Mr. Ward's Teaching Materials

Physics 001.001.018 Efficiency

8 min read

Physics 001.001.018 Efficiency

Alignment

Learning Intentions

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

  • Describe efficiency as a measure of how much input energy is converted into useful output energy.
  • Distinguish between useful energy output and wasted energy output.
  • Explain why real energy transfers are never perfectly efficient.
  • Represent efficiency using energy flow diagrams and Sankey diagrams.
  • Use the equation to describe the meaning of efficiency.

Success Criteria

By the end of the lesson, students have successfully:

  • Defined efficiency in terms of useful output energy and total input energy.
  • Identified useful and wasted energy transfers in everyday systems.
  • Explained why wasted energy is often transferred to the environment as heat or sound.
  • Interpreted a simple energy transfer diagram.
  • Described why increasing efficiency is important for energy use and sustainable technologies.

Syllabus Reference

  • Unit 1: Thermal, Nuclear and Electrical Physics
  • Topic 1: Heating Processes
  • Science Understanding: Describe the concept of efficiency.
  • Related content: Explain how energy transfers and transformations in mechanical systems always result in some heat loss to the environment, so that the amount of useable energy is reduced.
  • Related content: Solve problems involving the efficiency of heat transfers using and .

Phenomenon

A phone charger becomes warm while charging a phone.

The electrical energy supplied to the charger is not all stored usefully in the phone battery. Some energy is transferred to the surroundings as thermal energy. The phone still charges, but the useful energy output is less than the total energy input.

This raises the question:

Where does the rest of the energy go?

Key Idea

Efficiency describes how much of the energy input to a system becomes useful energy output.

A system is more efficient when a larger proportion of its input energy is transferred or transformed into the desired useful form.

A system is less efficient when more of the input energy is dissipated to the surroundings, often as heat or sound.

Concept

Efficiency is a ratio comparing useful energy output to total energy input.

Where:

  • is efficiency, measured as a percentage.
  • Useful energy output is the energy transferred for the intended purpose.
  • Total energy input is the energy supplied to the system.

For example, in a kettle:

  • Useful output: thermal energy transferred to the water.
  • Wasted output: thermal energy transferred to the air, kettle body and bench; sound energy.

Energy is conserved, but not all energy remains useful.

Convention

The key conventions associated with efficiency are below.

  • Efficiency is usually written as a percentage.
  • The useful energy output must be compared to the total energy input.
  • Efficiency cannot be greater than .
  • A real system is never perfectly efficient because some energy is dissipated to the surroundings.
  • Wasted energy is not destroyed; it is transferred into less useful forms.
  • In thermal systems, wasted energy is often thermal energy transferred to the environment.
  • A Sankey diagram can represent efficiency visually:
    • Wider arrows represent larger energy transfers.
    • The useful energy output arrow usually continues forward.
    • Wasted energy arrows usually branch away.

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.

  • Efficiency means how fast a device works.
  • Wasted energy disappears or is destroyed.
  • A machine can produce more useful energy than the energy supplied to it.
  • All heat is wasted energy. Heaters!
  • Efficiency is calculated using wasted energy output instead of useful energy output.

Further Reading

  • Energy conservation and the first law of thermodynamics.
  • Mechanical work and thermal energy.
  • Sankey diagrams and energy flow models. Chemistry covers these too.
  • Efficiency of engines, power stations, light bulbs, electric motors and heating systems.
  • Sustainable energy technologies and energy efficiency standards.

Explicit Instruction

Begin with the energy conservation idea:

Energy cannot be created or destroyed.

However, energy can become less useful after a transfer or transformation. This usually happens because some energy spreads into the environment as thermal energy.

For a device or process:

Efficiency focuses only on the useful part:

A high-efficiency device has a large useful output compared with its input.

A low-efficiency device has a large amount of wasted energy compared with its useful output.

Worked Examples

Worked Example 1

A lamp receives of electrical energy. It transfers as useful light energy. Describe its efficiency.

The lamp is efficient. This means of the input energy becomes useful light energy, while is transferred to the surroundings, mostly as thermal energy.

Worked Example 2

A kettle receives of electrical energy. It transfers of thermal energy to the water. Describe the useful and wasted energy transfers.

Useful energy output:

is transferred to the water.

Wasted energy output:

The kettle wastes by heating the kettle body, the surrounding air and the bench. It may also produce a small amount of sound energy.

Efficiency:

The kettle is efficient.

Worked Example 3

A petrol engine transfers chemical energy from fuel into kinetic energy of the car. Describe why the engine is not efficient.

The useful energy output is the kinetic energy of the car.

However, some energy is transferred to:

  • the engine block as thermal energy
  • the exhaust gases as thermal energy
  • the tyres and road as thermal energy due to friction
  • the surroundings as sound energy

The energy is not destroyed. It is dissipated to the environment in forms that are no longer useful for moving the car.

Therefore, the engine is not efficient.

Check for Understanding

Check 1

A speaker receives electrical energy and produces sound.

Identify:

  • the useful energy output
  • one wasted energy output

Expected response:

The useful output is sound energy. A wasted output is thermal energy transferred to the speaker and surroundings.

Check 2

A toaster receives of electrical energy and transfers usefully to the bread.

Describe the efficiency.

Expected response:

The toaster is efficient.

Check 3

A student says, “The wasted energy is gone.”

Explain why this statement is incorrect.

Expected response:

The energy is not gone. Energy is conserved. The wasted energy has been transferred to the environment, usually as thermal energy or sound energy, where it is less useful.

Investigation (Alternative to Explicit)

Hypothesis

If a heating device transfers a larger proportion of its input energy to the water, then it has a higher efficiency.

Data Collection

Students compare two heating methods, such as:

  • electric kettle
  • immersion heater
  • hot plate and beaker

Measure:

  • mass of water,
  • initial water temperature,
  • final water temperature,
  • electrical energy input, if available from a power meter
  • heating time
  • observations of heat loss to surroundings

Calculate useful energy transferred to the water:

Where:

  • is useful thermal energy transferred to the water
  • is mass of water
  • is specific heat capacity of water
  • is change in temperature

Then calculate efficiency:

Analysis

Students compare:

  • which device had the higher efficiency
  • where energy was wasted
  • how insulation, surface area and heating time affected energy loss
  • why the calculated efficiency may be lower than expected

Evaluation

Students evaluate:

  • uncertainty in temperature measurements
  • heat lost to the container
  • heat lost to the air
  • incomplete transfer of energy to the water
  • whether the system was open or insulated
  • how the investigation could be improved

Possible improvements:

  • use a lid
  • insulate the beaker
  • reduce heating time
  • use a power meter
  • repeat trials
  • measure the mass of water accurately

Problems

The following problems are designed to build conceptual understanding of efficiency before extended calculation work.

  1. Define efficiency in one sentence.

  2. A motor receives electrical energy and lifts a mass. Identify the useful energy output.

  3. A blender becomes warm while operating. Explain why this shows it is not perfectly efficient.

  4. A device has an efficiency of . Describe what this means in terms of energy input and useful energy output.

  5. A heater is designed to warm a room. Is thermal energy a useful or wasted output in this situation? Explain.

  6. A light bulb transfers of energy as light from of electrical energy input. Describe its efficiency.

  7. A car engine has a low efficiency because much of the fuel energy is transferred to the surroundings as heat. Explain why this does not break the law of conservation of energy.

  8. Sketch a Sankey diagram for a device with:

    • energy input
    • useful output
    • wasted output

  9. A student says that a device with efficiency wastes no energy. Explain why this is incorrect.

  10. Describe two ways engineers could improve the efficiency of a heating system.

Followup

Self-check

Students should be able to answer:

  • Can I define efficiency without using the word “speed”?
  • Can I identify useful and wasted energy outputs?
  • Can I explain that wasted energy is not destroyed?
  • Can I connect efficiency to conservation of energy?
  • Can I calculate efficiency using ?
  • Can I explain why real systems are never efficient?

Next Topic

Solve problems involving the efficiency of heat transfers using:

and

Graph View