Physics 001.001.011 Specific Latent Heat Problems

Alignment

Learning Intentions

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

• Identify when a heating problem involves latent heat rather than specific heat capacity.
• Define each variable in and use correct SI units.
• Solve problems involving melting, freezing, boiling and condensing using .
• Interpret whether energy is absorbed or released during a change of state.

Success Criteria

By the end of the lesson, students have successfully:

• Converted mass into kilograms before substituting into .
• Selected the correct latent heat value for the phase change.
• Rearranged to solve for , or .
• Written final answers with units and appropriate significant figures.
• Explained that temperature remains constant during a phase change because energy changes particle arrangement, not average kinetic energy.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Phase Changes and Energy Conservation
• Solve problems involving specific latent heat using .

Phenomenon

A wet towel feels cold when wrapped around your arm, even if the water in the towel is already at room temperature. This occurs because water evaporates from the towel. During evaporation, water requires energy to change from liquid to gas. This energy is transferred from your skin to the water, so your skin loses thermal energy and feels colder.

A similar idea explains why sweating cools the body, why steam burns are dangerous, why ice keeps drinks cold, and why boiling water stays at about while liquid water is still present.

Key Idea

During a phase change, energy is transferred into or out of a substance without changing its temperature. This energy is called latent heat.

The relationship is:

where:

= energy transferred, measured in joules

= mass of the substance, measured in kilograms

= specific latent heat, measured in joules per kilogram

Concept

Specific latent heat is the amount of energy required to change the state of of a substance without changing its temperature.

There are two common types:

• Specific latent heat of fusion: energy required to melt or freeze a substance.
• Specific latent heat of vaporisation: energy required to boil, evaporate or condense a substance.

For water:

The latent heat of vaporisation is much larger than the latent heat of fusion because separating liquid particles into a gas requires much more energy than loosening particles from solid to liquid.

Convention

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

• Use only when a substance is changing state.
• Use only when a substance changes temperature without changing state.
• Mass must be in kilograms.
• Specific latent heat must be in .
• Energy is absorbed during melting, boiling and evaporation.
• Energy is released during freezing and condensation.
• In most Year 11 problems, use the magnitude of energy unless the question asks for direction of energy transfer.
• If signs are used, energy absorbed by the substance may be treated as positive and energy released by the substance may be treated as negative.

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 think temperature must increase whenever energy is added.
• Students often use during a phase change, even though during the change of state.
• Students often forget to convert grams to kilograms.
• Students may confuse specific latent heat of fusion with specific latent heat of vaporisation.
• Students may think boiling and evaporation are identical; boiling occurs throughout the liquid at the boiling point, while evaporation can occur at the surface below the boiling point.

Further Reading

• Heating curves for water
• Specific latent heat of fusion
• Specific latent heat of vaporisation
• Thermal equilibrium
• Energy conservation in phase changes
• First law of thermodynamics

Explicit Instruction

Start with the decision question:

Is the temperature changing, or is the state changing?

If the temperature changes and there is no phase change:

If the state changes and temperature stays constant:

To solve latent heat problems:

1. Identify the phase change.
2. Select the correct latent heat value.
3. Convert mass to kilograms.
4. Substitute into .
5. Calculate and include units.
6. State whether energy is absorbed or released.

Rearrangements:

Worked Examples

Worked Example 1

A student melts of ice at . Calculate the energy required to melt the ice. Use .

Known:

Unknown:

Solution:

Final answer:

The ice absorbs of energy while melting.

Worked Example 2

How much water can be boiled away if of energy is supplied to water already at ? Use .

Known:

Unknown:

Solution:

Final answer:

Therefore, of water can be boiled away.

Worked Example 3

A freezer removes of energy from liquid water at . What mass of water freezes? Use .

Known:

Unknown:

Solution:

Final answer:

Therefore, of water freezes. The water releases energy to the freezer.

Check for Understanding

Check 1

A student says, “If energy is added to ice at , its temperature must increase.” Explain why this is not always true.

Expected response:

If the ice is melting, the added energy is used to change the arrangement of particles from solid to liquid. The average kinetic energy of the particles does not increase, so the temperature remains constant during the phase change.

Check 2

Which equation should be used for each situation?

a. Heating liquid water from to

b. Melting ice at

c. Boiling water at

d. Cooling steam from to

Expected answers:

a.

b.

c.

d.

Check 3

Calculate the energy required to vaporise of water at . Use .

Answer:

Investigation (Alternative to Explicit)

Hypothesis

If the mass of ice melted increases, then the energy required to melt it will increase proportionally because .

Data Collection

Practical: Estimating the specific latent heat of fusion of ice.

Materials:

• Polystyrene cup or insulated beaker
• Warm water
• Ice cubes near
• Thermometer or temperature probe
• Electronic balance
• Paper towel
• Stirring rod
• Safety glasses

Method:

1. Measure the mass of an empty insulated cup.
2. Add warm water and measure the combined mass.
3. Calculate the mass of the warm water.
4. Measure the initial temperature of the warm water.
5. Dry the ice with paper towel to remove surface water.
6. Add a measured mass of ice to the warm water.
7. Stir gently until the ice has completely melted.
8. Measure the final equilibrium temperature.
9. Record all measurements with correct units and uncertainty.

Suggested data table:

Quantity	Symbol	Value	Unit	Uncertainty
Mass of cup
Mass of cup and water
Mass of water
Mass of ice
Initial water temperature
Final temperature

Analysis

Assuming energy lost by warm water equals energy gained by ice:

Energy lost by warm water:

Energy gained by ice:

Energy conservation:

Rearrange to determine :

Use:

Students compare their experimental value of with the accepted value:

Percentage error:

Evaluation

Possible sources of error:

• Ice may begin below , requiring extra energy to warm it before melting.
• Ice may have liquid water on its surface, increasing the measured mass incorrectly.
• Energy may be transferred between the cup and surroundings.
• The thermometer may have a response delay.
• The final temperature may not be uniform if the mixture is not stirred.

Improvements:

• Dry ice before adding it.
• Use an insulated cup with a lid.
• Stir gently and consistently.
• Use a digital temperature probe.
• Repeat trials and calculate a mean value.

Problems

The following problems are designed to develop fluency with before moving into multi-step thermal equilibrium problems.

1. Calculate the energy required to melt of ice at . Use .

2. Calculate the energy released when of water freezes at . Use .

3. Calculate the energy required to boil of water at . Use .

4. A kettle supplies of energy to water already at . What mass of water is converted to steam? Use .

5. A freezer removes of energy from water at . What mass of water freezes? Use .

6. A sample of metal has a mass of . It requires to melt completely at its melting point. Calculate the specific latent heat of fusion of the metal.

7. A steam burn is often more severe than a burn from boiling water at the same temperature. Explain this using latent heat.

8. A student uses to calculate the energy needed to melt ice at . Explain why this method is incorrect.

Answers:

Energy is released.

7. Steam releases a large amount of latent heat when it condenses on the skin, transferring more energy than hot water at the same temperature.

8. During melting, temperature does not change, so . The energy goes into changing state, so must be used.

Followup

Self-check

Students should be able to answer the following without notes:

• What does specific latent heat mean?
• What are the units for , and ?
• Why must mass be converted into kilograms?
• What is the difference between and ?
• Why does temperature remain constant during a phase change?
• When should be used instead of ?

Next Topic

The next topic is solving problems involving specific heat capacity, specific latent heat and thermal equilibrium. This combines:

energy lost by one system = energy gained by another system