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Physics 001.001.012 Thermal Equilibrium

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Physics 001.001.012 Thermal Equilibrium

Alignment

Learning Intentions

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

  • Describe thermal equilibrium as the condition where two or more systems in thermal contact have the same temperature.
  • Relate temperature to the average kinetic energy of particles in a system.
  • Describe the direction of thermal energy transfer between systems before thermal equilibrium is reached.
  • Distinguish between total thermal energy and average kinetic energy.

Success Criteria

By the end of the lesson, students have successfully:

  • Stated that systems are in thermal equilibrium when they have the same temperature.
  • Explained that equal temperature means equal average kinetic energy of particles, not necessarily equal total internal energy.
  • Identified that thermal energy transfers from a higher-temperature system to a lower-temperature system until thermal equilibrium is achieved.
  • Used particle diagrams or written descriptions to compare systems before and after thermal equilibrium.

Syllabus Reference

  • Unit 1: Thermal, Nuclear and Electrical Physics
  • Topic 1: Heating Processes
  • Phase Changes and Energy Conservation
  • Describe the concept of thermal equilibrium in terms of the temperature and average kinetic energy of the particles in each of the systems.

Phenomenon

A metal spoon is placed into a hot cup of tea. At first, the spoon feels cool compared with the tea. After some time, the spoon becomes warm. Eventually, the spoon and tea are at the same temperature.

The important observation is that the spoon does not keep getting hotter forever. Thermal energy transfers between the tea and spoon until there is no temperature difference between them.

Key Idea

Thermal equilibrium occurs when two or more systems in thermal contact have the same temperature. Since temperature is related to the average kinetic energy of particles, systems at the same temperature have particles with the same average kinetic energy.

Concept

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

Temperature is a measure of the average kinetic energy of the particles in a system. If two systems have different temperatures, their particles have different average kinetic energies.

When the systems are placed in thermal contact, thermal energy transfers from the higher-temperature system to the lower-temperature system. This transfer continues until both systems reach the same temperature.

At thermal equilibrium:

  • the systems have the same temperature
  • the particles in each system have the same average kinetic energy
  • there is no net transfer of thermal energy between the systems

This does not mean the systems contain the same total thermal energy. A bathtub of water and a cup of water can be at the same temperature, but the bathtub contains much more total internal energy because it has many more particles.

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.
  • Thermal energy transfers from higher temperature to lower temperature.
  • Thermal equilibrium means equal temperature, not equal energy.
  • The symbol is commonly used for temperature.
  • The average kinetic energy of particles increases as temperature increases.
  • For a particle, kinetic energy can be represented by .
  • A system with faster-moving particles has a greater average kinetic energy and therefore a higher temperature.

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 two systems have the same amount of thermal energy.
  • A larger object must always be hotter than a smaller object.
  • Heat and temperature mean the same thing.
  • Thermal energy stops existing once equilibrium is reached.
  • Particles stop moving when thermal equilibrium is reached.

Further Reading

  • Kinetic particle model of matter
  • Temperature and average kinetic energy
  • Heat transfer by conduction, convection and radiation
  • Specific heat capacity
  • Thermal equilibrium and the laws of thermodynamics

Explicit Instruction

Thermal equilibrium describes what happens when systems in thermal contact reach the same temperature.

Consider a hot metal block placed beside a cold metal block so that they are touching.

Before contact:

  • the hot block has particles with greater average kinetic energy
  • the cold block has particles with lower average kinetic energy
  • there is a temperature difference between the two systems

During contact:

  • particles in the hotter block collide with neighbouring particles
  • energy is transferred through these interactions
  • the hotter block loses thermal energy
  • the colder block gains thermal energy

At thermal equilibrium:

  • both blocks have the same temperature
  • the particles in both blocks have the same average kinetic energy
  • there is no net transfer of thermal energy

The word net is important. Particles are still moving and energy is still being exchanged microscopically, but there is no overall transfer from one system to the other.

Worked Examples

Worked Example 1

A hot copper block at is placed in contact with a cold copper block at . Describe what happens to the temperature and average kinetic energy of the particles in each block.

Answer:

The hot block has a higher temperature, so its particles have a greater average kinetic energy. The cold block has a lower temperature, so its particles have a lower average kinetic energy.

Thermal energy transfers from the hot block to the cold block.

As this happens:

  • the hot block decreases in temperature
  • the average kinetic energy of its particles decreases
  • the cold block increases in temperature
  • the average kinetic energy of its particles increases

Eventually, both blocks reach the same temperature. At this point, they are in thermal equilibrium.

Worked Example 2

A cup of tea and a swimming pool are both at . Compare the average kinetic energy of the water particles and the total thermal energy in each system.

Answer:

Both systems have the same temperature, so the average kinetic energy of the water particles is the same in the cup of tea and the swimming pool.

However, the swimming pool contains far more water particles than the cup of tea. Therefore, the swimming pool has much more total thermal energy.

Same temperature means same average kinetic energy, not same total thermal energy.

Worked Example 3

A thermometer at is placed into a beaker of water at . Explain how the thermometer measures the water temperature.

Answer:

At first, the water is at a higher temperature than the thermometer. This means the water particles have a greater average kinetic energy than the particles in the thermometer.

Thermal energy transfers from the water to the thermometer.

The thermometer increases in temperature until it reaches thermal equilibrium with the water. Once both are at the same temperature, the thermometer reading represents the temperature of the water.

Check for Understanding

Check 1

Two objects are in thermal equilibrium. What must be the same for both objects?

Expected answer:

They must have the same temperature. This means the particles in each object have the same average kinetic energy.

Check 2

A hot object and a cold object are placed in contact. In which direction does thermal energy transfer?

Expected answer:

Thermal energy transfers from the hot object to the cold object until both objects reach the same temperature.

Check 3

A large bucket of water and a small cup of water are both at . Which has the greater average kinetic energy per particle?

Expected answer:

Neither. They have the same average kinetic energy per particle because they have the same temperature. The bucket has more total thermal energy because it contains more particles.

Investigation (Alternative to Explicit)

Hypothesis

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

Data Collection

Equipment:

  • hot water
  • cold water
  • two beakers
  • thermometer or temperature probe
  • measuring cylinder
  • stirring rod
  • safety glasses

Method:

  1. Measure of cold water into a beaker.
  2. Record its initial temperature.
  3. Measure of hot water into another beaker.
  4. Record its initial temperature.
  5. Mix the two samples of water.
  6. Stir gently.
  7. Record the final stable temperature of the mixture.
  8. Repeat with different volumes of hot and cold water.

Suggested data table:

TrialVolume of hot waterInitial hot temperatureVolume of cold waterInitial cold temperatureFinal equilibrium temperature
1
2
3

Analysis

Students should identify that:

  • the hot water decreases in temperature
  • the cold water increases in temperature
  • the final temperature lies between the two initial temperatures
  • the final temperature is the thermal equilibrium temperature
  • if the masses are different, the final temperature is closer to the initial temperature of the larger mass of water

Discussion prompts:

  1. Why does the final temperature not equal the hottest initial temperature?
  2. Why does the final temperature not equal the coldest initial temperature?
  3. What does the final temperature tell us about the average kinetic energy of the particles?
  4. Why might the measured value differ from the theoretical value?

Evaluation

Possible sources of error:

  • thermal energy transferred to the beaker
  • thermal energy lost to the surroundings
  • thermometer response time
  • incomplete stirring
  • uncertainty in volume and temperature measurements

Improvements:

  • use insulated cups instead of glass beakers
  • use a lid to reduce energy transfer to the surroundings
  • stir consistently
  • use digital temperature probes
  • repeat trials and calculate a mean final temperature

Problems

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

  1. Define thermal equilibrium.

  2. Explain thermal equilibrium using the terms temperature and average kinetic energy.

  3. A metal rod at is placed in water at . Describe the direction of thermal energy transfer.

  4. A cup of coffee is left on a desk. After one hour, it is at the same temperature as the room. Explain this observation in terms of thermal equilibrium.

  5. Two blocks are both at . One block has a mass of and the other has a mass of . Compare:

    • their temperatures
    • the average kinetic energy of their particles
    • their total thermal energies

  6. Explain why a thermometer must reach thermal equilibrium with an object before it can accurately measure the object’s temperature.

  7. A student says, “Two objects in thermal equilibrium contain the same amount of heat.” Explain why this statement is incorrect.

  8. A hot object and a cold object are placed in an insulated container. Describe what happens to:

    • the temperature of the hot object
    • the average kinetic energy of particles in the hot object
    • the temperature of the cold object
    • the average kinetic energy of particles in the cold object

  9. A swimming pool and a cup of tea are both at . Which has more total internal energy? Explain your answer.

  10. Draw a particle model diagram showing two systems before and after thermal equilibrium is reached. Annotate your diagram using the terms temperature, average kinetic energy and thermal energy transfer.

Followup

Self-check

Students should be able to answer the following without notes:

  • Can I define thermal equilibrium?
  • Can I explain why thermal energy transfers from hot to cold?
  • Can I describe temperature as a measure of average kinetic energy?
  • Can I explain why equal temperature does not mean equal total thermal energy?
  • Can I use particle motion to describe what changes before equilibrium is reached?
  • Can I explain why there is no net thermal energy transfer at equilibrium?

Next Topic

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.

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