1.6–1.7 Energy Dissipation and Efficiency

A free GCSE Physics lesson for AQA (8463) from OBA School: useful and wasted energy, dissipation, efficiency, Sankey diagrams and ways to reduce wasted energy. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Explain the difference between useful and wasted energy, and what happens to energy that is dissipated
• Calculate efficiency as a decimal or a percentage, and rearrange the equation
• Draw and read Sankey diagrams
• Describe how to measure the efficiency of an electric winch
• (Higher tier) describe ways to reduce wasted energy and increase efficiency

Key words

• Useful energy: Energy transferred to the store we want, by the pathway we want.
• Wasted energy: Energy transferred to stores we do not want, usually the thermal store of the surroundings.
• Dissipation: Energy spreading out into the surroundings, warming them slightly. It becomes less useful.
• Efficiency: The fraction of the energy supplied that is usefully transferred. No units.
• Sankey diagram: A flow diagram where the width of each arrow is proportional to the amount of energy.
• Lubrication: Putting oil or grease between moving parts to reduce friction.
• Thermal insulation: A material with low thermal conductivity used to reduce unwanted energy transfer by heating.

Useful and wasted energy

A machine transfers energy for a purpose. Only part of the energy supplied is useful – transferred to the store we want. The rest is wasted: it is dissipated (spread out) to the surroundings, mostly by heating, and sometimes by sound.

• An electric sander: useful energy goes to the kinetic store of the sanding pad; friction heats the pad, the wood and the motor (wasted), and the buzzing is sound (wasted).
• A rowing machine in a gym: your muscles do work against friction and air resistance in the machine, so the machine and the air warm up – and so do you.
• A car gearbox gets hot because of friction between gears. Energy goes from the kinetic store of the gears to the thermal stores of the gearbox and the air around it.

Even useful energy ends up in the surroundings eventually. The energy that turns a car’s wheels is transferred by friction and air resistance to the thermal stores of the tyres, road and air. Energy from a central-heating radiator warms a room, then leaks out through walls and windows.

Key fact: Energy is never destroyed when it is “wasted” – it is still there, but it is so spread out that we cannot use it again.

Calculating efficiency

Because energy is conserved: total input energy = useful output energy + wasted energy.

• efficiency = useful output energy transfer ÷ total input energy transfer useful output = efficiency × total input total input = useful output ÷ efficiency; Notes Both energies in the same unit (J or kJ). Efficiency has no unit. As a decimal it is always less than 1; multiply by 100 for a percentage.

Worked example: an electric motor

A motor is supplied with 150 J. It transfers 45 J to the GPE store of a load.
efficiency = 45 J ÷ 150 J = 0.30; percentage = 0.30 × 100 = 30%
wasted energy = 150 J − 45 J = 105 J

Answer: efficiency = 0.30 (30%)

Worked example: rearranging

A petrol engine is 35% efficient. It is supplied with 2400 J from its fuel.
useful output = 0.35 × 2400 J

Answer: 840 J of useful energy

Exam tip: No device can be more than 100% efficient, because you can never get more energy out than you put in. In practice no machine is 100% efficient: some energy is always dissipated. If your answer is bigger than 1 (or 100%), check you have not divided the wrong way round.

Sankey diagrams

A Sankey diagram shows the energy transfers in a device. The width of each arrow is drawn to scale. The useful energy goes straight on; wasted energy bends away (usually downwards).

Worked example: reading the Sankey diagram

Input = 200 J, useful output = 120 J
efficiency = 120 ÷ 200 = 0.60 = 60%

Answer: 60%

Investigating the efficiency of a winch

• 1. Reset the joulemeter. Switch on and raise a weight through a measured height (e.g. 0.80 m), then switch off.
• 2. Useful energy = increase in GPE store = weight (N) × height raised (m). Input energy = joulemeter reading.
• 3. Efficiency = useful energy ÷ input energy. Repeat with different weights and plot efficiency against weight.
• 4. Switch off and add a few drops of oil to the motor’s axle. Repeat to see if the efficiency increases.
• Safety: protect the floor and your feet from falling weights; stop the winch before the weight reaches the pulley.

Worked example: winch results

A 4.0 N weight is raised 0.80 m. The joulemeter reading goes up by 12.8 J.
useful energy = 4.0 × 0.80 = 3.2 J; efficiency = 3.2 ÷ 12.8 = 0.25

Answer: 25%

Reducing wasted energy (Higher tier)

Machines can be made more efficient by reducing the energy they waste:

• Friction between moving parts heats them; How to reduce it Lubricate with oil or grease; use smooth bearings
• Resistance of wires heats them when there is a current; How to reduce it Use thick wires with low electrical resistance
• Air resistance (drag) on moving objects; How to reduce it Streamline the shape
• Noise and vibration from loose parts; How to reduce it Tighten or fix parts, add damping
• Unwanted heating of the surroundings by a hot object; How to reduce it Add thermal insulation (e.g. lagging on a hot-water tank)

Exam tip: In a 6-mark answer, link each cause of wasted energy to a method and say what it does, e.g. “oiling the chain reduces friction, so less energy is transferred to the thermal store of the chain, so more of the input is useful”.

Common mistakes

• Dividing input by output (giving an efficiency bigger than 1).
• Giving efficiency a unit such as J. It is a ratio with no unit (or a percentage).
• Saying wasted energy is “destroyed” or “lost forever”. It is dissipated to the surroundings.
• Drawing a Sankey diagram where the output arrows do not add up to the input arrow.
• Saying lubrication “removes” friction. It reduces friction.

Revision questions

Try these, then check your answers below each one.

Question 1. A device is supplied with 400 J and transfers 100 J usefully. Calculate its efficiency as a percentage.

Answer: 25 %

Working: 100 ÷ 400 = 0.25 = 25%.

Question 2. A motor is 35% efficient. It is supplied with 2000 J. Calculate the useful energy it transfers.

Answer: 700 J

Working: 0.35 × 2000 = 700 J.

Question 3. What does it mean when energy is dissipated? (Choose from: It spreads out into the surroundings and becomes less useful., It is destroyed., It is stored in a battery., It is transferred usefully..)

Answer: It spreads out into the surroundings and becomes less useful.

Working: Dissipated energy spreads out, usually warming the surroundings slightly. It is still there but no longer useful.

Related lessons

• Previous lesson: 1.5 Kinetic Energy and Elastic Energy Stores
• Next lesson: 1.8 Electrical Appliances
• In this chapter: 1.1 Changes in Energy Stores
• In this chapter: 1.2 Conservation of Energy
• In this chapter: 1.3 Energy and Work

Continue in the full course

This lesson is section 1.6–1.7 (AGCPH0106) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.