Published in The Physics Teacher Vol. 42, Feb 2004, pp. 113-117.
Energy Flow Diagrams for Teaching Physics Concepts
Art Hobson, Dept of Physics, Univ of Arkansas, Fayetteville, AR 72701
web site: physics.uark.edu/hobson/
Abstract: Energy flow diagrams offer an excellent pedagogical approach to processes of all sorts. They picture energy transformations in an accurate, quantitative, and conceptually transparent manner. This paper proceeds from simple processes to complex socially significant processes such as global warming.
Key Words: energy, energy transformation, automobile, electric generating plant, global warming.
PACS numbers: 01.40Gb, 01.75, 46.04A, 46.05B, 89.30, 89.40
Energy is arguably the central unifying concept in physics. The validity of the principles of energy extends almost without change from "classical" physics through all of modern physics. Even processes that are too complex or too far outside the Newtonian regime to be easily described in terms of forces can be described in an accurate and conceptually transparent manner in terms of energy. Thus, energy is a useful central organizing principle in teaching physics conceptually.
Every physical process is an energy transformation of some forms of energy into other forms. "Energy flow diagrams" present these transformations visually and approximately quantitatively. Even for complex processes where analysis in terms of force and motion would be out of the question, energy flow diagrams show the physical fundamentals in a meaningful manner. This paper discusses energy flow diagrams for a few simple processes, and proceeds to complex socially significant processes.
Energy, and Its Forms
Energy is the ability to do work. Quantitatively, the energy of a system is the amount of (macroscopic) work the system can do. Most introductory textbooks specializing in energy define it this way. However, some physicists have objected to this standard definition on the grounds that mechanical energy is partly transformed into thermal energy in all real processes, and that the second law of thermodynamics tells us that thermal energy cannot be entirely used to do work. But, as has been correctly pointed out by others, the standard definition refers to the amount of work a system could do under ideal conditions. In the case of thermal energy, these ideal conditions amount to imagining absolute zero as the low temperature side of the heat engine. Other natural laws involve similar idealizations. For example, no material object in the real universe experiences absolutely no external forces, although this is precisely the situation imagined in Newton's first law.
Energy comes in many forms that are named somewhat differently in different textbooks. In my conceptual physics classes for non-scientists, I have found that a classification in terms of eight basic forms works well:
• Kinetic energy, due to the system's (macroscopic) motion;
• Gravitational energy, due to height (i.e. due to the force of gravity);
• Elastic energy, due to the ability of a deformed system to snap back (i.e. due to elasticity).
These three are the mechanical or Newtonian energy forms. The non-mechanical forms are:
• Thermal energy, due to temperature;
• Radiant energy of a light beam or other forms of radiation;
• Electromagnetic energy, due to (macroscopic) electromagnetic forces;
• Chemical energy, due to molecular structure;
• Nuclear energy, due to nuclear (i.e. sub-atomic) structure.
The term "potential energy" (energy due to position or configuration) is not necessary, but if one does want to use it then there are five potential forms of energy: gravitational, elastic, electromagnetic, chemical, and nuclear. The unqualified term "potential energy" can be ambiguous.
Energy Flow Diagrams
When a book falls to the floor, we commonly describe the energy transformation (using obvious abbreviations) as Grav E ® Kin E ® Therm E. An energy flow diagram is just an extension of such a description. If we include air resistance, this process could be described as Grav E ® Kin E + Therm E (due to air resistance), followed by Kin E ® Therm E (due to impact). But Figure 1 is more transparent and meaningful.
Fig. 1. Energy flow diagram for a falling book, with air resistance. Time increases in the direction of the arrows. The width of a pipe (or channel) indicates the relative amount of energy participating in that part of the process.
Figure 1 is a typical energy flow diagram for a physical process. It represents a series of energy transformations, with time increasing in the direction of the arrows. It pictures energy as an incompressible fluid flowing through a system of pipes (channels, really, since it’s a 2-dimensional diagram) that correspond to the different motions and transformations of energy in the system. Alternatively, it can be thought of as a power diagram, because it pictures the energy that flows through each part of the system in some fixed time interval, but “energy flow diagram” is perhaps a more meaningful title. Such a diagram can be quantitative, by letting pipe widths indicate relative magnitudes. The quantities can be either energies (in joules) during some fixed time interval such as 1 second or 1 year, or they can be powers (in watts). We see energy conservation in the way the pipe widths match at each transformation, and we see the second law of thermodynamics in the transformation of organized energy into thermal energy.
For another simple example, suppose a student gives a brief push to a book, and the book then slides across a table while coming to rest. As Figure 2 indicates, the student's bodily chemical energy starts this process. The figure also shows the inefficiency of human chemical energy conversions: Only a small part of the chemical energy goes into the book, while the remainder warms the student.
Fig. 2. A student gives a brief push to a book, and the book is then allowed to slide across a table while coming to rest. As this energy flow diagram indicates, the process is highly inefficient, with only a small fraction of the student’s chemical energy going into the motion of the book.
Heat Engines, and the Growth of a Leaf
The most obvious form of the second law is the "law of heating": Thermal energy will flow, without outside assistance, from a higher-temperature object to a lower-temperature object, but will not spontaneously flow the other way. A heat engine is any device that uses such a thermal energy flow to do work. Figure 3, a commonly-seen energy flow diagram, shows the set-up schematically. The law of heating implies that, if we are to get work out of this device, the work output (during some time interval) must be less than the thermal energy input: The work cannot exceed the input because that would violate conservation of energy. And the work cannot even equal the input because if it did then this work could create thermal energy at a higher temperature by for instance frictionally heating an object having a low heat capacity. This would violate the law of heating. Figure 3 emphasizes that the basic "driver" of heat engines is the second law, specifically the flow of thermal energy from high to low temperature. Some of this flow can be "shunted aside" to do work. Again, we see the quantitative aspect of the energy flow. You could ask your students: What is the approximate efficiency of the heat engine in Figure 3 (the answers should include 1/3 along with the "detractors" 1/2 and 2/3)?
A growing leaf is rather like a heat engine (Fig. 4). High-temperature radiation from the sun that strikes a typical leaf is mostly absorbed and partly reflected. The absorbed fraction, shown in Figure 4, equilibrates with the much lower-temperature Earth, a process involving a large entropy (or microscopic disorganization) increase. However, some of the thermal energy is used to convert disorganized CO2 and water molecules into more organized (i.e. lower-entropy) organic molecules. As the figure indicates, this process is only about 2% efficient in creating chemical energy. The diagram illustrates how solar radiation has organized Earth, without violating the universe's trend toward disorganization. Solar radiation is both the energizer and the organizer of life on Earth. This is a societal point worth making because anti-evolutionists ("creationists") sometimes argue that the second law prohibits evolution.
Fig. 3. Heat engines use a portion of the thermal energy that flows naturally from a high to a low temperature and convert it to work. The diagram emphasizes that this flow is the basic "driver" of heat engines. Some of this flow can be "shunted aside" to do work.
Fig. 4. Energy flowing through a leaf is similar to the energy flow through a heat engine. The diagram shows only the fraction of the incident solar energy that is actually absorbed by the leaf. The remaining energy is reflected.
Many socially significant processes are far too complex to be meaningfully analyzed in terms of forces and accelerations. For example, the automobile is a hallmark of modern civilization, and among the largest energy consumers, polluters and global warmers. It deserves an energy analysis in introductory physics courses.
Figure 5 shows the energy per second (i.e. the power) through a typical car moving at highway speed without acceleration. You can use this figure as the basis for many "peer instruction" questions such as:
• How many bright100 W electric light bulbs could the input light up? Answer: 700!
• What is the numerical efficiency of the engine?
• What is the efficiency of the overall car (useful energy out/total energy in)?
• What is the most significant reason for such a low efficiency? (The second law).
• How might rolling resistance be reduced? (Keep the tires well inflated, or use tires that flex less. For example, use steel tires on a steel road, i.e. use a train).
• How might air resistance per passenger be reduced? (Streamlining; use a train.)
Figure 5. Typical power flow in an unaccelerated car at highway speed. For a typical acceleration, these flows are multiplied by five.
There is a broad scientific consensus that global warming is happening now and will increase. The Intergovernmental Panel on Climate Change (IPCC), comprising thousands of scientists from some 100 nations, came to this conclusion in 2001 after evaluating tens of thousands of scientific papers..
Most scientists and others involved in climate change policy or study agree that the problem is large and serious. For example, F. Sherwood Rowland, winner of the 1995 Nobel Prize in Chemistry for his work on stratospheric ozone depletion, has stated that "None of the currently available remedial responses, such as the Kyoto Protocol, provide a solution to the problems brought about by climate change. ....Consequently, the climate change problem will be much more serious by the year 2050 and even more so by 2100." Richard Benedick, U.S. chief negotiator of the international treaty on ozone depletion, stated in 1992 that "of course, the overarching issue now is global warming."
In addition to its importance, this topic holds great scientific interest and pedagogical potential. We should try to include it in our introductory physics courses.
Earth's greenhouse effect is basic to understanding global warming. Like many natural processes, this effect is best understood in terms of energy flows. For starters, Figure 6 shows the energy flow near the surface of an imaginary Earth that has no greenhouse gases (these are trace gases, mainly water vapor and CO2) but has an otherwise normal atmosphere. The figure shows energy flows in percentage units where 100% represents the total daily radiant energy from the sun. As the figure shows, 30% of this energy is reflected while 70% is absorbed and re-radiated. But there is a crucial difference between the absorbed and re-radiated energy: The sun radiates at the sun's surface temperature while Earth radiates at Earth's much lower temperature. Thus the incoming radiation peaks in the visible part of the spectrum, while the outgoing radiation is nearly entirely in the infrared. In this scenario, without greenhouse gases, Earth's surface is at the -19oC temperature that Earth has when observed from space. That is, the bottom of the atmosphere has the same temperature as the top. The top of the atmosphere must be at -19oC in order to balance Earth's energy flows: A warmer Earth would radiate more energy and thus cool down, while a cooler Earth would radiate less energy and thus warm up.
Figure 6. Energy flow near the surface of an imaginary Earth that has no greenhouse gases but that has an otherwise normal atmosphere. The numbers represent percentages, relative to the radiant energy received daily from the sun.
Addition of the greenhouse gases, although it cannot change the temperature of the top of the atmosphere, radically alters the energy flows within the atmosphere (Fig. 7). Unlike the monatomic and diatomic molecules of nitrogen, oxygen and argon that form the bulk of the atmosphere, the more complex greenhouse gases, mainly water vapor and CO2 but also nitrous oxide, chlorofluorocarbons and methane, have strong vibrational frequencies in the infrared. Thus they absorb infrared radiation as it passes through the atmosphere. Once a photon is absorbed, it is re-emitted, but this emission is equally likely to be upward or downward. As you can see from the figure, this has a pronounced effect on the outgoing radiation: 50% of it is "recycled" back to Earth, resulting in the enormous energy loop shown in the figure. This energy loop is the greenhouse effect, in energy terms. Since more infrared radiation is striking Earth's surface in Figure 7 than in Figure 6, the "recycled" infrared warms Earth's surface by about 33 Celsius degrees. Because of the greenhouse gases, Earth's atmosphere keeps Earth warm much as a blanket keeps you warm, by intercepting the outgoing radiation.
Figure 7. Energy flow near Earth's surface. The very dilute greenhouse gases, forming far less than 1% of the atmosphere, cause the enormous difference between Figures 6 and 7.
Humans have been adding greenhouse gases to the atmosphere since the beginning of the industrial age. According to the IPCC, CO2 maintained a concentration of 280 parts per million or less for hundreds of thousands of years before 1750, but by 2001 the concentration had reached 373 ppm, a 33% increase. This raised Earth's average surface temperature by an additional 0.6oC during the 20th century.
The analysis in terms of energy flows highlights the true significance of the greenhouse effect. By comparing Figures 6 and 7, we see the huge leverage that a tiny admixture, measured in parts per million, of greenhouse gases has on Earth's energy flows. It’s like a small tail wagging a big dog. These gases strongly influence the energy relationship between our planet and our star. It is not surprising, then, that we are experiencing measurable climate change.
References and Notes
 The figures in this article are slightly altered versions of figures published in Art Hobson, Physics: Concepts and Connections, 3/E, (C)2003. Adapted by permission of Pearson Education, Inc., Upper Saddle River, NJ.
 Harold H. Schobert, Energy and Society (Taylor and Francis, New York, 2002); Robert A. Ristinen and Jack J. Kraushaar, Energy and the Environment (John Wiley & Sons, Inc., New York, 1999); Roger A. Hinrichs, Energy (Saunders College Publishing, Philadelphia, 2nd edition 1996); Gordon J. Aubrecht, Energy (Prentice Hall, Englewood Cliffs, NJ, 1995).
 Robert L. Lehrman, "Energy Is Not the Ability To Do Work," The Physics Teacher, January 1973, pp. 15-18.
 Mario Iona, "Energy Is the Ability To Do Work," The Physics Teacher, May 1973, pp. 259, 313.
 Eric Mazur, Peer Instruction (Prentice Hall, Upper Saddle River, NJ, 1997).
 Rolling resistance or rolling "friction" is caused by the backward torque exerted by the road on a tire that is slightly flattened by its contact with the road. See A. Domenech et al, "Introduction to the study of rolling friction," Am. J. Phys. 55 (3), March 1987, pp. 231-235.
 F. Sherwood Rowland, "Climate Change and Its Consequences," Environment, March 2001, pp. 28-34.
 Richard E. Benedick, "Science and Diplomacy: A New Partnership to Protect the Enviroment," in AIP Conference Proceedings 247, Global Warming: Physics and Facts, ed. by Barbara Goss Levi, David Hafemeister, and Richard Scribner (American Institute of Physics, New York, 1992), pp. 292-310.
 See Reference 7.