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A.3.9 Efficiency Formula — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 40 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.3.9 Efficiency Formula — IB PHYSICS SL notes: Calculate efficiency as a ratio of useful output to total input for energy or power, including multi-stage systems.Efficiency = the ratio of the useful power or energy output of a system to its total power or energy input.Equation —…

  • High and low
  • Never 100%
  • Depends on the system
  • Wasted energy
  • Closing the account
  • Same quantity and interval

Part 1 of 9Definition

Efficiency
Efficiency the ratio of the useful power or energy output of a system to its total power or energy input.
Equation
  • η = Eout/Ein = Pout/Pin.
  • η (eta) is the efficiency.
  • E is the energy in J and P the power in W.
In words
  • η = useful work out / total work in = useful power out / total power in.
Form
  • Form a ratio between 0 and 1, or a percentage when multiplied by 100.
No unit
  • No unit the numerator and denominator have the same units.
High and low
  • High and low a high efficiency means most of the energy is useful, and a low one means most is wasted.
Never 100%
  • Never 100% real devices always dissipate some energy as thermal energy; above 100% signals an error.
    • (or a heat pump, which uses the coefficient of performance)

Part 2 of 9Useful and wasted energy

Useful and wasted energy
Depends on the system
  • Depends on the system the useful transfer is the one wanted.
Kettle
  • Kettle energy to the water is useful, while energy to the casing and surrounding air is wasted.
Wasted energy
  • Wasted energy wasted = input − useful output = input × (1 − η).
Closing the account
  • Closing the account useful plus wasted must equal the input.

Part 3 of 9Using the formula

1Same quantity and interval
  • Same quantity and interval use energy or power on both top and bottom over the same time.
2Rearrangements
  • Rearrangements useful output = η × input, and input = useful output / η.
3Input larger than output
  • Input larger than output divide, do not multiply, to find the input.
4Wording
  • Wording a device that wastes 30% of its input has an efficiency of 70%.
5Required format
  • Required format give a ratio or a percentage as the question asks.
6Percentage of the right quantity
  • Percentage of the right quantity in a pump where only 20% of the kinetic energy becomes potential energy, apply 0.2 to the kinetic energy.

Part 4 of 9Where energy goes

Friction
  • Friction it produces thermal energy and sound.
Electrical resistance
  • Joule heating.
Other sources
  • Other sources air resistance, incomplete combustion and heat escaping through poor insulation.
Reducing waste
  • Reducing waste lubrication, better materials, streamlining, improved insulation and recovering waste heat.
DeviceTypical efficiency
Filament lampabout 5%
Modern LEDabout 40%
Petrol engine25 to 35%
Large electric motorabove 90%
Power-station chain35 to 45%

Part 5 of 9Systems in series

Systems in series
Chain
  • Chain the output of one device is the input of the next.
Overall efficiency
  • η = η1 × η2 × η3, which is smaller than the smallest individual efficiency.
Sankey diagram
  • Sankey diagram the useful arrow narrows repeatedly.

Part 6 of 9Mechanical machines

Efficiency
  • / (effort × distance moved by effort).
    • (load × distance moved by load)
More friction
  • More friction the effort is larger and the efficiency lower for the same output work.
Frictionless ramp
  • 100% efficient, as the work in lifting equals the work in pushing up the ramp.

Part 7 of 9Measuring efficiency

Method
  • Method measure the useful output and the input over the same time.
  • A motor lifting a massthe gain in gravitational potential energy compared with the electrical energy VIt.
Uncertainty
  • Uncertainty timing and meter readings, and friction in bearings lowers the result.
Improving
  • Improving reducing friction, using lighter moving parts and improving insulation.

Part 8 of 9Links

Heat engines
  • Heat engines the Carnot efficiency is the theoretical maximum and depends on the reservoir temperatures.
Power supply
  • Power supply useful power delivered divided by power drawn.
Transmission
  • Transmission high-voltage lines reduce I2R losses.

Part 9 of 9More from the specification

More from the specification
Efficiency
  • Efficiency useful output energy or power divided by total input, often given as a percentage
Elastic potential energy
  • Elastic potential energy half the spring constant times extension squared, stored in a deformed spring
Mechanical energy conservation
  • Mechanical energy conservation gravitational potential energy converts to kinetic energy,
    • so speed equals the square root of 2gh when released from a height
Horizontal spring system
  • Horizontal spring system an object on a spring exchanges kinetic and elastic energy, and any friction reduces efficiency
Final speed
  • Speed at the end, v
Elastic
  • Returns to original shape when force is removed.
Constant
  • Not changing.
Density
  • Mass per unit volume.
Component
  • Part of a vector along one axis.
Position
  • Location relative to a reference point.
Mechanical energy
  • Sum of kinetic and potential energy.
Energy density
  • The energy available per unit mass or area of a resource.
Energy conservation
  • Mgh = ½Mv2 + ½Iω2.
W = Fs
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)

Key terms

TermMeaning
EfficiencyRatio of useful output energy (or power) to total input energy (or power)
Useful energyEnergy transferred in the way that is wanted
Wasted energyEnergy transferred in ways that are not wanted
Energy dissipationSpreading of energy into the surroundings, usually as thermal energy
Overall efficiencyProduct of the efficiencies of devices in sequence
Percentage efficiencyEfficiency expressed as a ratio multiplied by 100

Avoid these mistakes

1
Multiplying by the efficiency when the input is wanted — divide the output by the efficiency.
2
Writing efficiency with a unit — it is a ratio.
3
Getting an efficiency above 100% — check the quantities and units.
4
Adding efficiencies in series — multiply them.
5
Applying a percentage to the wrong energy — apply it to the input of that stage.

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