Efficiency and Energy Dissipation

This lesson covers energy efficiency and dissipation as required by the Edexcel GCSE Physics specification (1PH0), Topic 3: Conservation of Energy. You need to understand how to calculate efficiency, interpret Sankey diagrams, and explain how wasted energy can be reduced.

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What Is Efficiency?

Efficiency is a measure of how much of the input energy is usefully transferred. It tells you what fraction (or percentage) of the total energy input is converted to useful output.

The Equations

As a decimal (fraction):

$\text{Efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}$Efficiency=total energy inputuseful energy output​

As a percentage:

$\text{Efficiency (\%)} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$Efficiency (%)=total energy inputuseful energy output​×100%

You can also use power instead of energy:

$\text{Efficiency} = \frac{\text{useful power output}}{\text{total power input}}$Efficiency=total power inputuseful power output​

Key Points

• Efficiency is always less than 1 (or less than 100%) — no device is 100% efficient.
• Efficiency has no units — it is a ratio.
• An efficiency of 0.75 means 75% of the input energy is usefully transferred, and 25% is wasted.

Exam Tip: Check whether the question asks for efficiency as a decimal or a percentage. If the answer is 0.8, that is 80%. If you are asked for a percentage and you write 0.8, you will lose the mark.

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Wasted Energy and Dissipation

In every energy transfer, some energy is wasted — transferred to stores that are not useful. This wasted energy is almost always transferred to the thermal store of the surroundings.

Dissipation means the wasted energy spreads out into the surroundings and becomes increasingly difficult to use for anything.

Why Is Wasted Energy a Problem?

• Once energy is dissipated into the surroundings as thermal energy, it cannot easily be recovered or used.
• The energy has not been destroyed — it still exists (conservation of energy) — but it is now spread out over a large area and at a low temperature, making it practically useless.

Common Sources of Wasted Energy

Source	Mechanism	Wasted Energy Goes To
Friction between moving parts	Surfaces rub against each other	Thermal store of surfaces and surroundings
Air resistance	Object pushes through air	Thermal store of air and object
Electrical resistance	Current flows through wires	Thermal store of wires and surroundings
Sound	Vibrations from moving parts	Thermal store of surroundings (eventually)

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Reducing Wasted Energy

There are several ways to improve the efficiency of a device by reducing energy dissipation:

Method	How It Reduces Waste	Example
Lubrication	Reduces friction between moving parts	Oil in a car engine
Streamlining	Reduces air resistance (drag)	Aerodynamic shape of a car or cyclist's helmet
Thermal insulation	Reduces unwanted energy transfer by heating	Insulation around a hot water tank
Using low-resistance components	Reduces electrical heating in wires	Thicker wires, superconductors

Exam Tip: When asked "How can the efficiency of X be improved?", always state the method and explain how it reduces wasted energy. For example: "Lubricate the moving parts to reduce friction, which reduces the energy wasted as thermal energy in the surroundings."

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Worked Examples

Example 1: Calculating Efficiency

Question: A motor uses 500 J of electrical energy and converts 350 J to useful kinetic energy. Calculate the efficiency as a percentage.

Solution:

$\text{Efficiency} = \frac{350}{500} \times 100\% = 70\%$Efficiency=500350​×100%=70%

Example 2: Finding Useful Output

Question: A light bulb is 15% efficient and uses 60 J of energy. How much useful light energy does it produce?

Solution:

$\text{Useful output} = \text{Efficiency} \times \text{Total input} = 0.15 \times 60 = 9 \text{ J}$Useful output=Efficiency×Total input=0.15×60=9 J

The remaining 60 − 9 = 51 J is wasted as thermal energy.

Example 3: Finding Total Input

Question: A motor has an efficiency of 0.4 and produces 200 J of useful energy. What was the total energy input?

Solution:

$\text{Total input} = \frac{\text{Useful output}}{\text{Efficiency}} = \frac{200}{0.4} = 500 \text{ J}$Total input=EfficiencyUseful output​=0.4200​=500 J

Example 4: Using Power

Question: A wind turbine has a power input of 25 000 W and a useful power output of 7500 W. What is its efficiency?

Solution:

$\text{Efficiency} = \frac{7500}{25{,}000} = 0.3 = 30\%$Efficiency=25,0007500​=0.3=30%

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Wasted Energy Calculation

You can also calculate the wasted energy:

$\text{Wasted energy} = \text{Total input} - \text{Useful output}$Wasted energy=Total input−Useful output

Example: A car engine has an input of 10 000 J and is 25% efficient.

• Useful output = 0.25 × 10 000 = 2500 J
• Wasted energy = 10 000 − 2500 = 7500 J (transferred to thermal store of surroundings)

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Sankey Diagrams

A Sankey diagram is a type of flow diagram that shows energy transfers. The width of the arrows is proportional to the amount of energy.

How to Read a Sankey Diagram

• The input arrow (on the left) shows the total energy input.
• The useful output arrow continues forward (usually to the right).
• The wasted energy arrow(s) branch off (usually downwards).
• The width of each arrow is proportional to the energy it represents.
• The total width of all output arrows must equal the width of the input arrow (conservation of energy).

Example: Sankey Diagram for a Light Bulb

flowchart LR
    A["100 J\nElectrical\nenergy input"] --> B["10 J\nUseful light\noutput"]
    A --> C["90 J\nWasted thermal\nenergy"]

In a proper Sankey diagram, the arrow for wasted thermal energy (90 J) would be 9 times wider than the useful light arrow (10 J).

Drawing a Sankey Diagram

To draw a Sankey diagram:

1. Draw the input arrow on the left — its width represents the total input energy.
2. Split the arrow into useful output (continuing right) and wasted output (branching down).
3. Make sure the widths are proportional to the energy values.
4. Label each arrow with the energy value and the type of energy.

Reading Efficiency from a Sankey Diagram

$\text{Efficiency} = \frac{\text{Width of useful output arrow}}{\text{Width of input arrow}}$Efficiency=Width of input arrowWidth of useful output arrow​

Exam Tip: In the exam you may be asked to draw or complete a Sankey diagram. Use a ruler to draw the arrows and make sure the widths are accurately proportional. If the input is 200 J and useful output is 50 J, the useful arrow should be exactly ¼ of the width of the input arrow.

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Comparing Efficiencies