Physics 001.001.009 Internal Energy in Phase Changes

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

• Explain why temperature remains constant during a change of state.
• Relate temperature to the average kinetic energy of particles.
• Describe internal energy as the total kinetic and potential energy of particles in a system.
• Use the kinetic particle model to explain melting, freezing, boiling and condensation.
• Interpret a heating or cooling curve in terms of particle energy changes.

Success Criteria

By the end of the lesson, students have successfully:

• Identified that temperature remains constant during state change because average particle kinetic energy remains constant.
• Explained that energy added or removed during state change changes the potential energy of particles.
• Used the terms internal energy, kinetic energy, potential energy and particle arrangement accurately.
• Explained the plateau regions of a heating or cooling curve.
• Corrected the misconception that energy is not being transferred during a phase change.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Phase Changes and Energy Conservation
• Explain, in terms of the internal energy of a system and the kinetic particle model of matter, why the temperature of a system remains the same during the process of state change.

Phenomenon

When ice is heated, its temperature rises until it reaches . While the ice is melting, energy continues to be transferred into the system, but the temperature remains at until all the ice has melted.

Similarly, when water boils, energy continues to be supplied, but the temperature remains approximately at standard atmospheric pressure until the liquid has changed into gas.

This creates a question:

If energy is still being added, why does the temperature stop increasing during melting and boiling?

Key Idea

During a change of state, the temperature of a system remains constant because the energy added or removed changes the arrangement and separation of particles, not their average kinetic energy.

Temperature is related to the average kinetic energy of particles. If the average kinetic energy does not change, the temperature does not change.

Internal energy is the total energy stored in the particles of a system:

where:

is internal energy

is the total kinetic energy of the particles

is the total potential energy associated with particle interactions and separation

During a state change, energy is used to change , not .

Concept

The concept and thought that best describes the cause of the phenomenon is below.

Temperature measures the average kinetic energy of particles in a system.

When a substance is heated within one state, such as solid ice warming from to , the particles vibrate faster. Their average kinetic energy increases, so the temperature increases.

During melting, the added energy is used to weaken or overcome attractive forces between particles. The particles become less fixed in position and can move past each other. This increases the potential energy of the particles because their arrangement and separation changes.

The average kinetic energy remains the same during the state change, so the temperature remains constant.

For example, during melting:

Solid water at plus energy becomes liquid water at .

The particles have changed arrangement, but their average kinetic energy has not increased.

Convention

The key conventions associated with the concept and in the branch of established knowledge is below.

• Temperature is measured in degrees Celsius, , or kelvin, .
• Temperature is related to average particle kinetic energy.
• Internal energy includes both kinetic and potential energy of particles.
• A change in temperature indicates a change in average kinetic energy.
• A change in state indicates a change in particle arrangement and potential energy.
• Energy added during melting or boiling is not lost; it is stored as increased potential energy within the system.
• Energy removed during freezing or condensation decreases particle potential energy as particles form stronger interactions or become more ordered.
• On a heating curve, sloped sections show temperature change.
• On a heating curve, flat sections show state change.
• The flat section of a heating curve is called a temperature plateau.

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.

• Students may think temperature must always increase when energy is added.
• Students may think no energy is being transferred during the flat section of a heating curve.
• Students may think particles stop moving during a state change.
• Students may think boiling water becomes hotter than while it is boiling at standard atmospheric pressure.
• Students may think internal energy and temperature mean the same thing.
• Students may think potential energy only applies to objects raised above the ground, rather than to particle separation and interactions.
• Students may think all particles change state at exactly the same instant.
• Students may think the bonds inside molecules are being broken during boiling, rather than the intermolecular attractions between particles being overcome.

Further Reading

• Heating curves and cooling curves
• Specific latent heat
• Internal energy and the first law of thermodynamics
• Kinetic particle model of matter
• Thermal equilibrium

Explicit Instruction

Begin with the particle model.

In a solid, particles are closely packed and vibrate about fixed positions. When a solid is heated, the particles vibrate more rapidly. This means their average kinetic energy increases. Since temperature depends on average kinetic energy, the temperature rises.

At the melting point, the particles already have enough kinetic energy for the solid to begin changing state. Extra energy supplied at this point does not make the particles move faster on average. Instead, the energy weakens the attractive forces holding particles in fixed positions.

This increases the potential energy of the particles. The particles become less ordered and more able to move past one another. The substance changes from solid to liquid.

Therefore, during melting:

• Energy is added.
• Internal energy increases.
• Particle potential energy increases.
• Average particle kinetic energy remains constant.
• Temperature remains constant.

The same reasoning applies to boiling.

During boiling, energy is added to separate particles much further apart so they can move freely as a gas. The energy increases particle potential energy by overcoming attractive forces between liquid particles. The average kinetic energy remains constant during the boiling process, so the temperature remains constant.

During cooling and freezing, the reverse happens.

As a liquid freezes, energy is removed. The particles form a more ordered arrangement and stronger interactions. Their potential energy decreases. However, during the freezing process, the average kinetic energy remains constant, so the temperature remains constant until the state change is complete.

Worked Examples

Worked Example 1

A sample of ice is heated from until it becomes liquid water at . Explain what happens to the energy of the particles.

Step 1: Identify the stages

Stage 1: Ice warms from to

Stage 2: Ice melts at

Step 2: Explain the warming stage

As the ice warms, energy is added to the system. The particles vibrate more rapidly. Their average kinetic energy increases.

Because temperature depends on average kinetic energy, the temperature increases.

Step 3: Explain the melting stage

At , the ice begins to melt. Energy is still being added, but the temperature remains constant.

The added energy is used to change the arrangement of the particles. The particles are no longer held in fixed positions and can move past each other.

The particle potential energy increases, but the average kinetic energy remains constant.

Answer

During warming, the added energy increases the average kinetic energy of the particles, so the temperature increases. During melting, the added energy increases the potential energy of the particles by changing their arrangement, so the temperature remains constant.

Worked Example 2

A student says:

“If water is boiling and the temperature stays at , then no energy is being absorbed.”

Explain why this statement is incorrect.

Step 1: Identify the misconception

The student assumes that energy transfer must always cause a temperature increase.

Step 2: Use the kinetic particle model

During boiling, water particles are changing from liquid to gas. The particles must become much more separated.

Step 3: Link to internal energy

The energy absorbed increases the potential energy of the particles. It is used to overcome attractive forces between particles.

The average kinetic energy of the particles does not increase during the state change.

Answer

The statement is incorrect because energy is still being absorbed during boiling. However, the energy does not increase the average kinetic energy of the particles. Instead, it increases the potential energy of the particles by separating them into the gas state. Since average kinetic energy remains constant, the temperature remains constant.

Worked Example 3

The graph below represents a heating curve for a substance.

Region A: solid warming

Region B: melting

Region C: liquid warming

Region D: boiling

Region E: gas warming

Explain what happens to kinetic energy, potential energy and temperature in regions B and D.

Region B: Melting

During melting, energy is added to the system. The particles change from a fixed solid arrangement to a less ordered liquid arrangement. Their potential energy increases.

The average kinetic energy remains constant, so the temperature remains constant.

Region D: Boiling

During boiling, energy is added to the system. The particles move from the liquid state to the gas state and become much more separated. Their potential energy increases.

The average kinetic energy remains constant, so the temperature remains constant.

Answer

In both region B and region D, the added energy increases the potential energy of the particles rather than their average kinetic energy. Therefore, the temperature remains constant during both state changes.

Check for Understanding

Check 1

Question

Why does the temperature of a substance remain constant during melting?

Expected Answer

During melting, energy is used to change the arrangement of particles from a solid to a liquid. This increases the potential energy of the particles. The average kinetic energy remains constant, so the temperature remains constant.

Check 2

Question

What is the difference between temperature and internal energy?

Expected Answer

Temperature is related to the average kinetic energy of particles. Internal energy is the total kinetic and potential energy of all particles in the system.

Check 3

Question

A liquid is condensing into a gas at constant temperature. Identify the error in this statement.

Expected Answer

Condensing means changing from gas to liquid, not liquid to gas. During condensation, energy is removed from the system and the potential energy of the particles decreases as they become closer together. The temperature remains constant because the average kinetic energy remains constant during the state change.

Investigation (Alternative to Explicit)

Hypothesis

If energy is added to ice and water at a constant rate, then the temperature will increase during warming stages but remain constant during melting because energy is used to change particle arrangement rather than average particle kinetic energy.

Data Collection

Students collect temperature data while heating ice in a beaker.

Equipment:

• Ice
• Beaker
• Hot plate
• Thermometer or temperature probe
• Stopwatch
• Stirring rod
• Safety glasses
• Heatproof mat

Method:

1. Place crushed ice into a beaker.
2. Insert the thermometer or temperature probe into the ice.
3. Record the initial temperature.
4. Begin heating the beaker gently.
5. Record the temperature every seconds.
6. Continue until the ice has melted and the water temperature begins to rise.
7. Plot temperature against time.

Safety:

• Wear safety glasses.
• Do not touch the hot plate or beaker while heating.
• Use tongs or heatproof gloves when handling hot equipment.
• Keep electrical equipment away from water spills.

Analysis

Students identify:

• The section where solid ice warms.
• The plateau where melting occurs.
• The section where liquid water warms.

Students answer:

1. When did the temperature increase?
2. When did the temperature remain constant?
3. Was energy still being added during the plateau?
4. What happened to the internal energy during the plateau?
5. What happened to the average kinetic energy during the plateau?
6. What happened to the particle potential energy during the plateau?

Expected analysis:

During the plateau, energy was still being added to the system. The temperature remained constant because the average kinetic energy of the particles remained constant. The internal energy increased because the potential energy of the particles increased as the solid changed into a liquid.

Evaluation

Students evaluate:

• Was the heating rate constant?
• Was thermal energy lost to the surroundings?
• Was the ice stirred evenly?
• Was the thermometer placed correctly?
• Did the beaker receive energy evenly from the hot plate?
• How could insulation improve the experiment?
• How could a digital temperature probe improve the precision of the data?

Problems

The following problems are designed to practise explanation using the kinetic particle model and internal energy.

1. Explain why the temperature of ice remains at while it melts.

2. Explain why the temperature of boiling water remains approximately at standard atmospheric pressure.

3. A student heats a substance and observes a flat section on the temperature-time graph. What does the flat section indicate?

4. During a phase change, does the internal energy of a system change? Explain your answer.

5. Compare what happens to particle kinetic energy and particle potential energy when:

   • a solid warms
   • a solid melts
   • a liquid warms
   • a liquid boils

6. Explain why steam at can transfer more energy than liquid water at when condensing.

7. A student says, “The particles stop speeding up during melting, so the energy being added disappears.” Rewrite this explanation correctly.

8. Draw a labelled heating curve for water showing:

   • ice warming
   • melting
   • liquid water warming
   • boiling
   • steam warming

9. On your heating curve, label where:

   • average kinetic energy increases
   • particle potential energy increases
   • temperature remains constant
   • state change occurs

10. Explain why freezing occurs at constant temperature even though energy is being removed from the system.

Followup

Self-check

Students should be able to answer the following without notes:

• What does temperature measure at the particle level?
• What two forms of energy make up internal energy?
• Why does temperature stay constant during melting?
• Why does temperature stay constant during boiling?
• What changes during a state change if average kinetic energy does not change?
• How is a heating curve used to identify a change of state?

Next Topic

Specific latent heat.

Students will next describe the concept of specific latent heat and use:

to calculate the energy transferred during a change of state.