3-2 Efficiency

What is Efficiency?

Let's revisit the three light bulbs from the previous section.

If you put each light bulb into a socket, they would each light up a room about the same. We would say that their light outputs are about the same.

But, energy goes into these bulbs as well, and the power rating on each of the bulbs tells you this information. (Remember, 1 W of power means 1 J of energy goes into it every second.)

• The left bulb has a power rating of 40 W. This means it takes in 40 J of energy every second.

• The middle bulb has a power rating of 13 W. It takes in 13 J of energy every second.

• The right bulb has a power rating of only 9 W, taking in 9 J of energy every second.

Again, all of these light bulbs have about the same light output, but their light inputs are very different. But obviously there's a difference between them.

Efficiency describes what fraction of energy that goes into a device comes out as useful energy. In the case of a light bulb, this is light energy.

Light bulbs, like most other electrical devices, will produce some heat, another type of energy. For a light bulb, heat is not the type of energy which is useful, so it is called waste energy.

There is a type of diagram called a Sankey diagram which can help show where energy goes. Here's one for the left-most light bulb, an incandescent light bulb. Since it has a power rating of 40 W, that means 40 J of energy go into it every second.

Read the diagram left-to-right: the input energy is 40 J, then the two different types of energy that come out (light and heat) are on the right. The sizes of the lines let you compare the amounts of energy.

Now we can calculate the efficiency of the light bulb using the following formula:

Example: Calculate the efficiency of the light bulb.

useful E out = 2 J

E in = 40 J

% efficiency = ?

% efficiency = (useful E out)/(E in) × 100% = (2 J)/(40 J) × 100% = 5%

If your calculator has a % key, don't press it here while doing this calculation. (The % symbol is just in the equation to make everything technically correct.) Hit the following sequence of keys on a normal calculator:

5 ÷ 100 = × 100 =

Here's a Sankey diagram for the middle light bulb:

If you need a little help with this type of calculation, here's a worked-out example:

Types of Energy

When looking at various devices, we have to think about a bunch of different types of energy. Here are a few:

• electrical energy: carried by current in wires

• kinetic energy: the energy of moving things

• chemical energy: stored in chemical bonds between atoms

• solar energy: carried by light, a type of electromagnetic wave

• thermal energy: felt as heat

• sound energy: carried by vibrations through a material such as air

• nuclear energy: held in the nucleus of an atom

Example: An electric fan is plugged into the wall, and is turned on.

a. What type of energy is coming into the fan?

b. What is the type of useful energy coming out of the fan?

Since the fan is plugged into the wall, it has electric energy going into it. That one is easy.

Now let's think about the type of energy coming out of the fan. The whole point of a fan is to make air move around. So, the useful type of energy is the kinetic energy of the air coming out of the fan.

Why is this Important?

In short: our future depends on it.

Canadians use a LOT of energy, when we look at everything we do in our lives. We heat our homes, drive a lot of (mostly) fossil-fuel-powered cars, eat a lot of meat, manufacture a lot of things, and generate a lot of electricity in various ways.

If Canada, and countries like us, were to keep doing what we've been doing for decades, that means more greenhouse gas emissions are going to be released. This changes the climate permanently, making life difficult for a lot of people and other living things.

Here's a short but effective video explaining how efficiency directly ties this all together.

Practice

The Basics

1. An electric fan takes in 480 J of energy, and the moving air has 225 J of kinetic energy. What is the fan's efficiency, in percent?

2. A large electric oven and a small toaster-oven are both used to bake a pan of brownies. Which one would probably be more efficient, and why do you think that is the case?

3. What are the types of energy that go into and out of a television? (Note: there may be more than one type of useful output energy.)

Extensions

1. Incandescent light bulbs used to be used almost everywhere, but now they are relatively rare. What have they been replaced by, and why?

2. Is it possible to have an efficiency over 100%? Why or why not?