Efficiency

Overview

Efficiency sits at the heart of OCR GCSE Physics Topic 2, Energy. It is the quantitative expression of a principle that underpins all of modern engineering and environmental science: no real device transfers all of its input energy into a useful output. Understanding efficiency means understanding where energy goes, why it matters, and how engineers and scientists work to minimise waste. For the exam, this topic rewards candidates who combine accurate calculation with precise scientific language — two skills that this guide will develop in parallel.

Exam questions on efficiency appear in a variety of formats. Candidates may be asked to calculate efficiency from given data (AO2, typically 2–3 marks), explain how to improve efficiency using specific mechanisms (AO2/AO3, typically 3–4 marks), or evaluate the effectiveness of a proposed improvement (AO3, typically 4–5 marks). The topic connects directly to energy stores and transfers, Sankey diagrams, the law of conservation of energy, and the broader context of energy resources and sustainability — all of which examiners exploit in synoptic questions.

This guide covers every aspect of Efficiency as assessed by OCR: the core equation, its application with both energy (joules) and power (watts), the language of energy dissipation, and the four key mechanisms for improving efficiency. Worked examples, memory hooks, and practice questions are included to build both confidence and exam technique.

Key Concepts

Concept 1: The Efficiency Equation

Efficiency is defined as the proportion of total input energy that is transferred to a useful energy store. The equation is:

**Efficiency = Useful Energy Output (J) ÷ Total Energy Input (J)**This produces a decimal between 0 and 1. To express efficiency as a percentage, multiply the decimal by 100:

Efficiency (%) = (Useful Energy Output ÷ Total Energy Input) × 100The critical constraint is that efficiency can never exceed 1 (or 100%). This is a direct consequence of the law of conservation of energy: you cannot get more useful energy out of a device than you put in. If a calculation produces a value greater than 1, the candidate has inverted the fraction — dividing total input by useful output rather than the other way round. Examiners award zero marks for a final answer greater than 1 and will not apply error carried forward in such cases.

Real-world analogy: Think of efficiency as the 'hit rate' of a basketball player. If they take 10 shots and score 7 baskets, their hit rate is 7/10 = 0.70 or 70%. They cannot score more baskets than they take shots — just as a device cannot output more useful energy than it receives as input.

Concept 2: Using Power Instead of Energy

A common source of confusion is that exam questions sometimes provide power (in watts, W) rather than energy (in joules, J). The efficiency formula applies identically:

**Efficiency = Useful Power Output (W) ÷ Total Power Input (W)**This works because power is simply energy per unit time (P = E/t). When you divide useful power by total power, the time cancels out, leaving the same ratio as the energy version. Candidates who recognise this can solve power-based efficiency questions without any additional steps.

Example: A motor has a total power input of 800 W and a useful mechanical power output of 600 W. Efficiency = 600 ÷ 800 = 0.75 = 75%.

Concept 3: Energy Dissipation — The Language of Wasted Energy

When a device is less than 100% efficient, the 'missing' energy is not destroyed. The law of conservation of energy states that energy cannot be created or destroyed, only transferred between stores. Wasted energy is dissipated — it spreads out into the thermal energy store of the surroundings, causing a very slight increase in temperature of the environment.

The word 'dissipated' is non-negotiable in exam answers. Examiners will not award marks for responses that state energy is 'lost', 'disappears', or is 'destroyed'. The correct phrasing is:

"The wasted energy is dissipated to the thermal energy store of the surroundings."

This matters because it reflects a genuine physical understanding: the energy still exists, it has simply been transferred to a store (the thermal store of the surroundings) from which it is extremely difficult to recover for useful purposes. This concept of energy becoming increasingly 'spread out' and less useful is related to the idea of entropy, though this is not required at GCSE level.

Concept 4: Calculating Wasted Energy

Candidates must be able to work fluently in both directions. Given total input and useful output, wasted energy is found by subtraction:

Wasted Energy = Total Energy Input − Useful Energy OutputConversely, if a question provides total input and wasted energy, the useful output must be calculated first before the efficiency formula is applied. This is a deliberate exam technique: questions that give wasted energy instead of useful output are specifically designed to test whether candidates understand the distinction. Misidentifying wasted energy as useful output is one of the most frequently penalised errors in OCR mark schemes.

Concept 5: Sankey Diagrams

Sankey diagrams are a visual representation of energy flow through a device. The width of each arrow is proportional to the amount of energy it represents. The input arrow enters from the left; useful output continues to the right; wasted outputs branch off (typically upward or downward). Key skills for Sankey diagrams include: reading off energy values from arrow widths, calculating efficiency from the diagram, and sketching a Sankey diagram for a described device. Examiners frequently ask candidates to compare two Sankey diagrams and identify which device is more efficient.

Concept 6: Improving Efficiency

Exam questions asking candidates to 'suggest how efficiency could be improved' require specific, mechanistically justified answers. Four key mechanisms must be known:

In every case, the answer must state the mechanism AND explicitly link it to reduced energy dissipation. A response that says only 'use insulation' without explaining the energy consequence will typically earn only 1 of 2 available marks.

Mathematical Relationships

Formula 1 — Efficiency (decimal form):
Efficiency = Useful Energy Output (J) / Total Energy Input (J)
Must memorise — not given on OCR formula sheet

Formula 2 — Efficiency (percentage form):
Efficiency (%) = [Useful Energy Output / Total Energy Input] × 100
Derived from Formula 1 — not separately given

Formula 3 — Power version:
Efficiency = Useful Power Output (W) / Total Power Input (W)
Same formula, different quantities — applies identically

Formula 4 — Wasted energy:
Wasted Energy = Total Energy Input − Useful Energy Output
Derived from conservation of energy

Unit note: Energy is always in joules (J); power is always in watts (W). Efficiency itself is dimensionless (no unit) as a decimal, or expressed in % as a percentage. Candidates frequently lose marks by attaching incorrect units to the efficiency value.

Practical Applications

Efficiency is not a purely theoretical concept — it has profound real-world significance. The transition from incandescent filament bulbs (approximately 5–10% efficient) to LED bulbs (approximately 80–90% efficient) represents one of the most impactful efficiency improvements in domestic energy use. In transport, the development of hybrid and electric vehicles addresses the relatively low efficiency of internal combustion engines (typically 25–40%). Industrial motors, power stations, and heating systems are all designed with efficiency as a central engineering constraint.

For OCR GCSE, candidates are not required to complete a specific required practical on efficiency, but they may encounter data from investigations involving ramps, pulleys, or electrical circuits in which efficiency is calculated from measured input and output energies. Graph skills relevant to this topic include plotting efficiency against a variable (such as load mass) and interpreting the shape of the resulting curve.