Building Proficiency in Efficiency

Building Proficiency in Efficiency Pre-­‐Lab: Efficiency in Theory and in Practice A Bit of History The early 1800s 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, but very useful terminology, the efficiency of anything is given by 𝑒 =
benefit
cost
. Exactly what the cost and 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, 𝑒!"#"$ =
work the motor does
electrical energy the motors uses
The concepts of work and energy were actually not especially well defined until the mid 1800s 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. Absolute efficiency of a light bulb would be 𝑒 =
1 energy emitted as visible light
electrical energy used by the bulb
. Unfortunately, we don’t have the equipment to measure the energy 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’ll 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 quotient (EQ) 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 quotient will be 𝐸𝑄 ≡ 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 EQ will be lux/watt. A large EQ indicates we get lots of brightness for a given power input, indicating an efficient bulb. By comparing the EQ of an LED bulb to the EQ 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 EQ 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: Use the Pre-­‐Lab Links page to watch the short video called Energy 101 : Lumens. Then answer PL2 -­‐ PL4 relating to the video. PL2. The video makes it sound like watts are 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. The claim is that this bulb will cost $1.57 to operate for a year. Using the assumption given on the package, check 2 their work and give the yearly energy costs to the nearest tenth of a cent. (Assume there are 365 days in the year.) Do This: Use the Pre-­‐Lab Links page to find the LED Facts article. 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 and download this virtual lab software produced by 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. Please do not change the voltage of the battery. PL9. What is the power used by the light bulb? 3 Part I: Rating Light Bulbs The Story Let’s all take a trip into the future…It’s mid-­‐June and you have just returned home after successfully completing your intro physics course 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 over 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 •
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LabPro interface Two Extech multimeters Test leads DC power supply 1. Seeing the Light Here you will determine the efficiency quotient (EQ) 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. 4 Checkpoint 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.) Checkpoint 1.2: What are the two pieces of equipment you can use to measure the current output by the power supply? Discuss the advantages and disadvantages of each method. Checkpoint 1.3: What are the two pieces of equipment you can use to measure the voltage produced by the power supply? Discuss the advantages and disadvantages of each method. STOP Important Equipment Notes: The LED is designed to be run at 3.4 V. The LED will be damaged by voltages larger than 3.4 V. Further, it is important that the red terminal of the LED is connected to the red terminal of the power supply. STOP Important Equipment Note: The incandescent bulb is designed to be run at 3.8 V. However, it is not nearly as easy to damage as the LED. S1
Synthesis Question 1 (40 Points): Devise and execute an experiment using the equipment provided in order to determine the EQ of the LED and the incandescent bulb that are inside the light box. (Make sure all measurements have at least two significant figures.) Then comment on whether or not your results are consistent with the information provided on the energy.gov website. Make sure you explain your procedure and analysis in detail. Part II: The Blackbody Spectrum The Story At this point your father is convinced that LEDs are, indeed, more efficient than incandescent bulbs, but now your mother chimes in. “When I was a girl,” she says, “I had an Easy-­‐Bake Oven that made delicious cupcakes using an incandescent bulb. How can you possibly say that an incandescent bulb isn’t efficient?” “Well,” you say, “It turns out that an incandescent bulb only works to bake cupcakes because it is inefficient as a light. Here’s what I mean…” 2. Incandescent Bulbs and the Blackbody Spectrum In this section you 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 & Freedman (pp. 1310-­‐1311). From this reading, we know that the spectrum emitted by a blackbody depends on its temperature. Electric current passing through the tungsten filament in an incandescent bulb 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.) 5 Checkpoint 2.1: Find the PhET blackbody spectrum applet on the In-­‐Lab Links on the course website. Then 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. (Make sure your sketch is large enough that you can really see the famous shape of the blackbody spectrum.) Checkpoint 2.2: Discuss how the picture you drew in Checkpoint 2.1 illustrates the fundamental limitations on the efficiency of an incandescent bulb as a light source. 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. Checkpoint 2.3: 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 most 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. Hint: it’s not microwave radiation.) Checkpoint 2.4: Find the sketch you drew of the blackbody spectrum of a light bulb. Shade in the area that represents the infrared portion of the spectrum. Read This: Just in case you were wondering, LED’s do not work by emitting a blackbody spectrum. LED’s emit light using semiconductor technology that is beyond the scope of this lab. S2
Synthesis Question 2 (20 Points): Finish the story. Explain to you mother why the incandescent bulb is good at cooking for the same reason that it is inefficient at lighting a room. A complete response will contain at least one figure. Part III: 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. 6 Equipment •
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2 Windmill/fans DC power supply Red LED •
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Multimeters Test leads 3. Shooting Down Your Friend’s Idea Checkpoint 3.1: What law of physics does your friend’s idea violate? Do This: 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, you decide to help your friend build a proof-­‐of-­‐concept experiment: you power one fan that creates the breeze that turns the other one. If you can generate more power than you use, then your friend might be on to something. •
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Treat the red LED like the toaster. If the red LED won’t light up, try switching the leads. LED’s are picky about which direction current can flow. You might need to flick the windmill to start it spinning. Warning: Do not turn the power supply past 6 V. But you’ll probably have to put the voltage close to that value. The voltage reading on the power supply might jump around a little (or a lot). If this is the case, unplug the fan from the power supply. The voltage reading will settle down. Report that value as your voltage reading. Checkpoint 3.2: How much power is used by the fan? Checkpoint 3.3: How much power is generated by the windmill? (The current that is generated may be quite small. If you only read one significant figure, that’s okay.) S3
Synthesis Question 3 (40 Points): Report the findings of your proof-­‐of-­‐concept experiment to your friend. Make sure your report includes the following. •
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A description of your model. A comparison of the power used and the power generated by your model. A value for the efficiency of your model. A comparison between the efficiency of your model and the efficiency that your friend expects to achieve. Some advice for your friend. 7 Appendix A: Efficiency of Heat Engines and Carnot The problem of efficiency in heat engines turns out to be a more complicated problem than for motors. Defining what we mean by benefit and cost is not especially difficult. The engine does work for us when we put in heat. 𝑒!"#$"! =
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 𝑒!"# = 1 −
𝑇!
𝑇!
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. 8