters it as it melts, so the answer must be positive. The unknown is the energy transferred, $Q$ .
Choose the model
Melting is a phase change, so use the latent heat relationship with the latent heat of fusion.
$Q=mL_f$
Substitute with units
Use the given mass and latent heat. The kilogram units cancel, leaving joules.
$Q=(0.250\text{ kg})(3.34\times10^5\text{ J/kg})$
Evaluate and check
The product is positive because energy enters the ice. The energy is a reasonable amount for melting a fraction of a kilogram.
$Q=+8.35\times10^4\text{ J}$

Answer: The ice absorbs

8.35\times10^4\text{ J}

of energy.

Check: The units reduce to joules, the sign is positive for melting, and the result is smaller than the latent heat for one kilogram because the sample is less than one kilogram.

Worked example

Freezing water

A

0.0800\text{ kg}

sample of water freezes at its freezing point. Use a latent heat of fusion of

3.34\times10^5\text{ J/kg}

. Find the energy transferred from the water.

Define the system and direction
The system is the water as it freezes. Energy leaves the system, so $Q$ is negative. The question asks for energy transferred from the water.
Choose the model
Freezing uses the same latent heat of fusion as melting. The magnitude comes from mass times latent heat; the sign is negative because energy leaves.
$Q=-mL_f$
Substitute with units
Substitute the mass and latent heat. Kilograms cancel, leaving joules.
$Q=-(0.0800\text{ kg})(3.34\times10^5\text{ J/kg})$
Evaluate and check
The calculation gives energy transferred out of the system. Three significant figures match the given values.
$Q=-2.67\times10^4\text{ J}$

Answer: The water releases

2.67\times10^4\text{ J}

of energy.

Check: The units are joules, and the negative sign matches energy leaving during freezing. The magnitude is less than the energy for one kilogram because the sample is only

0.0800\text{ kg}

.

Worked example

Boiling a small sample

A

0.0150\text{ kg}

sample of liquid water boils at its boiling point. Use a latent heat of vaporization of

2.26\times10^6\text{ J/kg}

. Find the energy transferred into the water.

Define the system and direction
The system is the liquid water undergoing boiling. Energy enters as liquid changes to gas, so $Q$ is positive.
Choose the model
Boiling is a liquid-to-gas phase change. Use the latent heat of vaporization.
$Q=mL_v$
Substitute with units
Multiply the mass by the latent heat. The kilogram units cancel.
$Q=(0.0150\text{ kg})(2.26\times10^6\text{ J/kg})$
Evaluate and check
The calculated energy is positive and has units of joules. Its magnitude is less than the latent heat for one kilogram, as expected for a smaller mass.
$Q=+3.39\times10^4\text{ J}$

Answer: The water absorbs

3.39\times10^4\text{ J}

of energy.

Check: The units reduce to joules, the direction is into the water, and the magnitude is consistent with a sample much smaller than one kilogram.

Common mistakes and how to avoid them

Assuming that any energy entering a substance must raise its temperature.

Correction: During a phase change, energy changes particle arrangement and the effects of attractions. The temperature stays constant while the change proceeds.

Giving freezing or condensation a positive energy-transfer sign for the system.

Correction: With energy into the system defined as positive, freezing and condensation have negative

Q

because energy leaves the substance.

Using latent heat to describe a temperature increase.

Correction: Latent heat applies to a phase change. A temperature change without a phase change is a different situation.

Saying particles stop moving during melting or boiling.

Correction: Particles continue moving. During the phase change, their average kinetic energy stays constant while their arrangement changes.

Lesson summary

Kinetic molecular theory describes matter as moving particles that attract one another.
Temperature relates to average particle kinetic energy.
During a phase change, energy transfer changes particle arrangement and does not change the temperature while the change is underway.
Melting and boiling absorb energy; freezing and condensation release energy.
Use $|Q|=mL$ for phase-change energy, then assign a sign based on whether energy enters or leaves the system.

Check your understanding

Question 1

A solid melts while its temperature stays constant. What is the main effect of energy entering it?

The particles gain average kinetic energy, so the temperature rises.
The particles move out of their fixed positions as attractions are overcome.
The particles stop moving until all the solid has melted.
The particles become more strongly held in fixed positions.

Show answer and explanation

The particles move out of their fixed positions as attractions are overcome.

During melting, energy changes the particle arrangement. The temperature stays constant, so average particle kinetic energy does not rise during the phase change.

Question 2

With energy into the system defined as positive, what sign does

Q

have when a liquid freezes?

Positive, because the liquid is changing phase.
Zero, because the temperature stays constant.
Negative, because energy leaves the system.
The sign cannot be decided without knowing the mass.

Show answer and explanation

Negative, because energy leaves the system.

Freezing releases energy to the surroundings. The transfer is out of the system, so

Q

is negative even though the temperature remains constant.

Question 3

A

0.020\text{ kg}

substance undergoes a phase change with

L=1000\text{ J/kg}

. What is the magnitude of its energy transfer?

$20\text{ J}$
$50\text{ J}$
$980\text{ J}$
$2.0\times10^4\text{ J}$

Show answer and explanation

20\text{ J}

Use

|Q|=mL

. The calculation is

(0.020\text{ kg})(1000\text{ J/kg})=20\text{ J}

. The kilogram units cancel.

Key terms

Kinetic energy: Energy associated with motion.
Kinetic molecular theory: A model that explains matter using moving particles and attractions between them.
Phase: A form of matter, such as solid, liquid, or gas.
Phase change: A change from one phase of a substance to another.
Latent heat: Energy needed per kilogram for a particular phase change at its phase-change temperature.
System: The substance being studied.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation D3.7. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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D3.7 · Explain phase-change energy transfer with kinetic molecular theory

Ontario Grade 11 Physics

Using kinetic molecular theory to explain melting, freezing, boiling, and condensation

What you will learn

1. Particle motion, temperature, and phase

2. What energy does during a phase change

3. Applying the phase-change model

Melting ice

Freezing water

Boiling a small sample

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SPH3U

About this lesson and its review