# Energy efficiency

> Physics · CIE A-Level 9702
> Source: https://www.owlsprep.com/study/cie-9702-u5-energy-efficiency/

This sub-topic explains how to calculate energy efficiency for any energy conversion system, distinguishes between useful and wasted energy outputs, and explores methods to improve efficiency, a common topic in both multiple choice and structured CIE exam questions.

**Prerequisites:** [Conservation of energy](https://www.owlsprep.com/study/cie-9702-u5-conservation-of-energy/); [Work, energy and power definitions](https://www.owlsprep.com/study/cie-9702-u5-work-energy-power-intro/)

## Learning objectives

- Calculate efficiency of energy conversion systems using energy and power
- Distinguish between useful and wasted energy outputs for different devices
- Apply efficiency concepts to solve quantitative exam problems
- Suggest methods to improve energy efficiency in real-world systems

## Key Definitions and Efficiency Formula

**Energy Efficiency** — A dimensionless measure of how much of the total input energy to a system is converted to useful output energy, ranging from 0 (no useful output) to 1 (all output is useful).

*Notation:* \eta

*Example:* An LED bulb with 30% efficiency converts 30% of input electrical energy to useful light, with 70% wasted as heat.

By conservation of energy, total input energy to any system equals the sum of useful output energy and wasted output energy: $E_{\text{total input}} = E_{\text{useful output}} + E_{\text{wasted output}}$. Efficiency can be calculated using either energy or power, since power is energy per unit time, so the ratio is identical.

$$\eta = \frac{E_{\text{useful output}}}{E_{\text{total input}}} = \frac{P_{\text{useful output}}}{P_{\text{total input}}}$$

**Worked example:** A cyclist pedals a bicycle, producing a total power output of 300 W. 210 W of this power is used to move the bicycle forward. What is the efficiency of the cyclist's body, and how much energy is wasted in 10 minutes?

1. Use the power form of the efficiency formula:
2. $$\eta = \frac{P_{\text{useful}}}{P_{\text{total}}} = \frac{210\ \text{W}}{300\ \text{W}} = 0.7 = 70\%$$
3. Calculate wasted power:
4. $$P_{\text{wasted}} = 300 - 210 = 90\ \text{W}$$
5. Calculate wasted energy over 10 minutes (convert time to seconds):
6. $$E_{\text{wasted}} = P_{\text{wasted}} \times t = 90 \times (10 \times 60) = 54000\ \text{J} = 54\ \text{kJ}$$

> **Exam tip:** Always check if the question asks for efficiency as a decimal or percentage; marks are awarded for the correct output format.

## Classifying Useful and Wasted Energy

A common CIE exam question asks you to identify which energy outputs are useful and which are wasted for a given device. The classification depends on the *intended purpose* of the device, not the type of energy itself.

- Electric kettle: Input = electrical, Useful = thermal (in water), Wasted = thermal to surroundings, sound
- Petrol car engine: Input = chemical (fuel), Useful = kinetic (movement), Wasted = thermal (exhaust/engine), sound
- LED bulb: Input = electrical, Useful = light, Wasted = small amount of thermal
- Phone battery charging: Input = electrical, Useful = chemical (stored), Wasted = thermal

**Check your understanding**

For a central heating boiler used to heat a house, which output energy is useful?

1. Which of the following is the useful output?

   - Thermal energy lost through the boiler flue
   - Thermal energy transferred to the water circulating around the house
   - Sound energy from the boiler pump

   *Answer:* Thermal energy transferred to the water circulating around the house

   *Why:* Correct! The purpose of the boiler is to heat the house, so thermal energy transferred to the circulating water is useful. All other outputs are wasted.

**Worked example:** A 100 W incandescent light bulb has an efficiency of 5%. What is the useful light energy output if it is left on for 2 hours? Identify the wasted energy.

1. Calculate total input energy over 2 hours (convert to joules):
2. $$E_{\text{total}} = P \times t = 100\ \text{W} \times (2 \times 3600\ \text{s}) = 720000\ \text{J}$$
3. Calculate useful light output from efficiency:
4. $$E_{\text{useful}} = \eta \times E_{\text{total}} = 0.05 \times 720000 = 36000\ \text{J}$$
5. Wasted energy is the remaining 95% of input, almost all of which is dissipated as heat to the surroundings, with a tiny amount as sound.

## Improving Energy Efficiency

Exams often ask to suggest practical ways to improve the efficiency of a system. Any improvement targets the source of wasted energy, reducing the amount of energy dissipated for the same useful output.

- Mechanical systems: Lubricate moving parts to reduce frictional heat loss, streamline shapes to reduce air resistance
- Electrical systems: Use low-resistance wires to reduce heat loss, replace incandescent bulbs with efficient LEDs
- Heating systems: Add insulation to reduce heat loss to surroundings, use heat exchangers to recover waste heat from exhaust

**Worked example:** An old home water heater has an efficiency of 55%. A new energy-efficient model has an efficiency of 90%. If a household uses 180 kWh of useful thermal energy per month, how much less electrical energy is used per month with the new heater?

1. Rearrange the efficiency formula to solve for total input energy: $E_{\text{input}} = \frac{E_{\text{useful}}}{\eta}$
2. Calculate input energy for the old heater:
3. $$E_{\text{old}} = \frac{180}{0.55} \approx 327.3\ \text{kWh}$$
4. Calculate input energy for the new heater:
5. $$E_{\text{new}} = \frac{180}{0.90} = 200\ \text{kWh}$$
6. Find the difference in input energy:
7. $$\Delta E = 327.3 - 200 = 127.3\ \text{kWh less per month}$$

> **Exam tip:** When suggesting efficiency improvements, always link your suggestion to the type of wasted energy it reduces to earn full marks.

## Common pitfalls

- **Wrong:** Flipping the efficiency formula to $\eta = \frac{\text{total input}}{\text{useful output}}$
  - Why it fails: This gives an efficiency greater than 1, which violates conservation of energy and is always wrong for real systems
  - Correct: Remember efficiency is the fraction of input that is useful, so always put useful output on top of the fraction
- **Wrong:** Classifying all heat output as wasted energy for any device
  - Why it fails: For devices designed to produce heat (like kettles or boilers), heat is the useful output, not waste
  - Correct: Always classify energy based on the intended purpose of the device, not the type of energy
- **Wrong:** Converting power to energy unnecessarily when efficiency is asked
  - Why it fails: Unnecessary conversions introduce calculation errors and waste exam time
  - Correct: You can use power directly in the efficiency formula, since the time units cancel out in the ratio
- **Wrong:** Accepting calculations that give efficiency greater than 100%
  - Why it fails: No real system can have more useful output than total input, so this always indicates a mistake
  - Correct: If you get efficiency greater than 100%, check your formula flipping first, that is the most common error

## Cheatsheet

| Concept | Key Information |
| --- | --- |
| Efficiency (energy) | $\eta = \frac{\text{Useful energy output}}{\text{Total energy input}}$ |
| Efficiency (power) | $\eta = \frac{\text{Useful power output}}{\text{Total power input}}$ |
| Valid range | $0 \leq \eta \leq 1$ (or $0\% \leq \eta \leq 100\%$) |
| Wasted energy | $E_{\text{wasted}} = E_{\text{total}} - E_{\text{useful}}$ |
| Classification rule | Useful = matches device purpose; Wasted = otherwise |

## What's next

Energy efficiency is a foundational concept that applies to almost all areas of CIE A-Level Physics, from thermal physics and electricity to power generation and renewable energy systems. It is regularly tested in both multiple choice and structured questions, so mastering the calculation and classification of energy outputs is critical for exam success. The principles of efficiency build directly on conservation of energy, and underpin more advanced topics in energy and thermal physics. Below are related topics to explore next:

- [Conservation of Energy](https://www.owlsprep.com/study/cie-9702-u5-conservation-of-energy/)
- [Deformation of solids](https://www.owlsprep.com/study/cie-9702-u6-overview/)
- [Stress, strain and Young modulus](https://www.owlsprep.com/study/cie-9702-u6-stress-strain-and-young-modulus/)

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