Wednesday, November 29, 2017

Six Ways to Measure Your Electricity Use

Maybe you want to save money. Maybe you want to save the planet. Maybe you just want to understand what’s going on inside your home. Or maybe, like me, you’re motivated in all three of these ways. Whatever the reason, let’s talk about how you can measure your household electricity use.

In this article I’ll describe six practical electricity measurement methods, starting with the simplest and progressing toward those that require more effort. Beginners will want to get comfortable with each method before moving on to the next. More advanced readers should feel free to skip ahead to the methods they don’t already know.

Ready? Here we go...

1. Look at your bills.

You probably receive an electricity bill every month. Of course the bill shows how much money you owe, but it also shows how much electricity you’ve used. (If your bill gets sent to a landlord who doesn’t let you see it, then you’ll have to skip this method and go on to the next one.)

Even if all you really care about is money, it’s not enough to look only at the dollar amount on your bill because that amount might not be a good measure of how much electricity you’ve used. It probably includes a base rate that you pay even if you use no electricity, and it might include other utilities besides electricity. Worse, your utility company might have you on an “equal billing” plan that averages your bill over the course of a year, hiding the interesting seasonal changes.

So you want to look on your bill for a number that’s not in dollars but rather in kilowatt-hours, or kWh for short. That number is the actual amount of electrical energy you used during the month. For example, here’s my bill from February 2014, during which I used 146 kWh:

Don’t be shocked if your monthly usage is a lot more than mine! According to official government data, the average American household uses nearly 900 kWh per month.

Besides comparing your monthly electricity use to the average American household (or, if you prefer, to my own), you can learn a lot by comparing to your own usage in other months. Look at a whole year’s worth of bills if you can, to see the seasonal patterns. Many Americans use the most electricity in the summer, when they use their air conditioners; others use the most in the winter, for heating and lighting.

What’s a kilowatt-hour anyway?

A kilowatt-hour is a unit for measuring energy, just as a mile is a unit for measuring distance and a dollar is a unit for measuring money. As with those other units, you’ll develop an intuitive feel for kilowatt-hours as you encounter more examples. Here are a few common household uses that typically consume approximately one kWh each:
  • Running a central air conditioner for 20 minutes
  • Running an electric space heater for 40 minutes
  • Running a modern no-frills refrigerator for one day
  • Baking a batch of cookies in an electric oven
  • Drying 1/3 of a load of laundry in an electric dryer
  • Leaving an LED light bulb on for a few days
  • Fully charging a laptop computer battery 10 times
And what does each of these activities cost? Most Americans pay between 10 and 20 cents for a kWh of electrical energy.

At some point you may want to compare electrical energy to other forms of energy, such as chemical energy (in food or fuels), or thermal energy (heat). Because we can convert one type of energy into another, we really should use the same unit to measure all types—but we don’t! Our inconvenient tradition is to measure food energy in Calories (abbreviated Cal, which scientists call large calories or kilocalories) and, here in the U.S., to measure heat in British thermal units (Btu). You can convert between kWh, Cal, and Btu using Google or various other web sites. The approximate conversion factors are
1 kWh = 860 Cal = 3400 Btu.
So the typical American consumes enough food to provide two to three kWh of energy each day (1700 to 2600 Cal), and a typical household furnace can provide about 22 kWh of heat each hour (75,000 Btu). A gallon of gasoline, if you’re curious, provides about 31,000 Cal, or 120,000 Btu, or 36 kWh of energy.

2. Read your meter.

The main problem with electricity bills is that you get only one per month! But the power company determines your billed usage by reading your meter, and you can read it yourself just as easily, as often as you like. (The exception would be if you live in a multi-unit building in which the electricity isn’t metered separately for each unit. In that case you’ll have to go on to method 3.)

Reading the old dial-style meters used to be a bit tricky, but nowadays nearly everyone has a digital meter with a simple numerical readout:

The number on the display, 24362 in this case, is the number of kWh of electricity used since some time far in the past—probably whenever the meter was first installed. (The number may blink off and back on every few seconds, in which case you may need to wait a moment to see it.)

So all you need to do is write down the number from the meter (and the time when you read it), then read it again an hour or a day or a week later, and subtract the two values to get the electrical energy usage during that time period. It’s a great exercise to read your meter once a day for a few weeks or months, and to keep a log of the readings, like this:

From this kind of data you can get a very good idea of what kinds of activity use the most electricity: When did you run your air conditioner? When did you do laundry? How much energy does your house use on days when nobody is home?

3. Multiply power by time.

Some electrical devices always use energy at the same rate, whenever they’re turned on. The most familiar example is an ordinary (non-dimmable) light bulb. The rate of energy use is what scientists call power, and we measure it in units of watts. Old incandescent light bulbs commonly used 60 or 100 watts, but modern LED bulbs put out just as much light while using only 10 or 15 watts.

To determine the amount of energy used by a device, you multiply its rate of energy use (that is, the power, in watts) by the amount of time that it’s on:
Energy = Power × Time.
If we measure the power in watts and the time in hours, then we get the energy in units of watt-hours. A kilowatt-hour is 1000 watt-hours, so we divide by 1000 to get the energy in kWh. For example, the energy consumed by a 10-watt bulb left on for 24 hours would be
Energy = (10 watts)(24 hours) = 240 watt-hours = 0.24 kWh,
where I divided by 1000 in the last step. You can similarly estimate the energy use of a 40-watt ceiling fan running for six hours, or of a 1500-watt hairdryer that’s turned on for 10 minutes. Look for power consumption ratings printed on the backs of appliances, or in the owner’s manuals or on the manufacturers’ web sites. Or consult an online list of typical power consumption values. The only catch is that many appliances use less than their nominal power rating under most conditions, or they cycle on and off automatically so that it’s hard to measure exactly how long they’re actually on.

4. Get a plug-in appliance meter.

For a mere $20 or so, you can buy a Kill A Watt P4400 meter, which makes it easy to measure the energy use of any plug-in 120-volt appliance. Use it for a few days to track down unnecessary energy use, and it can easily repay your investment many times over. (There are a number of competing products on the market, but the Kill A Watt is the most common, and is very affordable, so that’s the one I’ll describe. I’ve never seen one in a store, but you can purchase it through many online retailers.)

To use the Kill A Watt meter you simply plug it into a wall outlet (through an extention cord if necessary), then plug your appliance into the meter.  Initially it just displays the line voltage (120 or so), but if you press the rightmost button once, it will display the total energy used since you plugged it in, in kWh. Press the same button again and it displays the time since you plugged it in, so you don’t even need to write that down.

You’ll definitely want to use the meter to test your refrigerator(s), preferably for a day or longer. Other good candidates for testing include televisions, computers, washing machines, and electric blankets.

For some devices you may also want to try pressing the meter’s middle button. Then the display will show the instantaneous rate of energy use (power), in watts or kilowatts. This number will probably fluctuate, especially for something like a refrigerator that periodically cycles on and off. But if the power is reasonably steady and you already know how long the device will be in use, then a quick power reading can save you from having to wait for the energy measurement to build up. Just multiply the power by the time, as described above in method 3.

Don’t forget to test low-power devices that are on all the time, such as clocks and WiFi routers and televisions that never go completely off.

5. Time the little blinking squares.

The main drawback of a plug-in meter is that you can’t use it to measure hard-wired devices or 240-volt appliances. For these, and for those times when you’re caught without a plug-in meter within reach, you can go back out to the power company’s meter, equipped with a stopwatch (probably the one on your smartphone).

This time, instead of looking at the numbers on the display, you want to watch the little blinking squares at the bottom. They should go on and off following a six-step pattern:

(The pattern is meant to mimic the horizontal rotating disk in an old mechanical meter, as if half the disk’s edge is dark and the other half is light, with the front turning from left to right.) Each change in the pattern—a square going on or off—indicates one watt-hour of energy usage. Use your stopwatch to time how long it takes between one change and the next. Or, if the pattern is changing quickly, measure the time for the entire six-step cycle and divide by six. Either way, you can now calculate the power being used in your home as follows:
Power in watts = 3600 / (measured time in seconds).
Explanation: The energy used during your measured time interval was one watt-hour, or 3600 watt-seconds (since an hour is 3600 seconds). But energy = power × time, so to calculate the power, you divide the energy by the measured time.

You’ve now measured the rate at which all the electrical devices in your home are using energy at a particular moment. The trick, then, is to make this measurement with everything except the device(s) you care about turned off. Try it once with all the major appliances turned off, and the refrigerator unplugged or turned off at the breaker panel, to get a power value for all the little stuff in the home that’s using a small amount of power 24 hours a day. Then turn on a major appliance like the furnace or air conditioner or electric dryer, and make another measurement.

Once you know the power of some device of interest, calculate its total energy use by multiplying by how long it’s on, as in method 3.

6. Install a fancy monitoring system.

The five simple methods described above are more than enough to give you the big picture of your home electricity use, including the information you need to save a lot of money (and help save the planet). But if you want to understand every detail of what’s going on in your home, and you’ve exhausted what you can reasonably learn from the first five methods, then the next step is to install a home energy monitoring system. These systems start at about $150, and the installation process is nontrivial.

Electricity monitoring systems are available in several varieties, from several vendors. I have the Efergy Engage Elite Hub System (recommended by Mr. Money Mustache), which is one of the most affordable and easy to use. But I wish I had spent a little more for Efergy’s True Power Meter, which would be more accurate.

The main components of these systems are a pair of clamp-around sensors that you install on the main feed wires coming into your breaker panel. To install them you need to turn off the electricity (otherwise you may die!), open up the panel, and then hope that there’s enough room to fit the clamps around the stiff wires. (I had a tough time with one of them, but finally managed.) If you have any doubts about your ability to do this installation safely, you should hire an electrician.

For a true power meter there would also be a wire to make an electrical connection inside the panel. Either way, the Efergy sensors connect to a transmitter just outside the panel, which beams the data wirelessly to one or two receivers. The data is simply an instantaneous power measurement for your whole house (or at least as much as is powered by this particular panel), equivalent to what you measured in method 5 above. But the monitoring system makes these measurements continually, day and night, with no need for you to use a stopwatch or a calculator.

One type of Efergy receiver contains a digital display for immediate readout, updating every ten seconds. This can sometimes be handy, but in my opinion it’s not worth the price or the installation effort by itself. The other type of receiver, though, is a “hub” that uploads the data over your internet router to Efergy’s web site, where you can look up (and even download) minute-by-minute power levels at any later time, from any location, through your web browser. It’s a data junkie’s dream. Here’s a sample of my own data as viewed on the Efergy web site, showing a steady base load, the refrigerator and furnace cycling on and off, and a big spike from cooking breakfast on my electric stovetop:

As I mentioned above, my basic Efergy sensor isn’t always accurate. Specifically, it’s accurate for “resistive loads” like the stove and other heating appliances, but it reads too high a value for anything with a motor in it, like a furnace blower or a washing machine. The reason has to do with the intricacies of alternating current, and the best solution would be to use a slightly more sophisticated system such as the Efergy True Power Meter or The Energy Detective (a competing product that costs a bit more). The power company’s meter also makes accurate measurements, as does a Kill A Watt meter, so I’ve simply used those to calibrate my interpretation of the Efergy data.

Saturday, April 15, 2017

Qubits or Wave Mechanics?

A few days ago Sean Carroll tweeted a poll:

As someone who’s been wrestling with this question for 30 years, I perked up at this tweet, and not only voted but even tweeted a couple of responses. It’s a fascinating question! 

The second answer is the traditional one, and there are many good arguments for it: a solid experimental basis in phenomena that are easy to demonstrate; vivid images of wavefunctions for building intuition from classical waves; and a huge array of practical applications to atomic physics, chemistry, and materials science. The down-side is that the mathematics of partial differential equations and infinite-dimensional function spaces is pretty formidable. Mastering all this math takes up a lot of time and tends to obscure the logical structure of the subject. Especially if your main interest is in the new field of quantum information science, this is a long and indirect road to take.

Hence the alternative of starting with two-state systems, which are mathematically simpler, logically clearer, and directly applicable to quantum information science. The difficulty here is the high level of abstraction, with an almost complete lack of familiar-looking pictures and, inevitably, no direct connection to most of the traditional quantum phenomena or applications.

A fundamental challenge with teaching quantum mechanics is that it’s like the proverbial Elephant of Indostan, with many dissimilar parts whose connections are difficult for novices to discern. From various angles, quantum mechanics can appear to be about Geiger counters and interference patterns, or differential equations and their boundary conditions, or matrices and their eigenvalues, or abstract symbol-pushing with kets and commutators, or summing over all possible histories, or unitary transformations on entangled qubits. Stepping back to get a view of the whole beast is challenging even for experts, and bewildering for “blind” beginners.

I think most physicists would agree that an undergraduate degree in physics should include some experience with both wave mechanics and two-state systems. Carroll’s Twitter poll, though, asks not what a degree program should include, but how we should introduce physics students to quantum mechanics. That’s a hard question, and one’s answer could easily depend on any number of further assumptions:
  • Who exactly are these “physics students”? Students taking an introductory course, which may be their last course in physics? Typical undergraduate physics majors? Undergraduate physics majors at Caltech? What’s their math background?
  • How long an introduction are we talking about here? A single lecture, or a few weeks, or an entire course?
  • Will this introduction be followed by further study of quantum mechanics? In other words, is the question merely about the order in which we cover topics, or is it also about the totality of what we should teach, and what we can justifiably omit, when we design a course or a curriculum?
  • Are we constrained to use existing resources, including textbooks, instructor expertise, and locally available lab equipment? Or are we dreaming about an ideal world in which any resources we might want are magically provided?
Due to all these ambiguities, we should interpret the poll results with caution. Carroll’s interpretation was that the winning second option “probably benefits from familiarity bias. I’ll call it a tie”—so I infer that his own preference is to start with two-state systems. I agree that some respondents were probably biased in favor of what’s familiar, but I also suspect that Carroll’s Twitter followers have more interest in fundamental theory, and less interest in atoms and molecules, than would a random sampling of physicists.  I also wonder if some respondents weren’t biased in favor of what’s unfamiliar: it’s easy to suggest a radical curricular change if you’ve never actually tried it out and had to live with the unintended consequences. Carroll himself is currently teaching an advanced quantum course that emphasizes two-state systems, but as far as I can tell he has never taught a first course in quantum mechanics for undergraduates.

No professional quantum mechanics teacher should be completely unfamiliar with the two-state-systems-first approach, because it’s used, more or less, in Volume III of the Feynman Lectures on Physics, published in 1965 (thirty years before Schumacher and Wootters coined the term qubit!). I say “more or less” because Feynman actually starts with two-slit interference and other wave phenomena, and then he introduces a three-state system (spin 1) before settling into a lengthy treatment of spin 1/2 and other two-state systems.

There are also some well-known graduate-level texts that begin with two-state systems:  Baym’s Lectures on Quantum Mechanics (1969) and Sakurai’s Modern Quantum Mechanics (1985).

At the upper-division undergraduate level, the earliest text I know of that takes the two-state-systems-first approach is Townsend, which first appeared in 1992. Several others have appeared more recently: Le Bellac (2006), Schumacher and Westmoreland (2010), Beck (2012), and McIntyre (2012). Instructors who want to take this approach in such a course can no longer complain about the lack of suitable textbooks.

But at the lower-division level, where most students first encounter quantum mechanics, the pickings are still slim. Nobody actually teaches out the Feynman Lectures. You could try to use a few chapters out of one of the more advanced books (McIntyre would probably work best), or you could use Styer’s slim text The Strange World of Quantum Mechanics (2000, written for a course for non-science majors), or you could use the new (2017) edition of Moore’s introductory Six Ideas textbook (which inserts three short chapters on spin and “quantum weirdness” in between electron interference and wavefunctions), or you could try Susskind and Friedman’s Theoretical Minimum paperback (2014, an insightful tour of the formalism with little mention of applications—see Styer’s review here).

I suspect that the time is ripe for someone to write an otherwise-conventional sophomore-level “modern physics” textbook that introduces quantum mechanics via two-state systems and qubits before moving on to wave mechanics. I really wish Moore would expand his Units R and Q into a more complete “modern physics” text!

Personally, I’ve had a soft spot for spin ever since I took a quantum class from Tom Moore in 1982, at the end of my sophomore year (after a conventional “modern physics” class) at Carleton College. This half-term class was mostly based on Gillespie’s marvelous little book, which lays out the logic of quantum mechanics for a single spinless particle in one dimension. But Moore departed from the book to introduce us to two-state and three-state spin systems as well, even writing a simple computer simulation of successive spin measurements for us to use in a homework exercise. The following year I saw more spin-1/2 quantum mechanics in the philosophy of science course that I took from David Sipfle, using notes prepared by Mike Casper, probably inspired by the Feynman Lectures. So when I took Casper’s senior-level quantum course after another year, I was well prepared.

A few years later, while procrastinating on my thesis work during graduate school, I converted and expanded Moore’s computer simulation into a graphics-based Macintosh program. Moore and I published a paper about this program, and how to use it at various levels, in 1993. From there the concept made its way into Moore’s Six Ideas course, and also into the Oregon State Paradigms curriculum and McIntyre’s book. Last year I ported the program to a modern web app.

I recount this history mainly to establish my credentials as an experienced advocate for, and contributor to, the teaching of quantum mechanics via two-state (and three-state) spin systems. So you may be surprised to know that on Carroll’s quiz I actually voted against this approach and in favor of starting with the traditional wave mechanics. And in my own teaching I’ve actually never started with spin systems: I’ve always started with one-dimensional wave mechanics in both upper-division quantum mechanics and sophomore-level modern physics. In calculus-based introductory physics I teach a little about wave mechanics and don’t really cover two-state systems at all. My reasoning is simply that for these students, in these courses, the balance of the pros and cons listed above seems to weigh in favor of starting with wave mechanics.

Meanwhile, I think there are opportunities to improve on the way we teach wave mechanics. One serious drawback with most wave mechanics text materials is their relative neglect of systems of more than one particle. As a result, students tend to develop some misconceptions about multiparticle systems, and don’t hear about entangled states—an important and trendy topic—as early as they could. I’ve recently written a paper on how to address this deficiency, with some accompanying software to help students visualize entangled wavefunctions.

My bottom-line opinion, though, is that the best answer to Carroll’s question depends on both the students’ needs and the instructor’s inclinations. Back in 1989, Bob Romer published an editorial in the American Journal of Physics titled “Spin-1/2 quantum mechanics?—Not in my introductory course!” But he hastened to clarify: “not in my course, thank you, but maybe in yours”—enthusiastically encouraging instructors to innovate and to follow whatever teaching plan they believe in. I wholeheartedly agree.