recall and understand that the efficiency of a system is the ratio of useful energy output from the system to the total energy input

Energy Conservation and Efficiency

What is Efficiency?

Efficiency (denoted by the Greek letter η) is the ratio of useful energy output to the total energy input. It is a dimensionless number, usually expressed as a percentage.

Formula: \$η = \dfrac{W{\text{out}}}{Q{\text{in}}}\$

Example: A 100 J electric bulb produces 70 J of light. \$η = \dfrac{70}{100} = 0.70\$ or 70 %.

🧠 Remember: Efficiency can never be greater than 1 (or 100 %) because some energy is always lost as heat or friction.

Analogy: The Water‑Pipe System

Think of a pipe carrying water. Some water leaks out as it travels. The water that reaches the other side is the useful energy; the leaked water is lost energy. The efficiency is the fraction of water that makes it through.

  • Useful water: \$Q_{\text{useful}}\$

  • Lost water: \$Q_{\text{lost}}\$

  • Total water: \$Q{\text{total}} = Q{\text{useful}} + Q_{\text{lost}}\$

  • Efficiency: \$η = \dfrac{Q{\text{useful}}}{Q{\text{total}}}\$

Example Calculation

SystemInput Energy (J)Useful Output (J)Efficiency
Electric motor200150\$150/200 = 0.75\$ (75 %)
Thermal engine500200\$200/500 = 0.40\$ (40 %)

Exam Tip

When a question asks for efficiency:

  1. Identify the useful output (work, light, etc.).

  2. Identify the total input (energy supplied).

  3. Write the ratio as \$η = \dfrac{W{\text{out}}}{Q{\text{in}}}\$.

  4. Convert to a percentage if the question requires it.

🔍 Check units: Both numerator and denominator must be in joules (or equivalent).

📝 If power is given instead of energy, multiply by time to obtain energy before calculating efficiency.

Common Mistakes to Avoid

  • Using the wrong numerator (e.g., heat output instead of work output).

  • Forgetting to express the result as a percentage.

  • Assuming efficiency can exceed 100 %.

Quick Recap

Efficiency tells us how well a system converts input energy into useful work or light. Keep the formula \$η = \dfrac{W{\text{out}}}{Q{\text{in}}}\$ handy, practice with different examples, and remember that no real system can be 100 % efficient.