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# Making Sense of Energy and Power

James Watt was a great scientist and engineer, known mainly for his work on the steam engine.  Actually, that’s not true.  What he’s really known for is confusing a great many people who deal with energy.  But C. Wilhelm Siemens is to blame for that.  I’m getting ahead of myself, though, so let’s start at the beginning.

#### What is energy?

Energy is an endlessly fascinating subject that reaches into every part of our lives…and beyond.  Because it’s an abstract physical quantity, it took scientists centuries to get a good understanding of it.  Here are the main points.

1.  Energy is the ability to do work.  It’s also a measure of how much work has been done.
2.  Energy exists in many forms:  mechanical, thermal, chemical, nuclear, electromagnetic, gravitational…  It can transform from one form to another.
3.  Energy cannot be created or destroyed.  This is the law of conservation of energy, a  most important law of nature.

As stated above, energy is energy, no matter what form it takes.  For our purposes here, I want to focus mostly on electrical energy.

#### What is power?

Energy is a quantity associated with a certain amount of work.  If you’re going to lift a hundred pound weight, for example, the energy you need to do so depends only on that weight and the height to which you lift it.  You could lift it in one second or one day, and it still takes the same amount of energy.

But something is definitely different when you lift it faster.  And that’s where power comes in.  To use energy (or do work) faster, you need more power.  Power is the time rate of change  of energy.

#### The confusing unit of power

Let’s call one unit of energy a joule (J).  That’s what most of the world does after all.  This unit is named after James Prescott Joule, who did groundbreaking work on this subject.  A joule is a tiny unit of energy.  It takes over 4,000 of them to equal one calorie of food energy.  (What we call a calorie, though, is actually a kilocalorie.)

For an electrical example, turn on a lamp with a 3-way bulb.  On low, it uses energy.  On medium, it uses more energy and provides more light.  On high, it’s the brightest and uses the most energy.

Light bulbs, however, aren’t rated in joules for energy use.  They’re rated in watts, the unit of power.  Wait, watt?!

Yes, really.  If you’re wondering how a time rate of change (power) doesn’t have a per second or per hour or some other such per unit of time, well, now you know the problem.  A watt, thanks to  Herr C. Wilhelm Siemens, is defined as a joule per second.  So, the time unit is in there, but it’s hiding.

#### Calculating energy and power

The relation between energy and power is simple.  Since power is the time rate of change of energy, we can write it like this:

If you measure the amount of energy used in an hour, for example, and divide by one hour, that would give you the average power for that hour.  Let’s say you use 3,600 J in an hour.  The average power would be 3,600 J per hour.   To put it in the confusing unit of the watt, we’d need to convert to seconds for our time unit.  And guess what!  It turns out there are 3,600 seconds in an hour.  Here’s how I like to do the unit conversion:

When you set it up this way, you can see that the hour cancels out, leaving J/s, which is equal to the watt.

Going the other direction, we can find the amount of energy used if know the power and how long the device operates.

So if your three-way lamp operates on high at 20 W and you leave it on for 6 hours, you just multiply to find out how much energy you’ve used.  In this case, 20 W times 6 hours gives you 120 watt-hours (Wh).  Since the electric utility charges for kilowatt-hours (kWh), let’s convert.  As before, we want to cancel out one unit, the watt in this case, and replace it with kilowatts.

That’s not so hard, is it?  Unfortunately, a lot of people have trouble with this unit, the watt, because it hides the time unit.  One of the most common mistakes is that people want to add a time unit to make it look like a rate.  I saw a video recently that threw out a number in watts per hour.  What they really meant was watts.

#### An example

Let’s say you have a heat pump operating at 4,800 W.  How much energy does it use if it runs for 15 minutes?  Let’s do the numbers.

The watt-minute isn’t the unit we want to use, though, so let’s convert it to kilowatt-hours.  I’ll do it in two steps, first going from watt-minutes to watt-hours.  Again, we set up the conversion factor (1 hr = 60 min) as a fraction so the minutes cancel out.  That means the 60 minutes goes in the denominator.

Now, the last step is easy and you can probably do it in your head by just moving the decimal.  But let’s do the whole thing.

#### Keeping things clear

If Herr Siemens had never proposed using the watt as a substitute for joules per second, there’d be a lot less confusion about this.  But that’s not the world we live in.  That means we have to remember that anytime we see units with watts, there’s a hidden time unit within.

One tendency is for people to say, OK, my blow dryer uses 1,500 watts so if I use it for an hour, that’s 1,500 watts per hour.  Nope!  You should multiply there so you end up with watt-hours or kilowatt-hours.  The real answer is that you used 1,500 Wh, or 1.5 kWh.

Units of watts per hour is an important unit in some cases, but it’s not energy.  It tells you have fast the power is changing.  A power plant operator would care about that when they have to make decisions about whether or not to bring on extra capacity as the amount of power being drawn from their grid increases.  (See my article about the duck curve.)

In home energy use, though, the units we deal with are watts (or its multiples or fractions, as noted by prefixes) and watt-hours (also modified by prefixes).

Easy peasy!  Right?

Allison A. Bailes III, PhD is a speaker, writer, building science consultant, and the founder of Energy Vanguard in Decatur, Georgia. He has a doctorate in physics and writes the Energy Vanguard Blog. He also has written a book on building science. You can follow him on Twitter at @EnergyVanguard.

Related Articles

Energy and Power and Confusion and Consternation

Electricity Demand and the Duck Curve

The #1 Reason to Have an All-Electric Home

Photo of electric meter closeup by theilr from flickr.com, used under a Creative Commons license.

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#### This Post Has 16 Comments

1. Allison,

In Point 3, you said “Energy cannot be created or destroyed”
What about conversions between energy and mass? Energy is not conserved, but mass and energy are according to Einstein (E=mc^2).
The only reason that I am nitpicking you on this is that in Point 2, you included nuclear energy, but more importantly, I am an engineer that likes to harass physicists whenever I get the chance!
Now I have to get back to working on my fusion-powered heat pump that requires no external power sources.

1. Roy: Of course you’d be the one to raise that point. Yeah, the broader law includes mass because of Einstein’s most famous equation (but not what got him the Nobel Prize; that was the photoelectric effect). In cases where you do have conversion between mass and energy, you include those conversions and you still have conservation. Well, until someone finds an exception, that is.

Now, tell me more about your perpetual motion machine!

1. My heat pump comes pre-charged with whatever substance I choose (TBD, but probably hydrogen) to fuse to release the energy for the rest of the cycle. For heating, I will just use the energy directly and settle for 100% efficiency. For cooling, I will need to include a heat pump cycle, probably vapor compression, but I am not concerned about its efficiency since my fuel will be very cheap. This will not be a perpetual motion machine, but I do plan to include enough embedded fuel to last 50 years. I could add more, but I want to eventually also have a service business for refueling it. I will release further details during my future development.

2. Paul Szymkiewicz says:

If Einstein’s energy/mass equivalency is to hold, energy is conserved during conversion from mass to energy, or vice versa.

2. David says:

You had to use a hour for the hair dryer example just to confuse my sleepy head. It still works out to 1.5kwh or 1500 watt hours. You had me wondering how many spreadsheets I was going to have to fix.

3. Matt Gancz says:

As a high school physics teacher — and building science aficionado — I loved your article. I spend quite a bit of time conveying this point to 15 and 16-year-olds, and it is a real challenge. For even more fun, try explaining thermal conductance vs resistance values to teenagers!

4. Allison,
I am assuming that you will do a follow up on IP units (formerly known as English) for energy and power to show the superiority of these units. Power = Energy (Btu)/Time(hr), i.e., Btu/hr. But then again, some of these IP clowns express it as Btuh which drives me crazy.

1. Paul Szymkiewicz says:

Superiority of English units? You’re kidding, right?

1. Would I kid about a thing like this 😉
But seriously, IP units (Inch-Pounds, even the English abandoned them, so we had to rename them) are a fact of life in the U.S., especially in our industry. Almost all engineering schools only teach SI and completely ignore IP. They seem to think that they can help accelerate the transition by doing this, but really it is just laziness. SI units are easier to use and teach. I taught engineering for quite a few years at a major university and all of my classes were dual units. The students didn’t like it, but at least they were better prepared for jobs in the U.S. I have been in industry for quite few more years, and am disappointed that I have to hire new graduates who don’t understand our measurement system.

1. Paul Szymkiewicz says:

Well, K-12 schools, at least around Southeast, have been trying hard to introduce SI units. The dinosaur in the room seems to be the industry. Change is hard.

And yet, for some reason, as Allison already mentioned, we’ve been calling light bulbs in Watts! This SI/IP cacophony is quite unique to the US.

1. I fully support teaching SI at all educational levels, but not at the expense of IP units. We need both. Our industry uses both, especially, those of us that serve global markets. As for “watts”, that is an IP unit for electricity, it just isn’t used for thermal power.

This is somewhat analogous to schools that quit teaching cursive writing as being outdated. Many schools have regretted that decision and are now putting cursive back in the curriculum.

2. Paul Szymkiewicz says:

Watt is SI.

1. Chris Edwards says:

With a nod to Abbott and Costello: it’s an international system of units of measurement, derived from the metric system. 😀

5. Chris Edwards says:

People do find this confusing, so thank you for addressing it so clearly! The “kW/h” confusion always reminds me of the common use of “24/7” to mean “24×7”. And thank you for using SI units, without which it would probably be even more confusing! (Speaking of which, are there any plans for an SI edition of your new book?)

6. Bob Seaton says:

I agree with RoyC — the expression “btuh” is especially egregious. It seems to be meaningless, like kWhh or “foot-pound minutes” or “mile hours” would be meaningless.

1. Chris Edwards says:

Apparently btuh would measure angular momentum. 🙂 I sometimes have to reassure myself that kWh/day is just a measure of (usually average) power.

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