Physics 001.001.015 Thermal Energy to Mechanical Work

Alignment

Learning Intentions

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

• Explain that thermal energy can be transformed into mechanical work.
• Describe how particle motion and pressure allow a heated gas to move a boundary, such as a piston.
• Connect thermal expansion, pressure, force and displacement to the idea of work.
• Recognise that not all thermal energy becomes useful mechanical work.

Success Criteria

By the end of the lesson, students have successfully:

• Described thermal energy as energy associated with the random motion and arrangement of particles.
• Explained that heating a gas can increase particle kinetic energy, collision frequency and pressure.
• Explained how gas pressure can exert a force on a movable object.
• Linked force and displacement to mechanical work using .
• Explained a real example, such as a steam engine, internal combustion engine, turbine or syringe-piston model.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 1: Heating Processes
• Phase Changes and Energy Conservation
• Explain how a system with thermal energy has the capacity to do mechanical work.

Phenomenon

A sealed syringe contains air. When the air inside the syringe is heated, the plunger can be pushed outward.

The air does not have a hand, motor or spring, yet it can move the plunger. This shows that a system with thermal energy can have the capacity to do mechanical work.

Key Idea

A system with thermal energy contains particles in random motion. If this energy is transferred in a way that causes expansion against an external force, some of the thermal energy can be transformed into mechanical work.

Concept

Thermal energy is associated with the random kinetic energy and potential energy of particles in a system.

When a gas is heated, the particles usually move faster. Faster particles collide with the walls of the container more often and with greater change in momentum. These collisions create pressure.

If one wall of the container can move, such as a piston or plunger, the pressure force can move it through a distance. When a force causes displacement, mechanical work is done.

Mechanical work is given by:

where:

= work done in joules, = force in newtons, = displacement in metres,

For a gas expanding at constant pressure, the idea can also be represented as:

where:

= pressure in pascals, = change in volume in cubic metres,

This equation is useful conceptually because it shows that a gas does mechanical work when it expands against a pressure.

Convention

The key conventions associated with the concept are below.

• Thermal energy is microscopic and disordered.
• Mechanical work is macroscopic and organised.
• A system does mechanical work when it applies a force over a displacement.
• Heating can increase the internal energy of a gas.
• If the gas expands, some internal energy can be transferred as work.
• In the QCAA convention used later, the first law may be written as , where is work done on the system.
• If the system does work on the surroundings, then energy leaves the system as mechanical work.

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems.

• Thermal energy and mechanical work are the same thing.
• A hot object automatically does work, even if nothing moves.
• Temperature is the same as thermal energy.
• A gas needs to be “pushing in one direction” at the particle level to do work.
• All thermal energy can be converted into useful mechanical work.

Further Reading

• Heat engines
• Steam engines
• Internal combustion engines
• Turbines in power stations
• First law of thermodynamics
• Energy efficiency and waste heat

Explicit Instruction

Thermal energy gives a system the capacity to do work because the particles in the system are moving and interacting.

In a gas, particles move randomly and collide with the container walls. Each collision applies a tiny force. Across a large number of particles, these collisions create pressure.

Pressure is force per unit area:

Rearranging gives:

If the gas is inside a container with a movable boundary, the gas can push on that boundary. If the boundary moves, then work is done.

Therefore:

• thermal energy can increase particle motion
• particle motion can create pressure
• pressure can create a force
• force can cause displacement
• force through displacement is mechanical work

This is why hot gases are useful in engines. In a steam engine, water is heated to form high-pressure steam. The steam expands and pushes a piston or turbine blade. Thermal energy is transformed into mechanical work.

However, the transformation is never perfect. Some energy remains as internal energy, and some is transferred to the surroundings as waste heat.

Worked Examples

Worked Example 1

A gas in a cylinder pushes a piston with a force of . The piston moves . Calculate the mechanical work done on the piston.

The gas does of mechanical work on the piston.

Worked Example 2

A gas expands at a constant pressure of . Its volume increases by . Calculate the work done by the expanding gas.

The expanding gas does of mechanical work.

Worked Example 3

A small heat engine receives of thermal energy. It transfers as useful mechanical work. The rest is transferred to the surroundings as waste heat. Determine the waste energy.

Energy input equals useful energy output plus waste energy.

The engine transfers to the surroundings as waste heat.

Check for Understanding

Check 1

A hot block of metal sits on a bench. It has thermal energy, but it does not move anything.

Question: Is it doing mechanical work?

Expected answer: No. It has thermal energy, but mechanical work requires a force causing displacement.

Check 2

A heated gas expands and pushes a piston outward.

Question: Why can the gas do work?

Expected answer: The heated gas particles collide with the piston, creating pressure. This pressure creates a force that moves the piston through a distance.

Check 3

A gas pushes a piston with a force of over a distance of .

Question: Calculate the work done.

The work done is .

Investigation (Alternative to Explicit)

Hypothesis

If the air inside a syringe is heated, then the plunger will move outward because the gas particles will exert greater pressure on the movable boundary.

Data Collection

Equipment:

• Plastic syringe with sealed tip or tubing clamp
• Warm water bath
• Cold water bath
• Thermometer
• Ruler
• Retort stand and clamp
• Safety glasses

Method:

1. Place a small volume of air inside the syringe.
2. Seal the syringe tip.
3. Record the starting position of the plunger.
4. Place the syringe in a warm water bath.
5. Wait until the air temperature changes.
6. Record the final position of the plunger.
7. Repeat using different water temperatures.
8. Record temperature and plunger displacement.

Safety:

• Do not use boiling water.
• Do not point the syringe at anyone.
• Ensure the syringe is not over-pressurised.
• Wear safety glasses.

Analysis

Students should look for a relationship between temperature and plunger displacement.

Guiding questions:

• What happened to the plunger when the air was heated?
• What happened to the particles inside the syringe?
• Why did the pressure inside the syringe change?
• How does the movement of the plunger show mechanical work?
• Where did the energy come from?

Evaluation

Students should evaluate:

• Whether the syringe was sealed properly.
• Whether the temperature of the air was actually equal to the water bath temperature.
• Whether friction affected the motion of the plunger.
• Whether the plunger moved smoothly or suddenly.
• Whether heat was lost to the surroundings.

Problems

The following problems are designed to help students explain and apply the relationship between thermal energy and mechanical work.

1. Define mechanical work.

2. Explain why a hot object does not necessarily do mechanical work.

3. Describe how heating a gas can allow it to push a piston.

4. A gas applies a force of to a piston. The piston moves . Calculate the work done.

5. A gas expands at a constant pressure of . Its volume increases by . Calculate the work done by the gas.

6. A steam engine transforms thermal energy into mechanical work. Describe the energy transformation occurring.

7. A heat engine receives of energy by heating and produces of useful mechanical work. Calculate the energy transferred as waste heat.

8. Explain why heat engines cannot convert all thermal energy into useful mechanical work.

9. A heated gas expands and lifts a small mass. Explain how this demonstrates conservation of energy.

10. Compare the energy in a hot gas before and after it expands and does work on a piston.

Followup

Self-check

Students should be able to answer the following:

• Can I explain the difference between thermal energy and mechanical work?
• Can I describe how particle motion creates pressure?
• Can I explain why expansion of a gas can do work?
• Can I use to calculate mechanical work?
• Can I explain why some energy is wasted during thermal energy transformations?

Next Topic

The next topic is the first law of thermodynamics:

Students will learn that the change in internal energy of a system depends on energy transferred by heating and work done on or by the system.