Physics 001.001.013 Heat

Alignment

Learning Intentions

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

• Explain how thermal energy transfers between two systems due to a temperature difference.
• Describe how thermal equilibrium is achieved when systems reach the same temperature.
• Recognise how thermal equilibrium relates to the laws of thermodynamics.
• Use particle-level reasoning to explain macroscopic heat transfer.

Success Criteria

By the end of the lesson, students have successfully:

• Identified the direction of heat transfer between two systems.
• Explained that thermal energy transfers from a hotter system to a cooler system until both systems reach the same temperature.
• Described thermal equilibrium in terms of temperature and average kinetic energy of particles.
• Connected thermal equilibrium to the zeroth, first and second laws of thermodynamics.
• Applied the concept to everyday examples such as cooling drinks, thermometers and heat engines.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Phase Changes and Energy Conservation
• Explain the process in which thermal energy is transferred between two systems until thermal equilibrium is achieved, and recognise the relevance of this to the laws of thermodynamics.

Phenomenon

A hot metal spoon is placed into a cup of cold water.

At first, the spoon is hotter than the water. After some time, the spoon feels cooler and the water is slightly warmer. Eventually, the spoon and water reach the same temperature.

The key question is:

Why does the thermal energy transfer stop?

Key Idea

Thermal energy is transferred between systems when there is a temperature difference. Energy transfers from the hotter system to the cooler system until both systems reach the same temperature. At this point, the systems are in thermal equilibrium and there is no net transfer of thermal energy.

Concept

Thermal equilibrium occurs when two or more systems in thermal contact reach the same temperature.

Temperature is related to the average kinetic energy of particles. A hotter system has particles with a greater average kinetic energy than a cooler system. When the systems interact, faster-moving particles transfer energy to slower-moving particles through collisions and interactions.

Thermal energy continues to transfer until the average kinetic energy of particles in each system becomes equal. This means the systems have the same temperature.

Convention

Important conventions:

• Thermal energy transferred because of a temperature difference is called heat.
• Heat is represented by .
• Temperature is represented by .
• Thermal energy naturally transfers from a higher temperature system to a lower temperature system.
• Thermal equilibrium is reached when .
• At thermal equilibrium, there is no net heat transfer between the systems.
• Heat transfer does not mean “coldness” moves. It means energy is transferred.

The process can be summarised as:

Thermal energy transfers from hot to cold.

At equilibrium:

Therefore:

For an isolated system:

Laws of Thermodynamics

Thermal equilibrium is relevant to the laws of thermodynamics.

Zeroth Law of Thermodynamics

If system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is also in thermal equilibrium with system C.

This law allows temperature to be measured using thermometers.

Example:

If a thermometer reaches thermal equilibrium with a cup of water, then the thermometer reading is the temperature of the water.

First Law of Thermodynamics

The first law is a statement of energy conservation.

Energy is not created or destroyed. When heat transfers from a hot system to a cold system, the energy lost by the hot system is gained by the cold system, assuming no energy is lost to the surroundings.

This can be written as:

For simple heat transfer with no work done:

Second Law of Thermodynamics

The second law explains the direction of spontaneous heat transfer.

Thermal energy naturally transfers from a hotter system to a cooler system. It does not naturally transfer from a cooler system to a hotter system without external work.

This explains why:

• hot drinks cool down in a room
• ice melts in warm water
• objects left together eventually reach the same temperature
• useful energy becomes less available after energy transfers

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.

• Thermal equilibrium means there is no thermal energy in the systems.
• Heat and temperature are the same thing.
• Coldness transfers from a cold object to a hot object.
• The larger object always has the higher temperature.
• Heat transfer stops because all particles stop moving.
• Thermal equilibrium means both systems have the same total internal energy.
• Energy disappears when a hot object cools down.
• A thermometer instantly measures temperature without reaching thermal equilibrium.

Further Reading

• Zeroth law of thermodynamics
• First law of thermodynamics
• Second law of thermodynamics
• Thermal equilibrium
• Heat transfer
• Internal energy
• Kinetic particle model of matter

Explicit Instruction

Thermal energy transfer occurs when two systems at different temperatures are placed in thermal contact.

Consider a hot metal block placed into cooler water.

Initially:

The particles in the metal have a higher average kinetic energy than the particles in the water. When the metal and water interact, energy is transferred from the metal particles to the water particles.

As energy leaves the metal:

• the average kinetic energy of the metal particles decreases
• the temperature of the metal decreases

As energy enters the water:

• the average kinetic energy of the water particles increases
• the temperature of the water increases

Eventually:

At this point, the metal and water are in thermal equilibrium.

There may still be energy transfers at the particle level, but there is no net transfer of thermal energy between the two systems.

Worked Examples

Worked Example 1

A hot copper block is placed into a beaker of cooler water. The copper is initially at and the water is initially at .

Explain the direction of heat transfer.

Solution

The copper block is hotter than the water:

Therefore, thermal energy transfers from the copper block to the water.

The copper loses thermal energy and cools down. The water gains thermal energy and warms up.

Thermal energy continues to transfer until:

At this point, the copper and water are in thermal equilibrium.

Worked Example 2

A thermometer is placed into a cup of tea. Explain why the thermometer reading changes before showing the tea’s temperature.

Solution

The thermometer and the tea are initially at different temperatures.

If the tea is hotter than the thermometer, thermal energy transfers from the tea to the thermometer.

The particles in the thermometer gain kinetic energy, so the thermometer’s temperature increases. The reading changes until the thermometer and tea reach thermal equilibrium.

At equilibrium:

The thermometer can now be used to measure the temperature of the tea.

This relates to the zeroth law of thermodynamics because temperature measurement depends on systems reaching thermal equilibrium.

Worked Example 3

Two objects are placed in thermal contact inside an insulated container.

Object A loses of thermal energy. Assuming no energy is lost to the surroundings, how much energy does Object B gain?

Solution

The container is insulated, so energy is conserved.

The energy lost by Object A is equal to the energy gained by Object B.

Therefore, Object B gains of thermal energy.

This relates to the first law of thermodynamics because energy is conserved during the transfer.

Check for Understanding

Check 1

A hot mug is placed on a cool table.

State the direction of thermal energy transfer.

Expected response

Thermal energy transfers from the hot mug to the cool table.

Check 2

Two systems are in thermal equilibrium.

What can be said about their temperatures?

Expected response

They have the same temperature.

Check 3

A student says:

“Heat stops transferring because both objects have the same amount of energy.”

Identify the misconception and correct it.

Expected response

The misconception is that thermal equilibrium means both objects have the same total energy.

Thermal equilibrium means both objects have the same temperature, not necessarily the same total internal energy. A large object can have more total internal energy than a small object even if both are at the same temperature.

Investigation (Alternative to Explicit)

Hypothesis

If hot water and cold water are mixed in an insulated cup, then thermal energy will transfer from the hot water to the cold water until the mixture reaches one final equilibrium temperature.

Data Collection

Materials:

• hot water
• cold water
• insulated cup or foam cup
• thermometer or temperature probe
• measuring cylinder
• stopwatch
• safety glasses

Method:

1. Measure the temperature of the hot water.
2. Measure the temperature of the cold water.
3. Add equal volumes of hot and cold water to an insulated cup.
4. Stir gently.
5. Record the temperature every for .
6. Identify the final stable temperature.

Data table:

Time,	Temperature,

Analysis

Students should:

• graph temperature against time
• identify the final equilibrium temperature
• explain why the final temperature is between the hot and cold starting temperatures
• describe the direction of heat transfer
• explain why the temperature eventually becomes stable

Key analysis statement:

Thermal energy transferred from the hotter water to the cooler water until the particles in the mixture had the same average kinetic energy. Once the mixture reached a stable temperature, it was in thermal equilibrium.

Evaluation

Possible limitations:

• Energy may be transferred to the cup and surroundings.
• The thermometer may not respond instantly.
• Water may not be stirred evenly.
• Some energy may be lost while pouring.
• Measurement uncertainty affects the temperature readings.

Possible improvements:

• Use a lid on the cup.
• Use a better insulated calorimeter.
• Use a digital temperature probe.
• Stir consistently.
• Repeat the experiment and calculate an average final temperature.

Problems

The following problems are designed to develop conceptual understanding of thermal energy transfer and thermal equilibrium.

1. A metal spoon at is placed into water at .

   a. State the direction of heat transfer. b. Describe what happens to the average kinetic energy of particles in the spoon. c. Describe what happens to the average kinetic energy of particles in the water. d. State the condition required for thermal equilibrium.

2. A thermometer is placed in a beaker of water. The thermometer reading rises from to .

   a. Which system was initially hotter? b. Which system gained thermal energy? c. Explain why the thermometer reading eventually stopped changing. d. Identify which law of thermodynamics is most directly related to using a thermometer to measure temperature.

3. A hot object and a cold object are placed in an insulated container.

   The hot object loses of energy.

   a. How much energy does the cold object gain? b. Which law of thermodynamics does this demonstrate? c. State one assumption made in your answer.

4. Two objects are in thermal equilibrium at .

   A student says that both objects must contain the same amount of internal energy.

   Explain why the student is incorrect.

5. A cold can of soft drink is placed in a warm room.

   a. State the direction of heat transfer. b. Explain why the can warms up. c. Explain why the can does not continue warming forever. d. Identify how this example relates to the second law of thermodynamics.

6. Explain the process of thermal energy transfer between two systems until thermal equilibrium is achieved. Your answer should refer to:

   • temperature difference
   • average kinetic energy of particles
   • direction of heat transfer
   • final equilibrium condition
   • one law of thermodynamics

Followup

Self-check

Students should be able to answer:

• Can I explain why heat transfers from hot to cold?
• Can I describe thermal equilibrium using temperature?
• Can I describe thermal equilibrium using average kinetic energy of particles?
• Can I explain why there is no net heat transfer at thermal equilibrium?
• Can I connect thermal equilibrium to the zeroth law of thermodynamics?
• Can I connect energy conservation during heat transfer to the first law of thermodynamics?
• Can I connect the direction of heat transfer to the second law of thermodynamics?

Next Topic

Solve problems involving specific heat capacity, specific latent heat and thermal equilibrium.

This includes using:

and conservation of energy: