IGCSEPhysicsEdexcelRevision Notes4. Energy Resources & Energy TransfersEnergy Stores & TransfersEfficiency

Efficiency (Edexcel IGCSE Physics)

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Efficiency

What is efficiency in an energy transfer?

  • The efficiency of a system is a measure of the amount of wasted energy in an energy transfer
  • Efficiency is defined as:

The ratio of the useful energy output from a system to its total energy output

  • If a system has high efficiency, this means most of the energy transferred is useful
  • If a system has low efficiency, this means most of the energy transferred is wasted

The equation for efficiency

  • Efficiency is represented as a percentage
  • The equation for efficiency is:

efficiency space equals fraction numerator space useful space energy space output over denominator total space energy space output end fraction space cross times space 100 percent sign

  • Total energy output is equal to total energy input due to the principle of conservation of energy

total energy input = total energy output

  • Total energy output is the sum of the useful energy output and the wasted energy

total energy output = useful energy output + wasted energy 

Worked example

The blades of a fan are turned by an electric motor. In one second, 300 J of energy is transferred electrically from the mains supply. 85 J is wasted due to friction and sound.

Calculate the efficiency of the motor.

Step 1: List the known quantities

  • Total energy input = 300 J
  • Total wasted energy = 85 J

Step 2: State the equation for efficiency

efficiency space equals fraction numerator space useful space energy space output over denominator total space energy space output end fraction space cross times space 100 percent sign 

Step 3: Determine total energy output

  • Due to the conservation of energy:

total energy input = total energy output

  • Therefore, total energy output = 300 J

Step 4: Calculate the useful energy output

total energy output = useful energy output + wasted energy

useful energy output = total energy output − wasted energy

useful energy output = 300 − 85  = 215 J 

Step 5: Substitute these values into the equation for efficiency

efficiency space equals fraction numerator space useful space energy space output over denominator total space energy space output end fraction space cross times space 100 percent sign

efficiency space equals fraction numerator space 215 space over denominator 300 end fraction space cross times space 100 percent sign

efficiency space equals space 72 percent sign

Examiner Tip

The equation for efficiency can be used to give a ratio (between 0 and 1) or percentage (between 0 and 100%)

If the question asks for efficiency as a ratio, give your answer as a fraction or decimal (do not multiply by 100%)

If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it:

  • if the ratio = 0.25, percentage = 0.25 × 100 = 25 %

Remember that efficiency has no units (only %)

Sankey diagrams

What are Sankey diagrams?

  • Sankey diagrams are visual representations of energy transfers
    • Sankey diagrams are characterised by the splitting arrows that show the proportions of the energy transfers taking place

  • The different parts of the arrow in a Sankey diagram represent the different energy transfers:
    • The left-hand side of the arrow (the flat end) represents the energy transferred into the system
    • The straight arrow pointing to the right represents the energy that ends up in the desired store; this is the useful energy output
    • The arrows that bend away represent the wasted energy

Example of a Sankey diagram

8-1-2-sankey-diagram-demonstration_sl-physics-rn

Total energy in, wasted energy and useful energy out shown on a Sankey diagram

  • The width of each arrow on a Sankey diagram is proportional to the amount of energy being transferred
  • As a result of the conversation of energy:

Total energy in = total energy out

 

Total energy in = Useful energy out + Wasted energy

  • A Sankey diagram for a modern efficient light bulb will look very different from that for an old filament light bulb
  • A more efficient light bulb has less wasted energy
    • This is shown by the smaller arrow downwards representing the heat energy

Sankey diagram of light bulbs

cie-igcse-1-7-4-phy-rn-sankey-comparison-new

Sankey diagram for modern vs. old filament light bulb

Worked example

An electric motor is used to lift a weight. The Sankey diagram below represents the energy transfers in the system.

WE Sankey Question image, downloadable IGCSE & GCSE Physics revision notes

Calculate the amount of wasted energy.

 

Answer:

Step 1: State the conservation of energy

  • Energy cannot be created or destroyed, it can only be transferred from one store to another
  • This means that:

total energy in = useful energy out + wasted energy

Step 2: Rearrange the equation for the wasted energy

wasted energy = total energy in – useful energy out

Step 3: Substitute the values from the diagram

500 – 120 = 380 J

Examiner Tip

How to draw a Sankey diagram

  • Drawing a good Sankey diagram takes practice.
  • Start by planning your diagram using graph paper or a ruler:
    • How many squares or mm wide will you make the input arrow?
    • How many squares or mm wide will the useful energy out arrow need to be?
    • How many squares or mm wide must the wasted arrow be?

  • Next, start drawing the diagram one step at a time:
    • Draw the left-hand side of the arrow, along with the line going across the top
    • Next add the useful energy out arrow, making sure it is the correct width
    • Now carefully mark the start and end of the wasted arrow – make sure your marks are the correct distance apart
    • Finally join the markings together, finishing the wasted energy arrow

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    Leander

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    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.