Building Proficiency in Efficiency

Pre-Lab: Efficiency in Theory and in Practice

A Bit of History

The early 1800’s saw the birth of motors, generators, and heat engines. Naturally, scientists of the era sought to understand the fundamental limitations of these devices. Were there even limitations? Could perpetual motion be achieved?

Perhaps the simplest way to describe the limitations of such a machine is with its efficiency. In very loose benefit but very useful terminology, the efficiency of anything is given by � = . Exactly what the cost and cost benefit are depends on what kind of device you are considering.

For an electric motor, the efficiency is a pretty simple concept. The benefit of a motor is the work that it does while the cost is the electrical energy that we put into it. That is,

work the motor does � = !"#"$ electrical energy the motors uses

The concepts of work and energy were actually not especially well defined until the mid 1800’s when James Joule was doing his famous work. Eventually, though, it became clear that motors could not have an efficiency greater than 1. Today we see this simply as a statement of conservation of energy, also known as the First Law of Thermodynamics. In practice, no motors achieve perfect efficiency because of friction and the formation of eddy currents. These are practical constraints, however, rather than fundamental theoretical constraints. (The same analysis holds true for electrical generators, so we will not discuss them in any detail.)

Efficiency is often discussed in regard to heat engines, devices that use a temperature difference in order to do work. Heat goes into the engine and some work comes out. Conservation of energy requires that the work done is no more than the heat that goes in (that is, that the efficiency is less than or equal to 1). Heat engines have a history which dates back hundreds of years B.C. Many intellectual titans have worked on heat engines (Leonardo da Vinci, Robert Boyle, Christiaan Huygens, James Watt, Nikola Tesla, and many others). One man, Sadi Carnot, found that no matter how perfect your heat engine, you can never harvest all the energy put into the engine, meaning the efficiency of any heat engine must be strictly less than 1. This unavoidable imperfection is a loose statement of the Second Law of Thermodynamics. If this subject gets you all hot and bothered you should check out Appendix A.

Defining the Efficiency of a Light Bulb

Your goal in Part I of this lab is to quantify how the efficiency of an LED bulb compares to the efficiency of an incandescent bulb. This is a relative efficiency. We say relative because we don’t have the tools to find the absolute efficiency. An absolute efficiency for a light bulb would be energy emitted as visible light � = . Unfortunately, we don’t have the equipment to measure the energy electrical energy used by the bulb emitted as visible light. It turns out, though, that the relative efficiency we will find is in some ways more meaningful than the absolute efficiency given by the equation above.

You will be measuring the light output from the bulbs using the Vernier Light Sensor. The light sensor won’t give you a reading in watts; rather, it will give you a reading in a unit called lux. The lux is a unit of brightness as perceived by a typical human. There is no simple way to convert it into units of energy or power, which is why finding an absolute efficiency won’t be possible for us. But let’s think about this. A light bulb is designed to allow humans to see. Isn’t the perceived brightness of a light bulb the benefit of the bulb? We want to know how much brightness we get for the power we put in.

There’s a second problem with calculating the absolute efficiency of a bulb: it’s tough to collect all the light emitted by the bulb. However, we can leap over this hurdle fairly easily. Think about what we usually want a bulb to do: we want it to light a room. And it tends to be the case that rooms are more or less uniformly lit. That is, you can look all around the room and the brightness doesn’t seem to change (as long as you don’t look directly at the bulb).

Inspired by the recent discussion regarding the purpose of light bulbs, we will define a term called the efficiency factor (EF) of a light bulb. (Note that this is not a standard term. It is simply a useful definition for this experiment.) The equation for the efficiency factor will be

brightness in lux of a standard room lit by the bulb �� ≡ electrical power used by the bulb where the Vernier Light Sensor is the tool used to measure the term in the numerator. The units of the EF will be lux/watt. A large EF indicates we get lots of brightness for a given power input, indicating an efficient bulb. By comparing the EF of an LED bulb to the EF of an incandescent bulb, we will find a meaningful comparison of the efficiencies of the two types of bulb.

PL1. Just to make sure you read at least part of that, what’s the EF for a bulb that uses 15 W to light the standard room with a brightness of 250 lux?

A Tour of Energy.gov

This lab is motivated in part by claims made at energy.gov, the website of the United States Department of Energy. Here’s a sample of some of the information that is available on the site.

Do This: Go to www.energy.gov/public-services/homes/saving-electricity/lighting and watch the short video called Energy 101 : Lumens. Then answer PL2 - PL4 relating to the video.

PL2. The video makes it sound like watts is a unit of energy. Is this accurate?

PL3. What does a lumen quantify? PL4. At the 1:09 point in the video, we see an estimated yearly energy cost. Show the work that leads to the estimate on the label.

Do This: Go to www.energy.gov/articles/top-8-things-you-didn-t-know-about-leds and read the list. Answer PL5 - PL8 based on the information in the article.

PL5. How much more efficient is an LED bulb compared to a traditional incandescent bulb?

PL6. What happens to 90% of the energy that is put into an incandescent bulb?

PL7. How long can an LED last? How does this compare to the lifetime of a traditional incandescent bulb?

PL8. When was the first visible-spectrum LED produced?

Power Used by a Simulated Light Bulb

In this lab you will have to use voltmeters and ammeters to determine the power used by various circuit elements. In the final Pre-Lab exercises, you will simulate this process.

Do This: Find the PhET DC circuit applet on the Pre-Lab links on the course website to visit http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab and download this virtual lab software from the University of Colorado Boulder.

Do This: Connect the battery, light bulb, voltmeter, and ammeter in such a way that you can determine the power used by the light bulb.

PL9. Sketch the simulated circuit that you just built.

PL10. What is the power used by the light bulb? Show your calculation.

Part I: Rating Light Bulbs

The Story

Let’s all take a trip into the future…It’s June and you have just returned home from a successful year at Wash U (congrats!). While having dinner with your parents one night, the topic of energy comes up. The conversation proceeds more or less as a debate with you supporting the development of green energy and your parents playing the role of fossil fuel enthusiasts.

After a while, it becomes obvious that you aren’t going to change their minds, so you decide to change your strategy. A little annoyed, you say “Look, Pops, we may disagree about what the source of our energy should be, but at least we can agree on one thing.” You make the case that no matter where the energy is coming from, we will use less energy if we are smarter about our energy consumption. More efficient energy consumption can save money and promote world peace. (Okay, maybe that second point is a bit of a stretch, but remember you are an ambitious Wash U student.) You continue, telling them they can start by replacing all the incandescent light bulbs in the house with LED bulbs. In fact, energy.gov tells us that the LED bulbs are 5 times more efficient than incandescent bulbs.

That really gets your dad in defense mode. “But you know energy.gov is a government sponsored website,” he replies. “And you can’t believe anything the government says! In fact, I think this LED thing is just a big conspiracy to help someone get rich.”

Now you’ve got him backed into a corner because you know that the efficiency of LED bulbs is no conspiracy. How do you know this? Well, you tested it in physics lab, of course! Eager to prove him wrong, you whip out the data that you took in your Introduction to Efficiency lab.

Now we return to the present, having learned the moral of our time travel adventure: if you want to win the unavoidable energy-related arguments with your parents this summer, concentrate on this lab!

Equipment

• Light Box o Vernier Light Sensor o White LED o Incandescent flashlight bulb • LabPro interface • Two Extech multimeters • Test leads • DC power supply

1. Seeing the Light

Here you will determine the EF of an LED and an incandescent bulb, allowing you to make a conclusion regarding relative efficiency. The “standard room” that you will use is the light box provided to you. It contains an LED, an incandescent bulb, and a Vernier Light Sensor that’s peeking in on the room to check out how well the lights are doing.

1.1. What do you need to measure in order to determine the power used by a light? [Hint: both lights are non-ohmic, meaning the resistance is not easy to work with.]

Read This: First, you will do an experiment to find the EF of the incandescent bulb. You can use the digital displays on the power supply to determine the voltage across the bulb and the current through the bulb. You do not have to use the multimeters.

Do This: Set the voltage of the power supply to 3.8 V and connect the power supply to the incandescent bulb.

Do This: Measure the light output using Logger Pro. 1.2. Record the voltage across the incandescent bulb, the current through the incandescent bulb, and the light output from the incandescent bulb.

1.3. Estimate the uncertainty in the voltage and current values that you recorded in Step 1.2. Justify your estimates.

1.4. Calculate the EF of the incandescent bulb.

Read This: Your next task will be to determine the EF of the LED. This time, you need to use multimeters to determine the voltage across the LED and the current through the LED. See Appendix B for details about multimeters.

NWarning: The LED will be damaged by voltages larger than 3.4 V.

1.5. Sketch the circuit that you will use to determine the power delivered to the LED. Get this

STOP checked out by your TA before you move on.

Do This: Set the voltage on the power supply to 3.4 V. Build the circuit that you drew in Step 1.5. If necessary, adjust the power supply until the voltage across the LED is 3.4 V, according to the multimeter.

Do This: Measure the light output using Logger Pro.

1.6. Record the voltage across the LED, the current through the LED, and the light output from the LED.

1.7. Estimate the uncertainty in the voltage and current values that you recorded in Step 1.6. Justify your estimates.

1.8. Calculate the EF of the LED.

1.9. How efficient is the LED relative to the incandescent bulb? Are your results similar to the claims made by light bulb manufacturers?

1.10. Explain why you were instructed to use the multimeters to make measurements with the LED instead of using the digital displays on the power supply like you did with the incandescent bulb.

1.11. Hopefully, you’ve shown that LEDs are, in fact, quite a bit more efficient than incandescent bulbs. They clearly save energy, but let’s take a look at whether or not they really save you money. One of the leading brands of LED bulbs is Switch Lighting. They have a 12-W LED bulb whose light output is very similar to the output from a typical 60-W incandescent bulb. Further, the LED bulb has a lifetime of 25,000 hours, compared to 1000 hours for a typical incandescent bulb. However, the LED bulb costs $50 while an incandescent bulb will cost around 75¢. If your electric company is charging you 10¢/kWh (an average price), is the LED bulb a good investment? Show your calculations. Read This: The last few steps of this section will explore the physics of the disappointing performance of the incandescent bulb. An incandescent bulb works by emitting blackbody radiation. For more information about blackbody radiation please read the first part of section 39.4 in Young and Freedman (pp. 1310-1311). From this reading we know that the spectrum emitted by a blackbody depends on its temperature. Electric current passing through a tungsten filament raises the temperature of the filament to about 3000 K. (This is likely the hottest object you will ever encounter. For comparison, the temperature of an oven is in the neighborhood of 500 K, while the surface of the sun in around 6000 K.)

1.12. Find the PhET blackbody spectrum applet on the In-Lab links on the course website or use your computer to visit http://phet.colorado.edu/en/simulation/blackbody-spectrum. Find the blackbody curve for an incandescent bulb by adjusting the temperature (notice the labeled thermometer). Sketch this blackbody spectrum in your notebook. Shade in the area under the curve that is in the visible spectrum.

1.13. Explain how the picture you drew in Step 1.12 illustrates the fundamental limitations on the efficiency of an incandescent bulb. For starters, where are your cost and benefit in the picture?

Read This: You have seen that there is more than just conservation of energy limiting the efficiency of an incandescent bulb. There is no possible way for the filament to radiate entirely in the visible spectrum. The well-defined shape of the blackbody spectrum puts an additional constraint on the efficiency of an incandescent bulb, much like the Second Law of Thermodynamics puts an additional limitation on the efficiency of a heat engine.

1.14. It may not be entirely true that non-visible light emitted by a bulb is wasted. In the classic toy the Easy Bake Oven, an incandescent bulb was used to bake delicious snacks. (You have probably also noticed that an incandescent bulb feels warm when you bring your hand near it.) What part of the electromagnetic spectrum is associated with thermal processes such as heating an oven? (See Figure 32.4 on page 1054 in Young & Freedman for details about the electromagnetic spectrum.)

Read This: Just in case you were wondering, LED’s do not emit a blackbody spectrum. LED’s emit light using semiconductor technology that is beyond the scope of this lab.

Part II: Perpetual Motion

The Story

One day your friend approaches you and says, “Hey! I just had a million-dollar idea! I’ve invented a perpetual motion machine.” Your friend then proceeds to describe the device: A fan is pointed at a windmill, causing the windmill to turn, generating the electricity that powers the fan! Your friend claims that there would even be additional electricity that could be used “for whatever, like a toaster maybe.” Having learned a thing or two about energy over the past several months, you excitedly prepare to crush your friend’s high spirits by explaining a little physics.

Equipment

• 2 Windmill/fans • DC Power Supply • LED • Multimeters • Test Leads

2. Shooting Down Your Friend’s Idea

2.1. What law of physics does your friend’s idea violate? Explain.

2.2. Though most people probably think you go to school in the Evergreen State, we all know that we’re in the Show-Me State. With that in mind, set up the equipment such that one windmill creates the breeze that turns the second one, as in your friend’s design. (You might have to flick the windmill to start it spinning.) Treat the LED like the toaster. (If the LED won’t light up, try switching the leads.) Further, come up with a way to determine the power used by the fan and the power generated by the breeze. Sketch your set-up. (NWarning: Don’t turn the power supply past 6 V.)

2.3. How much power is used by the fan? Show your work.

2.4. How much power is generated by the windmill? Show your work.

2.5. Based on your experiment, how much money will your friend make with this invention?

2.6. Discuss how the efficiency of this set-up compares to what your friend expected. Start by making it clear what you consider to be the cost and what you consider to be the benefit.

Head-Scratchers

Don’t forget to complete the following problems. They should be at the end of your lab report. If you want to work on them during lab, start a new page in your lab notebook.

• 1.10 • 1.11 • 2.6

Appendix A: Efficiency of heat engines and Carnot

The problem of efficiency in heat engines turns out to be a more complicated problem than motors. Defining what we mean by benefit and cost is not especially difficult. The engine does work for us when we put in heat.

work the engine does � = !"#$"! heat put into the engine

If that was so easy, where is the difficulty in the problem? The main cause of the difficulty is that, in addition to the First Law of Thermodynamics, heat engines must obey the Second Law of Thermodynamics. In other words, the flow of heat must obey conservation of energy while also not decreasing the entropy of the universe.

It was the French scientist Sadi Carnot who did the foundational research on the fundamental limitations on heat engines. In 1824 he published a work that analyzed an imaginary heat engine that is now given his name. The Carnot Engine operates using a reversible cycle of two adiabatic processes and two isothermal processes. The engine is reversible due to the fact that it does not create any entropy, which Carnot correctly reasoned would result in the greatest possible efficiency for a heat engine operating between given hot and cold reservoirs of temperatures TH and TC, respectively.

By looking at his imaginary engine, Carnot found that the maximum theoretical efficiency of a heat engine is

�! �!"# = 1 − �!

Notice that this expression always gives an efficiency less than 1. Thus Carnot showed that even in the absence of friction, no engine could be 100% efficient. This result is profoundly different from the constraints that govern electric motors. In a sense, thermal energy is fundamentally less useful to us than the same amount of electrical energy.

This lab will not actually look at the efficiency of any heat engines. However, you should keep in mind that different devices have different constraints on their efficiency. Sometimes, the only thing keeping a device from 100% efficiency is a practical constraint such as friction. Other times, there are truly fundamental limitations keeping an efficiency well below 1.

Appendix B: Voltmeters, Ammeters, and Multimeters

Hopefully, you remember most of this from the Circuits Lab, but multimeters definitely take some getting used to.

Voltmeters

A voltmeter is used to measure the voltage drop across a circuit element or set of circuit elements. For our purposes, we will just consider measuring the voltage across a single light bulb. The most important thing to remember is that the voltmeter should be connected in parallel with the light bulb. That means you can always connect the voltmeter last. You do not have to disconnect any cables in order to properly add the voltmeter to a circuit. A voltmeter is designed to have a very high resistance so that it does not affect the rest of the circuit (Think about why this implies that you must connect the voltmeter in parallel.)

In a circuit diagram, a voltmeter is represented by a circle with a “V” inside.

Ammeters

An ammeter is used to measure the current through a circuit element. (Once again, we will consider a light bulb.) The most important thing to remember is that an ammeter must be connected in series with the light bulb. This means that you must break the circuit in order to add an ammeter. That is, you must disconnect a lead or two in order to use an ammeter in a circuit. If you add an ammeter without disconnecting anything, you have added it incorrectly.

Ammeters are designed to have very low resistance. That means that connecting an ammeter in parallel with a circuit element will cause a short circuit, possibly blowing a fuse in the ammeter. You must be very careful with ammeters. Always feel free to ask your TA for help if you are unsure about the use of an ammeter.

In a circuit diagram, an ammeter is represented by a circle with an “A” in it.

Multimeters

A multimeter is a digital instrument that can function as a voltmeter, ammeter, ohmmeter, and possibly several other instruments. (An ohmmeter measures resistance.) The versatility of a multimeter makes them very useful. However, the versatility also makes multimeters notoriously confusing. Here are some tips that should help you out.

Picking the correct input jacks: You must take care when connecting leads to a multimeter. One lead should always be connected to the “COM” input jack. Where the second lead goes depends on how you’re using the multimeter. If you’re using it as a voltmeter, plug the second lead into the terminal that has a “V” next to it. If you’re using the multimeter as an ammeter, then your choice depends on how large your currents will be. Plug the second lead into the jack that has “10 A” next to it if you are expecting to measure large currents or if you are unsure about how big the current will be. For smaller currents, use the jack labeled with “μA” and “mA”. Current is displayed as positive if current flows out of the COM jack. If your multimeter is not giving you the reading you expect, the first thing you should check is that your leads are in the proper jacks.

Selecting the range: Many multimeters (like this one) have multiple settings or ranges for a given function. For example, when using the Extech meter as an ammeter, we can choose from:

• μA - use this range for currents up to 4000 μA. • mA - use this range for currents up to 400 mA. • 10A - use this range for currents up to 10 A.

AC vs. DC: Many multimeters can measure both AC and DC quantities. The DC voltmeter/ammeter is often a separate setting from the AC voltmeter/ammeter. For these multimeters, the “Mode” button switches between AC and DC measurements. In this lab we will only measure DC quantities.