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Lesson 7 of 8Principles & Applications of Electricity
Unit 4 · Lesson 7 of 8

Efficiency and Energy Transformations in Devices

Every electrical device transforms electrical energy into other forms, some useful and some wasted (usually as thermal energy). Percent efficiency compares the useful output energy to the total input energy. Learn to calculate efficiency, read Sankey diagrams, compare common devices, and use ENERGY STAR and EnerGuide labels and heat pumps to save energy.

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Key things to remember

  1. 1Conservation of energy: energy is never created or destroyed, only transformed. Input energy = useful output + wasted energy.
  2. 2Percent efficiency
  3. 3Wasted energy is usually thermal energy (and some sound) that spreads into the surroundings.
  4. 4In a Sankey diagram, arrow widths are proportional to energy, and the output arrows add up to the input arrow.
  5. 5LED bulbs are several times more efficient than incandescent bulbs; ENERGY STAR and EnerGuide labels help compare products.

If you ever touched an old-style incandescent light bulb after it had been on, you know it gets hot enough to burn you. That heat is not what the bulb was for. The bulb's job is to make light, and most of the energy it takes in comes out as thermal energy instead. An LED bulb gives the same light while staying much cooler, because far less of its energy is wasted. Comparing how well devices turn energy into what we actually want is called efficiency, and it is one of the biggest tools we have for saving energy and money.

Energy transformations in devices

The law of conservation of energy says energy cannot be created or destroyed; it can only change from one form to another. An electrical device takes in electrical energy and transforms it. Some of the output is the form you want, the useful energy. The rest is wasted energy (sometimes called "lost" energy), most often thermal energy that warms the surroundings, plus some sound. The energy is not destroyed; it just spreads out in a form that is no longer useful to us. So: input energy = useful output energy + wasted energy.

DeviceInputUseful outputMain wasted output
LampElectricalLightThermal
Electric fanElectricalKinetic (moving air)Thermal, sound
KettleElectricalThermal (in the water)Thermal (to the room), sound
SpeakerElectricalSoundThermal
Charging a phoneElectricalChemical (stored in the battery)Thermal (the charger and phone get warm)
BlenderElectricalKinetic (spinning blades)Sound, thermal
The input is electrical for every device; what counts as useful depends on the device's job.

Percent efficiency

Efficiency is the fraction of the input energy that comes out in the useful form. It is usually written as a percentage. A device that turns 20 J of every 100 J into the useful form is 20% efficient. Because energy cannot be created, the useful output can never be more than the input, so a device's efficiency cannot be more than 100% (heat pumps seem to break this rule; see the callout below for why they do not). You can use power instead of energy in the formula too, as long as both are in the same unit.

Both energies must be in the same unit (for example both in joules).
Incandescent bulbefficiency = 5 J ÷ 100 J = 5%Electricalenergy in100 JLight5 J (useful)Thermal energy95 J (wasted)LED bulbefficiency ≈ 40 J ÷ 100 J = 40%Electricalenergy in100 JLight40 J (useful)Thermal energy60 J (wasted)Widths to scale (10 J = 8 px). LED values approximate.
Fig 1Sankey diagrams for two bulbs, with arrow widths drawn to scale. Incandescent: 100 J of electrical energy in, 5 J out as light and 95 J as thermal energy. LED: 100 J in, roughly 40 J as light and 60 J as thermal energy (approximate).

A Sankey diagram shows where the energy goes. The input arrow enters on the left. Its width stands for the amount of energy. The arrow splits: the useful energy continues straight on, and the wasted energy branches off, usually bending downward. Because widths are to scale, the branches must add up to the width of the input arrow. A glance tells you how efficient the device is: a wide useful arrow means high efficiency.

Energy changes form at every arrow. The total never changes.Chemicalwaste heatThermalwaste heatKineticwaste heatElectricalwaste heatLightwaste heatEvery step loses some energy to the surroundings as heat — that loss is what efficiency measures.Nothing is destroyed. It simply ends up in a form too dispersed to be useful.
Fig 2A chain of energy changes from a fuel to a lamp: chemical energy in the fuel becomes thermal, then kinetic (a spinning turbine), then electrical, then light. Some energy leaves as waste heat at every step, which is what efficiency measures.
Device or systemApproximate efficiency
Incandescent light bulb (light out)about 5%
Typical solar panelabout 20%
Gasoline car engineabout 20 to 30%
LED light bulb (light out)roughly 30 to 40%
Large electric motorabout 90% or more
Hydroelectric generating stationabout 90%
Rough values; real devices vary with design and how they are used. In a long chain of transformations, like fuel to electricity to light, the efficiencies of the steps multiply, so the overall efficiency is lower than that of any single step.

Choosing efficient devices

  • ENERGY STAR is a symbol on products, such as fridges, washers, TVs and windows, that meet strict efficiency standards; certified models are among the most efficient in their category.
  • EnerGuide labels on major appliances in Canada show how many kWh the appliance is expected to use in a year, so you can compare models and estimate running costs before you buy.
  • Heat pumps heat a home by moving thermal energy that is already outdoors (even from cold winter air) to the inside, the way a fridge moves heat out of its food compartment. Cold-climate heat pumps can work through most Ontario winters.
  • Small habits add up: switching to LED bulbs, air-drying laundry, using cold-water wash cycles, sealing drafts and turning off devices when not in use.
Do heat pumps break the 100% limit?
A heat pump can deliver about 2 to 4 joules of heat to your home for each joule of electrical energy it uses. That does not break conservation of energy, because most of that heat is not made from electricity: it is moved from outside. The electrical energy only runs the pump. That is why Ontario is encouraging heat pumps as a way to heat homes with less natural gas.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1
An incandescent bulb takes in 100 J of electrical energy and gives out 5 J of light. Find its percent efficiency and the energy wasted.
Example 2
An electric motor is 80% efficient. It takes in 500 J of electrical energy. How much useful kinetic energy does it produce, and how much energy is wasted?
Example 3
A 1500 W kettle runs for 2.0 minutes. The water gains 153 000 J of thermal energy. What is the kettle's percent efficiency?

Where marks get lost

  • Dividing the useful energy by the wasted energy instead of by the total input. Efficiency compares useful output to total input.
  • Getting an efficiency above 100%. That usually means the numbers were flipped (input divided by output). Useful output always goes on top.
  • Saying wasted energy is destroyed. It is still there, mostly as thermal energy spread through the surroundings; it is just no longer useful.
  • Forgetting to multiply by 100%. An answer of 0.85 is the decimal; the percent efficiency is 85%.
  • Calling a heat pump more than 100% efficient at making heat from electricity. It moves heat from outdoors; the electricity only runs the pump.

Flashcards 8

Law of conservation of energy
Useful energy
Wasted energy
Percent efficiency
+ 4 more

Practice

1
A device takes in 200 J of electrical energy and gives out 50 J of useful energy. What is its percent efficiency?
%
2
A motor is 90% efficient and takes in 2000 J of electrical energy. How much useful kinetic energy does it produce, in joules?
J
3
A blender is 75% efficient and takes in 800 J of electrical energy. How much energy is wasted, in joules?
J
4
A 1000 W kettle runs for 3.0 minutes, and the water gains 144 000 J of thermal energy. What is the kettle's percent efficiency?
%
5
In a Sankey diagram for a fan, the input arrow is 100 units wide and the useful (kinetic) arrow is 70 units wide. What does the rest of the diagram show?
6
Why does an LED bulb cost less to run than an incandescent bulb that gives the same amount of light?
7
Match each device to its main useful energy transformation.
Electric fan
Speaker
LED bulb
Kettle
Charging a phone
8
Sort these from LOWEST to HIGHEST typical efficiency.
  1. 1Gasoline car engine
  2. 2Incandescent light bulb
  3. 3Large electric motor
9
What is the name of the symbol found on products that meet strict energy-efficiency standards, such as fridges and TVs?
10
A heat pump delivers 3 J of heat to a house for every 1 J of electrical energy it uses. Which explanation is correct?

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