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.