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Device Energy
Efficiency

Learn how to measure and evaluate the energy efficiency of real-world devices using the relationship between useful output and total input energy.

High School Physics

What Is Energy Efficiency?

Every device that uses energy converts it from one form to another. A light bulb converts electrical energy into light and heat. A car engine converts chemical energy into motion and heat. But not all of the input energy ends up where we want it.

Visualizing Energy Flow

Total Input Energy DEVICE (energy converter) Useful Output (desired energy) Wasted Energy (heat, sound, etc.)
\(E_{\text{input}} = E_{\text{useful}} + E_{\text{wasted}}\)

Why Efficiency Matters

★ Cost Savings
More efficient devices need less fuel or electricity to do the same job, reducing energy bills.
★ Environment
Higher efficiency means less fuel burned and fewer greenhouse gas emissions for the same output.
★ Performance
Efficient devices waste less energy as heat, so they run cooler and often last longer.

The Efficiency Equation

$$\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\%$$
Useful Output
The energy that does the job you want: light from a bulb, motion from a motor, heat from a heater.
Total Input
All energy supplied to the device: electrical energy from the outlet, chemical energy from fuel, etc.

Efficiency Using Power

Since power is energy per unit time (\( P = \frac{E}{t} \)), we can also write:

$$\eta = \frac{P_{\text{useful}}}{P_{\text{input}}} \times 100\%$$

Efficiency vs. Effectiveness

Efficiency Effectiveness
Meaning How much input energy becomes useful output How well a device performs its task
Measured as Percentage (0% to 100%) Task-specific (lumens, speed, etc.)
Example LED bulb: 40% efficient LED produces 800 lumens (bright enough)
Can it be > 100%? Never Not applicable

How to Calculate Efficiency

1
Identify the useful output. What form of energy is the device designed to produce? (light, motion, heat, sound, etc.)
2
Identify the total input. How much energy (or power) is supplied to the device?
3
Apply the formula. Divide useful output by total input: \(\eta = \frac{E_{\text{useful}}}{E_{\text{input}}} \times 100\%\).
4
Check your answer. The result must be between 0% and 100%. If it is not, re-examine which energy is "useful."

Example 1: Incandescent Bulb

\(60 \text{ W}\)
input
Light: \(6 \text{ W}\)
(useful output)
Heat: \(54 \text{ W}\)
(wasted energy)
$$\eta = \frac{6 \text{ W}}{60 \text{ W}} \times 100\% = 10\%$$

Example 2: Electric Motor

An electric motor is supplied with 500 J of electrical energy. It produces 400 J of kinetic energy (motion) and 100 J of heat and sound.

\(500 \text{ J}\)
Input
\(400 \text{ J}\)
Motion
\(100 \text{ J}\)
Waste

Example 3: Finding Wasted Energy

A television has an efficiency of 25% and uses 200 J of electrical energy per second. How much energy is wasted per second?

1
Find useful output: \(\eta = \frac{E_{\text{useful}}}{E_{\text{input}}}\), so \(E_{\text{useful}} = \eta \times E_{\text{input}} = 0.25 \times 200 = 50 \text{ J}\).
2
Find wasted energy: \(E_{\text{wasted}} = E_{\text{input}} - E_{\text{useful}} = 200 - 50 = 150 \text{ J}\).

Reading a Sankey Diagram

\(1000 \text{ J}\)
Input
\(350 \text{ J}\)
Useful (light)
\(650 \text{ J}\)
Wasted (heat) useful branch is thinner wasted branch is wider

Real-World Device Efficiencies

LED Bulb
\(\sim 40\%\)
 Electric Motor
\(\sim 85\%\)
 Solar Panel
\(\sim 22\%\)
 Car Engine
\(\sim 25\%\)
 Incandescent Bulb
\(\sim 10\%\)
 Electric Heater
\(\sim 100\%\)
 0% 50% 100%

Improving Efficiency

Reduce Friction
Lubricate moving parts to reduce heat generated by friction in engines and motors.
Insulation
Insulate heaters and ovens to prevent useful heat from escaping to the surroundings.
Better Materials
Use superconducting wires or LED technology to reduce energy lost as heat in electrical devices.

Common Mistakes

✕ Swapping Input and Output
Putting input energy on top and useful output on bottom inverts the fraction. Useful output is always the numerator.
✕ Forgetting the 100%
Efficiency is a percentage. Dividing output by input gives a decimal (e.g. 0.8). Multiply by 100 to get 80%.
✕ Misidentifying "Useful"
For a heater, heat IS the useful output: not wasted. Always ask: "What is this device designed to do?"

Summary Table

Concept Key Point Formula / Detail
Efficiency Fraction of input that becomes useful output \(\eta = \frac{E_{\text{useful}}}{E_{\text{input}}} \times 100\%\)
Power form Same ratio but using power \(\eta = \frac{P_{\text{useful}}}{P_{\text{input}}} \times 100\%\)
Wasted energy Energy not converted to useful form \(E_{\text{wasted}} = E_{\text{input}} - E_{\text{useful}}\)
Range Always between 0% and 100% Conservation of energy: no device > 100%
Sankey diagram Arrow width proportional to energy Wider wasted arrow means lower efficiency

Question 1 of 5

A motor uses 800 J of electrical energy and produces 600 J of kinetic energy. What is its efficiency?

Question 2 of 5

A device has an efficiency of 40% and receives 500 J of input energy. How much energy is wasted?

Question 3 of 5

An electric heater converts all of its electrical energy into heat. If the purpose of the device is to heat a room, what is its efficiency?

Question 4 of 5

A car engine has an efficiency of 25%. If the fuel provides 40,000 J of chemical energy, how much useful kinetic energy does the car gain?

Question 5 of 5

Which of the following could never be the efficiency of a real device?