Physics 001.001.008 Specific Heat Capacity With Phase Change

Alignment

Learning Intentions

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

• Identify when a heating or cooling problem includes phase change.
• Separate a thermal energy problem into temperature-change and phase-change stages.
• Use for temperature-change stages.
• Use for phase-change stages.
• Calculate total energy transferred across multiple stages.

Success Criteria

By the end of the lesson, students have successfully:

• Interpreted a heating curve and identified sloped and flat sections.
• Explained why temperature remains constant during melting and boiling.
• Used , and appropriately.
• Used during melting or vaporisation.
• Added energy values from each stage to calculate total energy transfer.
• Determined the final state and temperature of a substance when a limited amount of energy is supplied.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Explain why the temperature of a system remains the same during state change.
• Describe the concept of specific latent heat.
• Solve problems involving specific latent heat using .
• Solve problems involving specific heat capacity, specific latent heat and thermal equilibrium.

Phenomenon

A metal cup can be placed over a flame and used to boil water. The metal does not immediately melt because much of the energy transferred by the flame goes into heating the water and then changing liquid water into steam.

Guiding question:

Where does the energy go when the temperature stops increasing during melting or boiling?

Key Idea

When a substance changes temperature but does not change phase, use:

When a substance changes phase but its temperature remains constant, use:

During a phase change, added energy increases the internal potential energy of the particles rather than increasing their average kinetic energy. Since temperature is related to average kinetic energy, the temperature remains constant during melting or boiling.

For water:

• ice warms below using
• ice melts at using
• liquid water warms between and using
• water boils at using
• steam warms above using

Unless otherwise given, use:

Concept

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

Thermal energy can increase particle kinetic energy or particle potential energy.

When temperature changes, average particle kinetic energy changes. This is modelled using .

When phase changes, particle arrangement changes. The energy changes the internal potential energy of the system, so temperature remains constant. This is modelled using .

Convention

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

• Use only for sloped sections of a heating or cooling curve.
• Use only for flat sections of a heating or cooling curve.
• Melting and freezing occur at for water at normal pressure.
• Boiling and condensing occur at for water at normal pressure.
• Total energy is calculated by adding each stage:
• Do not use during a phase change because the temperature is constant.
• Use for melting or freezing.
• Use for boiling or condensing.

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 often use across an entire problem even when phase change occurs.
• Students often include a temperature change during melting or boiling.
• Students may think temperature staying constant means no energy is being transferred.
• Students may forget to include the energy required to melt ice before heating the liquid water.
• Students may use the specific heat capacity of water when the substance is actually ice or steam.

Further Reading

• Heating curves for water
• Cooling curves and energy removal
• Latent heat of fusion and vaporisation
• Internal energy and the kinetic particle model
• Thermal equilibrium and calorimetry

Explicit Instruction

Worked Examples

Worked Example 1

Calculate the energy required to change of ice at into water at .

This problem has three stages:

1. Warm ice from to .
2. Melt ice at .
3. Warm water from to .

Stage 1: Warm the ice.

Stage 2: Melt the ice.

Stage 3: Warm the water.

Total energy:

Answer: of energy is required.

Worked Example 2

Calculate the energy required to change of water at into steam at .

This problem has three stages:

1. Warm water from to .
2. Boil water at .
3. Warm steam from to .

Stage 1: Warm the water.

Stage 2: Boil the water.

Stage 3: Warm the steam.

Total energy:

Answer: of energy is required.

Worked Example 3

of energy is transferred to of ice at . Determine the final state and final temperature.

Step 1: Convert energy.

Step 2: Energy required to warm ice to .

Energy remaining:

Step 3: Energy required to melt all the ice.

Since is greater than , all the ice melts.

Energy remaining after melting:

Step 4: Use remaining energy to warm liquid water.

Final temperature:

Answer: The final state is liquid water at .

Check for Understanding

Check 1

Calculate the energy needed to change of ice at into water at .

Expected answer:

Warm the ice:

Melt the ice:

Total:

Check 2

Calculate the energy needed to convert of water at into steam at .

Expected answer:

No temperature change occurs, so use .

Check 3

of energy is supplied to of ice at . Determine the final state and temperature.

Expected answer:

Energy to warm ice to :

Energy remaining:

Energy to melt all ice:

Since is greater than , all ice melts.

Energy remaining:

Warm the liquid water:

Final answer: liquid water at .

Investigation (Alternative to Explicit)

Hypothesis

If energy is supplied steadily to ice, then the temperature will increase during single-phase heating but remain constant during melting.

Data Collection

Students heat crushed ice in a beaker using a hot plate or immersion heater.

Record:

• time,
• temperature,
• observations of state
• heating power, , if available
• energy input, , if power is known

Students record temperature every until the sample has melted and warmed as liquid water.

Analysis

Students graph temperature against time.

Students identify:

• sloped regions where applies
• flat regions where applies
• melting point
• evidence that energy is still transferred during the flat section

Students explain why temperature remains constant during phase change using the kinetic particle model.

Evaluation

Students evaluate:

• heat loss to the surroundings
• uneven heating
• thermometer lag
• whether the ice was initially below
• uncertainty in mass and temperature readings
• whether the hot plate supplied constant power

Problems

The following problems are designed to practise solving problems that combine specific heat capacity and phase change.

Use:

1. Calculate the energy required to change of ice at into water at .
2. Calculate the energy required to change of ice at into water at .
3. Calculate the energy required to change of water at into steam at .
4. Calculate the energy required to change of water at into steam at .
5. of energy is supplied to of ice at . Determine whether all the ice melts.
6. of energy is supplied to of ice at . Determine the final state and temperature.
7. Calculate the energy removed when of steam at becomes water at .
8. Calculate the total energy removed when of water at becomes ice at .

Answers:

5. Not all the ice melts; could melt, so all melts and energy remains to warm the water.
6. Liquid water at
7. removed
8. removed

Followup

Self-check

Students should be able to answer:

• Does the problem include a phase change?
• What state is the substance in at each stage?
• Which stages use ?
• Which stages use ?
• Did I use , or correctly?
• Did I include all stages in ?
• Is my final state physically reasonable?

Next Topic

Thermal equilibrium problems, where energy lost by one system equals energy gained by another system.