D2.7 · Compare input, useful output, and efficiency of energy systems

Ontario Grade 11 Physics

Energy and Society

Input energy, useful output, and efficiency

What you will learn

• Identify the energy input and useful energy output of a system.
• Explain why some input energy is not useful for the system’s purpose.
• Calculate and compare the efficiency of energy systems.
• Use energy values and units to judge what an efficiency comparison means.

1. Set the boundary and identify the energy

• Define the system and its purpose before deciding which output is useful.
• Input crosses into the system; output crosses out.
• Energy is measured in joules and is a scalar.

2. Compare input, useful output, and other output

• Other outputs still carry energy, even when they do not serve the chosen purpose.
• Efficiency is a ratio of useful output energy to input energy.
• A larger efficiency means a larger fraction of the input becomes useful output.

3. Read comparisons with care

• Efficiency compares fractions; useful output compares amounts.
• A higher efficiency alone does not prove that a system produces more useful energy.
• Make the intended purpose explicit.

4. A reliable calculation routine

• Keep energy units consistent before substituting.
• Report efficiency as a percentage and check that it is physically reasonable.
• Check both the result and what the comparison actually tells you.

Worked example

Efficiency of a lamp

1. Define the system
   The system is the lamp. Its purpose is producing light, so the useful output is 180 J. The input is 1,200 J. Energy is a scalar, so no positive direction is needed.
2. Use the efficiency relationship
   Divide useful output energy by input energy, then multiply by one hundred to express the fraction as a percentage.
   $$\text{efficiency} = \frac{180\ \mathrm{J}}{1200\ \mathrm{J}} \times 100\%$$
3. Calculate and check
   The joule units cancel. The inputs have two significant figures, so report two significant figures. The result is below one hundred percent, as expected.
   $$\text{efficiency} = 15\%$$

Worked example

Compare energy transfers in a motor

1. Identify the purpose and values
   The system is the motor, and its purpose here is to produce motion. The useful output is 1.8 kJ and the input is 2.4 kJ. The values are already in the same unit.
2. Calculate efficiency
   Use the useful output divided by the input. The kilojoule units cancel, leaving a percentage.
   $$\text{efficiency} = \frac{1.8\ \mathrm{kJ}}{2.4\ \mathrm{kJ}} \times 100\% = 75\%$$
3. Find other output energy
   For this simple comparison, subtract the useful output from the input. This gives energy in outputs that are not the motor’s intended motion output.
   $$E_{\text{other output}} = 2.4\ \mathrm{kJ} - 1.8\ \mathrm{kJ} = 0.6\ \mathrm{kJ}$$

Worked example

Same efficiency, different useful output

1. Calculate System A’s efficiency
   For each system, divide useful output by input. Both values are in joules, so the units cancel.
   $$\text{efficiency}_{A} = \frac{200\ \mathrm{J}}{500\ \mathrm{J}} \times 100\% = 40\%$$
2. Calculate System B’s efficiency
   Use the same relationship for System B. Keeping the method the same makes the comparison fair.
   $$\text{efficiency}_{B} = \frac{600\ \mathrm{J}}{1500\ \mathrm{J}} \times 100\% = 40\%$$
3. Compare the results
   The efficiencies are equal, but the useful output amounts are not. System B produces more useful energy because it receives more input energy.
   $$600\ \mathrm{J} > 200\ \mathrm{J}$$

Common mistakes and how to avoid them

Lesson summary

• Define the system boundary and intended purpose before sorting energy transfers.
• Input energy enters the system; output energy leaves it.
• Useful output is the output that serves the system’s stated purpose.
• Efficiency is useful output energy divided by input energy, expressed as a percentage.
• Compare both efficiency and energy amounts when deciding what a system produces.

Check your understanding

Key terms

System

The object or group of objects being studied.

Boundary

The chosen edge separating the system from its surroundings.

Input energy

Energy transferred into the system across its boundary.

Useful output

Output energy that serves the system’s stated purpose.

Efficiency

The fraction of input energy that becomes useful output, often stated as a percentage.

Scalar

A quantity with a size but no direction, such as energy.

Continue through SPH3U

View the complete SPH3U Ontario Grade 11 Physics curriculum and lessons

• D1.1 · Analyse a technology that transfers or transforms thermal energy
• D1.2 · Assess societal and environmental impacts of energy technologies
• D2.1 · Use work, power, mechanical, thermal, and nuclear energy terminology
• D2.2 · Solve work, force, and displacement problems
• D2.3 · Solve problems using conservation of energy
• D2.4 · Investigate transformations between gravitational and kinetic energy

About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation D2.7. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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