Physics 001.001.007 Specific Heat Capacity Problems Without Phase Change

Alignment

Learning Intentions

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

• Identify when a heating problem does not involve phase change.
• Use to solve for heat energy, mass, specific heat capacity or temperature change.
• Select the correct specific heat capacity for ice, water or steam.
• Communicate calculations using correct SI units and significant figures.

Success Criteria

By the end of the lesson, students have successfully:

• Defined each variable in .
• Converted mass to kilograms and temperature change to kelvin or degrees Celsius.
• Solved problems using , and .
• Explained why is only used when temperature changes without phase change.
• Checked whether the final temperature stays within the same state of matter.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Explain that a change in temperature is due to the addition or removal of energy from a system without phase change.
• Describe the concept of specific heat capacity.
• Solve problems involving specific heat capacity using .
• Interpret data from specific heat capacity experiments.

Phenomenon

A metal spoon, a glass of water and a block of ice are each given the same amount of thermal energy. They do not increase by the same temperature.

Students observe or discuss:

• A kettle heating water.
• Ice warming from to without melting.
• Steam warming from to without condensing.
• Sand heating faster than water at the beach.

Guiding question:

Why does the same amount of energy cause different temperature changes in different substances?

Key Idea

When energy is added to or removed from a substance without a phase change, the temperature changes. The size of the temperature change depends on:

• the amount of energy transferred
• the mass of the substance
• the specific heat capacity of the substance

The relationship is:

where:

• is heat energy transferred in joules,
• is mass in kilograms,
• is specific heat capacity in
• is temperature change in or

Since a change of is the same size as a change of , students may use in either kelvin or degrees Celsius.

Concept

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

Specific heat capacity describes how much energy is needed to raise the temperature of of a substance by .

A substance with a high specific heat capacity requires more energy for the same temperature increase. Water has a high specific heat capacity, so it heats and cools slowly compared with many other materials.

Convention

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

• Use only when there is no phase change.
• Use mass in kilograms, not grams.
• Use energy in joules, not kilojoules, unless converting at the end.
• Use .
• A positive means energy is added to the system.
• A negative means energy is removed from the system.
• The specific heat capacities used in this lesson are:
  • for ice
  • for water
  • for steam

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 grams instead of kilograms.
• Students often use final temperature instead of temperature change.
• Students may think must always be converted to kelvin, even though a temperature interval of equals .
• Students may use across a phase change, such as ice at to water at , without separating stages.
• Students may think a larger temperature change always means more energy was added, ignoring mass and specific heat capacity.

Further Reading

• Specific heat capacity in everyday materials
• Heating curves without phase change
• Energy transfer in kettles and cooling systems
• Why water is used as a coolant in car engines

Explicit Instruction

Worked Examples

Worked Example 1

A sample of water is heated from to . Calculate the energy transferred.

Step 1: Identify the known values.

Step 2: Use the equation.

Step 3: Substitute.

Step 4: Round appropriately.

Answer: of energy is transferred to the water.

Worked Example 2

A block of ice absorbs of energy while remaining solid. Calculate the temperature increase.

Step 1: Convert energy to joules.

Step 2: Identify the known values.

Step 3: Rearrange.

Step 4: Substitute.

Answer: The temperature of the ice increases by , or .

Worked Example 3

of energy is transferred to steam. The steam temperature increases from to . Calculate the mass of steam.

Step 1: Convert energy.

Step 2: Calculate temperature change.

Step 3: Use the specific heat capacity of steam.

Step 4: Rearrange.

Step 5: Substitute.

Answer: The mass of steam is .

Check for Understanding

Check 1

A sample of water is heated from to . Calculate .

Expected answer:

Check 2

A block of ice absorbs of energy without melting. Calculate .

Expected answer:

Check 3

of energy heats of steam by . Calculate the specific heat capacity.

Expected answer:

Investigation (Alternative to Explicit)

Hypothesis

If the same amount of energy is transferred to equal masses of different substances, then the substance with the lower specific heat capacity will have the greater temperature increase.

Data Collection

Students heat equal masses of water and another safe material, such as sand or metal shot, using the same heating time and power input.

Record:

• mass,
• initial temperature,
• final temperature,
• heating time,
• heater power,
• energy input,

Analysis

Students calculate:

Students compare the measured value of with an accepted value and calculate percentage error:

Evaluation

Students evaluate:

• heat loss to the surroundings
• thermometer uncertainty
• whether the sample was heated evenly
• whether all electrical energy became thermal energy in the sample
• whether insulation improved the result

Problems

The following problems are designed to practise solving specific heat capacity questions without phase change.

1. Calculate the energy needed to heat of water from to .
2. Calculate the energy removed when of water cools from to .
3. A block of ice warms from to . Calculate .
4. A sample of steam cools from to . Calculate the energy removed.
5. of energy is added to of water. Calculate .
6. of energy warms a block of ice by . Calculate the mass of ice.
7. A sample of water absorbs and its temperature rises from to . Calculate its mass.
8. A sample of steam with mass absorbs . Calculate its temperature increase.

Answers:

2. removed
4. removed

Followup

Self-check

Students should be able to answer:

• Did I convert grams to kilograms?
• Did I calculate correctly?
• Did I choose the correct value of ?
• Did the substance stay in the same phase?
• Did I include a unit in my final answer?

Next Topic

Solving energy transfer problems that include phase change, where must be combined with .