# 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  =
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, !"#"\$ =
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  =
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  ≡ brightness in lux of a standard room lit by the bulb
electrical power used by the bulb
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 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. !"#\$"! =
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 −
!
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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 ```