Energy efficiency

Physics· Unit 5: Work, energy and power· 15 min read

1. Key Definitions and Efficiency Formula★★☆☆☆⏱ 4 min

📘 Definition

Energy Efficiency

\eta

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).

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: $E_{total input} = E_{useful output} + E_{wasted output}$ . 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.

2. Classifying Useful and Wasted Energy★★☆☆☆⏱ 5 min

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

✓ Quick check

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

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
Reveal answer
1 —
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.

3. Improving Energy Efficiency★★★☆☆⏱ 6 min

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: $E_{input} = \frac{E _{useful}}{η}$
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.

4. Common Pitfalls

Wrong move:

Flipping the efficiency formula to $η = \frac{total input}{useful output}$

Why:

This gives an efficiency greater than 1, which violates conservation of energy and is always wrong for real systems

Correct move:

Remember efficiency is the fraction of input that is useful, so always put useful output on top of the fraction

Wrong move:

Classifying all heat output as wasted energy for any device

Why:

For devices designed to produce heat (like kettles or boilers), heat is the useful output, not waste

Correct move:

Always classify energy based on the intended purpose of the device, not the type of energy

Wrong move:

Converting power to energy unnecessarily when efficiency is asked

Why:

Unnecessary conversions introduce calculation errors and waste exam time

Correct move:

You can use power directly in the efficiency formula, since the time units cancel out in the ratio

Wrong move:

Accepting calculations that give efficiency greater than 100%

Why:

No real system can have more useful output than total input, so this always indicates a mistake

Correct move:

If you get efficiency greater than 100%, check your formula flipping first, that is the most common error

5. Quick Reference Cheatsheet

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

6. Frequently Asked

Can efficiency ever be 100%?

No, for all real-world energy conversion systems, some energy is always dissipated as waste heat, so efficiency is always less than 100%. Only ideal theoretical systems can have 100% efficiency.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · Paper 1
Calculate efficiency of a heater
2023 · Paper 2
Suggest efficiency improvements for a car
2024 · Paper 1
Classify useful/wasted energy for a fan

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: