D. Physics: Principles and Applications of Electricity · Electricity: Charges, Circuits and Energy

Energy Transformations and the Efficiency of Electrical Devices

D2.8 D1.2 A1.2 A1.5About 70 minutes

Learning goals

I can identify the energy transformations in devices that consume or produce electrical energy.
I can explain that energy is conserved, and that the energy that is not useful is usually thermal energy.
I can calculate efficiency = useful output energy ÷ total input energy × 100%.
I can determine the efficiency of a real device by measurement, and compare devices.
I can draw and read a Sankey diagram.

Words to know

energy transformation
A change of energy from one form to another.

law of conservation of energy
Energy cannot be created or destroyed; it can only be transferred or transformed. Total energy out = total energy in.

useful energy
The output energy in the form you want from a device, such as light from a lamp.

wasted energy
Output energy in forms you do not want, usually thermal energy (and sometimes sound). It is not destroyed, just not useful for the job.

efficiency
The percentage of input energy that becomes useful output energy: (useful output ÷ total input) × 100%.

Sankey diagram
A flow diagram where the width of each arrow shows the amount of energy.

EnerGuide label
A Canadian label on major appliances that shows how much electrical energy the model uses in a year, in kWh.

Hot bulbs and cool bulbs

If you have ever touched an old-style incandescent bulb that had been on for a while, you know it gets very hot. An LED bulb that gives the same light is only warm. Both bulbs turn electrical energy into light, but one wastes much more of it as heat. Today you will measure how efficient a device is: how much of the energy put in comes out in a useful form.

Energy transformations in devices

Every electrical device transforms energy. Some devices consume electrical energy, and some produce it.

Devices that consume electrical energy:

Lamp: electrical → light + thermal
Kettle or toaster: electrical → thermal (+ a little sound)
Fan or blender motor: electrical → kinetic (motion) + thermal + sound
Speaker: electrical → sound + thermal
Charging a phone battery: electrical → chemical potential + thermal

Devices that produce electrical energy:

Battery: chemical potential → electrical
Generator (in hydro, wind, nuclear and gas stations): kinetic → electrical
Solar (photovoltaic) panel: radiant (light) → electrical

The useful output is in bold above. In almost every transformation, some energy also becomes thermal energy that is not useful.

Energy transformations in devices that produce electrical energy. A generator turns the kinetic energy of a spinning turbine into electrical energy; a solar panel turns light energy directly into electrical energy.

Conservation of energy and efficiency

Energy is never created or destroyed. So:

total input energy = useful output energy + wasted energy

The efficiency of a device tells you what percentage of the input becomes useful:

efficiency = (useful output energy ÷ total input energy) × 100%

You can also use power instead of energy (useful output power ÷ input power × 100%), since both are measured over the same time.

No device is 100% efficient, because some energy always becomes thermal energy through resistance, friction or sound. The higher the efficiency, the less energy (and money) is wasted.

Sankey diagrams for two bulbs (example numbers). The width of each band shows how much energy goes where. Out of every 100 J in, the incandescent bulb gives 5 J of light (5% efficient); the LED gives 40 J of light (40% efficient).

Worked example

Example 1: Efficiency of a bulb

A 60 W incandescent bulb gives out 3.0 J of light energy each second. What is its efficiency? How much energy is wasted each second?

Input energy each second = 60 J (60 W = 60 J/s).
Efficiency = 3.0 J ÷ 60 J × 100% = 5.0%
Wasted = 60 J − 3.0 J = 57 J each second, mostly as thermal energy.

The bulb is 5.0% efficient; 57 J per second is wasted as thermal energy.

Worked example

Example 2: Efficiency of a kettle from measurements

A 1500 W kettle takes 4.0 minutes to bring 1.0 kg of water from 20 °C to 100 °C. Heating that water needs 334 400 J of energy. What is the kettle's efficiency?

Input energy: E = P × t = 1500 W × 240 s = 360 000 J.
Useful output energy (to heat the water) = 334 400 J.
Efficiency = 334 400 ÷ 360 000 × 100% ≈ 93%.

The kettle is about 93% efficient. The other 7% heats the kettle itself and the surrounding air, and makes some sound.

Worked example

Example 3: A device that produces electrical energy

On a sunny day, 1000 J of sunlight energy falls on a solar panel each second, and the panel produces 200 W of electrical power. What is its efficiency?

Input power = 1000 J/s = 1000 W.
Useful output power = 200 W (electrical).
Efficiency = 200 ÷ 1000 × 100% = 20%.

The panel is 20% efficient. The rest of the sunlight's energy is reflected or warms the panel.

Device	Input energy	Useful output	Main wasted form
Incandescent bulb	Electrical	Light	Thermal
LED bulb	Electrical	Light	Thermal (less)
Electric kettle	Electrical	Thermal (of the water)	Thermal (of the kettle and air), sound
Electric motor	Electrical	Kinetic	Thermal, sound
Generator	Kinetic	Electrical	Thermal, sound
Solar panel	Radiant (light)	Electrical	Thermal, reflected light

Energy transformations in devices that consume or produce electrical energy.

Efficiency checklist

Efficiency can never be more than 100%. If you get more, the numbers are upside down.
Use the same units on top and bottom (J and J, or W and W).
Look for Canada's EnerGuide label on appliances, which shows the yearly kWh, and the ENERGY STAR symbol on the most efficient models.

Hands-on activity

Measure the efficiency of your kettle

You need: an electric kettle with its power rating on the label, a measuring cup, a kitchen thermometer, a timer, and a grown-up.

Find the kettle's power rating (W) on its label.
Measure exactly 1.0 L of cold tap water (1.0 L of water has a mass of about 1.0 kg) and pour it into the kettle. Measure its starting temperature.
Switch on the kettle and start the timer. Stop the timer when the kettle switches itself off. (Do not remove the lid or put the thermometer in boiling water.) Take the final temperature as 100 °C.
Calculate: input energy = power (W) × time (s).
Calculate the useful energy: 4180 J × mass (kg) × temperature rise (°C). (This formula, for heating water, is given to you here; you will meet it again in later science courses.)
Efficiency = useful ÷ input × 100%.

Model answer: 1500 W for 260 s gives 390 000 J in. Water from 10 °C to 100 °C: 4180 × 1.0 × 90 = 376 200 J. Efficiency = 376 200 ÷ 390 000 × 100% ≈ 96% (your kettle will differ). Ideas for sources of error: the kettle keeps heating for a moment after the water first boils, some water evaporates, and the label power is not exact.

Safety (grown-up note): A grown-up must handle the kettle and the boiling water. Keep hands and face away from the steam, keep the cord away from the counter edge, and never open the lid while it is boiling.

Just for fun

An old incandescent bulb is really a small heater that happens to glow a little. In our example, 95 out of every 100 joules became thermal energy, so the "light" bulb was mostly a "warm" bulb.

Your turn

Give the energy transformation in (a) a fan, (b) a solar panel, (c) a battery-powered radio.

Write the formula for efficiency.

A motor uses 500 J of electrical energy and produces 400 J of kinetic energy. Find its efficiency and the energy wasted.

A 10 W LED bulb gives 3.5 W of light. What is its efficiency?

Why can no device be 100% efficient?

What does the width of an arrow show in a Sankey diagram?

More practice: warm-up

What is the useful output of a toaster?

What form of energy is usually wasted?

A device has an input of 200 J and a useful output of 50 J. Efficiency?

Which device produces electrical energy from motion?

State the law of conservation of energy.

More practice: on your own

A 1200 W hair dryer runs for 5.0 minutes. 1.0 × 10⁵ J of its output is wasted as sound and heating of the dryer itself. Find the useful output and the efficiency.

A generator at a small hydro station receives 5.0 MJ of kinetic energy from the water each second and produces 4.5 MW of electrical power. What is its efficiency?

A 40% efficient device must deliver 600 J of useful energy. How much input energy is needed?

Two fridges do the same job. The EnerGuide label says fridge A uses 380 kWh/year and fridge B uses 520 kWh/year. At 12¢/kWh, how much would fridge A save over 10 years?

Identify all the energy transformations when you charge a phone and then watch a video on it.

Challenge

Sketch (or describe) a Sankey diagram for a 2000 W electric motor that is 85% efficient, where the wasted energy is 250 W thermal and the rest sound.

Energy from natural gas passes through a power station (40% efficient), then power lines (95% efficient), then an incandescent bulb (5% efficient). What percentage of the original chemical energy becomes light?

Design a fair test to compare the efficiency of two kettles. Name the variables and the calculation.

Check your understanding

Quiz

What is the main useful energy output of a fan?

A solar panel transforms:

A device uses 800 J and gives 200 J of useful energy. Its efficiency is:

Which statement is true?

A generator produces 90 kJ of electrical energy from 100 kJ of kinetic energy. Its efficiency is:

What does an EnerGuide label show?

For parents and teachers

Big idea: Expectation D2.8 asks students to determine the efficiency of electrical devices that consume or produce electrical energy and to identify the energy transformations. The kettle activity is a real measurement (A1.2) that needs a grown-up for safety (A1.5).

Common difficulties:

Efficiency upside down (giving more than 100%). Useful output always goes on top.
Mixing units, such as W on top and J on the bottom, or minutes instead of seconds.
"Wasted energy disappears." It is still there, mostly as thermal energy; it just is not useful.

How to help: Do the kettle activity together (you handle the boiling water). Look for EnerGuide and ENERGY STAR labels when shopping and compare yearly kWh. The bulb efficiencies in this lesson are example numbers for practice; real values depend on the product.