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Capturing the essence of energy: a graphical representation.

This article describes a way of representing energy that is particularly appropriate for the middle years of schooling. The method, using bar graphs, provides a framework that helps the student analyse events in terms of energy transfers and transformations while making the application of the law of conservation of energy explicit. A range of contexts that include mechanics, electricity, chemical reactions and ecology, are explored. While the major focus described is qualitative, there is a natural extension to quantitative work that lends itself to the use of spread sheets. The potential of the representation for assessment is considered. Finally, extension of the representation to include the second law, and thus the prediction of spontaneous change, is canvassed and advantages deriving from its inclusion in the middle years curriculum discussed.


Energy governs our lives from the moment our egg is fertilised to our last breath. One of the wonders of science is that it has allowed us to develop a framework for thinking about energy that starts simply and can be elaborated throughout life. The framework allows us to look at a huge range of different events in terms of the energy they contain and how the energy can be transferred and transformed. This leads us to powerful explanations of changes that occur.

This article describes a way of representing energy that is particularly appropriate for rehearsing the basic ideas of energy in the middle years of schooling. At the same time it is a device that elicits higher-order thinking about the concepts and results in useful explanations for real life events.

In the middle years of schooling students are expected to become familiar with the abstract concept of energy, identifying its forms and the ways in which they are transferred and transformed (Curriculum Framework --Science, 2004; Science : Years 1-10 Syllabus, 1999; Science Years 7-10 Syllabus, 2003; Science: a curriculum profile for Australian schools, 1994). Additionally, there is international agreement that this is an appropriate time for students to be introduced to one of the major unifying concepts of science, the law of conservation of energy, the First Law (1) (National Science Education Standards, 1995; Science: The Level Descriptions, 2006).

This article focuses on these aspects of energy, canvassing a range of applications to demonstrate the utility and scope of the representation. At the end of the article the small step required to introduce the Second Law (2), the law that covers whether or not events will occur spontaneously, is illustrated. While the Second Law is not generally mandated in middle year's syllabuses, there is good evidence that most students can use it in a qualitative form and that it helps students overcome misconceptions about the First Law because it covers many students' common sense ideas about energy.

Understanding energy

Tools required to help students build useful conceptions of energy need to represent the various forms of energy involved in an event while making the application of the law of conservation of energy obvious (Energy, 2006; Hewitt, 2005). It is easier to focus on the concept of energy if the method of representation is familiar to the students.

An application of bar graphs is an excellent candidate because drawing a bar graph is one of the first graphing skills students learn. They are also particularly well suited to thinking about events involving change and hence energy.

The representation of energy that is developed in this paper is illustrated in Figure 1. Each bar in the graph represents a point in time in the event, or the result of a transformation of energy. Each bar contains all the energy in its different forms present at that point in the event. (3)

The initial bar will usually represent all the energy at the start of the event or process. Portions of the energy will be transformed and transferred as the event unfolds. The height of the bar remains constant representing the application of the law of conservation of energy.


Bouncing balls

Bouncing balls is a familiar event that can lead to a wide variety of investigations and provide an excellent setting for establishing the utility of concepts about energy.

Figure 2 shows a simple representation that involves graphing the endpoints of a single bounce. At the start, the ball is motionless and held in the air above a surface.


It has gravitational potential energy relative to the surface. This is represented in the initial bar. (4)

At the end of the first bounce the ball is stationary once again but at a lower height above the surface. It therefore has less gravitational potential energy after the bounce. We can identify the energy that has been transformed into heat and sound due to frictional forces.

Elaborating the investigation

An investigation like this leads to questions about the detail of the bounce. For example, the gravitation potential energy present at the start of the bounce is transformed into the energy of motion (kinetic energy) so that, at the bottom of the bounce, there is no gravitational potential energy remaining. This, then, is a suitable point for another bar in the graph.


The next part of the event involves the ball getting compressed against the bounce surface. The point of maximum compression, at which the ball has stopped, is another suitable point for a bar of the graph because the kinetic energy will have been transformed into elastic potential energy as well as sound and heat.

Figure 3 shows the more detailed analysis that provides a vivid 'picture' of the bounce.


Graphs invite the possibility of quantification, a necessary step for many student investigations.

Measuring the bounce height invites a range of investigations such as varying the drop height, the nature of the bounce surface, the mass or volume of the ball. The height is proportional to the gravitational potential energy and so the energy can be quantified in units of length, or, if the formula for gravitational potential energy has been covered, the potential energy can be calculated directly.

For example we might measure the ball's mass as 50g (0.05kg), drop it from a height of 1.2m and catch it after the bounce at a height of 0.85 m. The gravitational potential energy before the bounce is then:

E = mgh = 0.050 x 10 x 1.20 = 0.60J

The representation is well suited to using spread sheets that allow students to explore the relationship between the energy before the bounce and the energy after the bounce and hence calculate the amount of energy that is transferred into the surroundings as heat and sound. In the calculation they are using the law of conservation of energy at least intuitively.

This type of calculation leads to explanations, for example, about the bounce characteristics of different types of ball. These are ideas that can be usefully applied to sports to investigate the optimum inflation for basketballs for example.

Analysing the bounce in more detail adds ideas about kinetic energy that might be measured by videotaping the speed of the ball. This information can then be used to estimate the air resistance component of the bounce and hence make estimates of the frictional loss involved in the bounce and the elastic potential energy. In each case, the law of conservation of energy is invoked to determine missing components.

Combustion reactions

The bar graphs work equally successfully for exploring the nature of chemical energy. Combustion reactions are a productive context for such explorations in the middle years of schooling.

If we start with a simple reaction such as the burning of alcohol (ethanol) we can represent the reaction as a simple two bar graph in which the first bar represents the chemical potential energy in the alcohol and the second the heat and light generated by the reaction and the chemical potential energy of the products of the reaction.

We could elaborate the investigation to quantify the reaction by using the ethanol flame to heat a can of water and measure most of the heat energy.

A closely related process is the related reaction in which we metabolise compounds such as sugars for energy. In this metabolic process, glucose is turned into carbon dioxide and water, with some of the energy converted into chemical energy in other substances that are important for life.



Food Chains

The graphs can also be used to address biological issues such as tracking energy in food chains. Figure 6 shows the diagram for a food chain just three organisms long. Using the common assumption that each step in the chain involves conversion of just 10% into biomass (chemical potential energy) of the new level (Campbell, Reece, & Meyers, 2006), it is easy to visualise why food chains are usually very short on energetic grounds alone.

It is tempting to follow the energy path all the way from the Sun, but the efficiency of conversion of sunlight into chemical energy in photosynthesis is less than 5% making the size of the bars to be used in the representation problematic.


The bar graphs can also be used as assessment tasks. The construction of the graphs can be assessed as part of an investigation and this is an obvious and important use. However they can also be used to test conceptual understanding more directly.

For example, students can be asked for explanations of events represented by graphs or asked to draw or complete graphs that represent variations of an event, or an entirely new event.


Figure 7 shows such an example. In this example, students will have to decide whether to represent the school gate at the same level as the bike rack and deal with the issue of the gravitational potential energy appropriately.

The Second Law

The discussion so far has used bar graphs to introduce the First Law (conservation of energy) into analysis of everyday events. Students' ideas about energy can be deepened further by introducing the Second Law. This law signals whether or not change will occur spontaneously by identifying the dispersal of energy as the key driver for spontaneity.

This law is an incredibly powerful idea because it connects students' ideas about energy with a common sense notion that energy gets used up (Driver, 1994). Of course the energy does not get used up--that is the point of the First Law--energy is conserved. Rather, energy is progressively transformed into less useful, more dispersed forms. The idea is illustrated in Figure 8 showing a torch that is turned on. Chemical energy is transformed into electrical energy that flows round the circuit. Then it is transformed into light in the bulb and some is converted into heat. The heat that leaks out of the torch is a tell-tale sign of the Second Law in action because it gets dispersed into the environment.

In each of the figures in this paper it is possible to identify some of the energy that is transformed into a less useful, more dispersed form, providing the drive to make the process spontaneous.


Alternative ways of representing ideas are important tools in a teacher's knowledge about teaching their subject. Many of these devices, such as conceptual cartoons and concept map, are general devices applicable across a range of subjects. However there is another level of pedagogical tools that are subject, or topic, specific (Wright, 2003). The tailored bar graphs described in this paper fall into this category. They are not part of the knowledge structure of the subject, but rather form a part of the knowledge about teaching the subject. Having a repertoire of such representations is one of the hallmarks of the expert teacher.


Energy stands as one of the most important ideas to be grasped for scientifically literacy and hence mastery of the concept is particularly important in the middle, compulsory years of school.

It is also particularly challenging because the concept is abstract to the point that no general images are available to help students. Instead students are asked to master the concept by learning about the different forms of energy, how they are transferred and transformed and the scientific laws that have been discovered associated with energy.

The representation described here has been designed with these ideas in mind:

* It can be used almost anywhere that change is occurring, whether in a science unit of work, or as part of an integrated theme (Wright, 2006)

* It provides a sound basis for scientific explanations that contribute to understanding and problem-solving

* It directly addresses the major ideas about energy contained current P-10 syllabuses and can be easily extended to give students a more complete understanding through an introduction to the Second Law

* While presented as a qualitative tool, it invites quantitative treatment

* It provides a good vehicle for assessment of student understanding of energy.


Atkins, P. W. (1994). The Second Law. New York: Scientific American Books.

Campbell, N. A., Reece, J. B., & Meyers, N. (2006). Biology (7th ed.). Frenchs Forest, NSW: Pearson Education.

Curriculum Framework--Science. (2004). Retrieved 3rd August, 2006, from http://www.

Driver, R. (1994). Making Sense of Secondary Science: Research into Childrens' Ideas. London: Routledge.

Energy. (2006). Retrieved 3 September 2006, from http://en/ nerg&oldid=73518119

Hewitt, P. (2005). Conceptual Physics (10th ed.). New York: Addison-Wesley.

National Science Education Standards. (1995).). Washington D.C.: National Academy Press.

Science : Years 1-10 Syllabus. (1999).). Brisbane: Queensland School Curriculum Council.

Science Years 7-10 Syllabus. (2003). Retrieved 3rd August, 2006, from http://boardofstudies. sc/pdf doc/science 710

Science: a curriculum profile for Australian schools. (1994).). Carlton: Curriculum Corporation.

Science: The Level Descriptions. (2006). Retrieved 03/07/2006, 2006, from http://www.

Wright, T. (2003). Images of Atoms. Australian Science Teachers' Journal, 49(1), 18-24.

Wright, T. (2006). Science in the Middle Years: Building a Model for the Integrated Curriculum Australian Journal of Middle Schooling, (in press).


(1) The First Law: The law of conservation of energy has a number of titles including the First Law of Thermodynamics. In its most general form it suggests that the total energy in the Universe is constant. In this paper the term 'the First Law' will be used because it is brief and less intimidating.

(2) The Second Law: This is the Second Law of Thermodynamics which is expressed in a number of ways describing changes that will occur spontaneously. Statements of the Second Law include one of the original statements that: 'heat flows spontaneously from hotter to cooler bodies.' This generalises to 'energy becoming more dispersed in spontaneous processes' and, more rigorously, in statements that 'the entropy of the universe increases in a spontaneous process.' The first statement is probably the most accessible for middle years students and can be applied readily in everyday situations. The concept of entropy, on the other hand can be very confusing for students who are trying to develop their conception of energy. However the Second Law is sufficiently thought provoking that starting students on the journey of understanding it is a valuable goal (Atkins, 1994).

(3) Systems: To keep track of all the energy involved, the most straight forward approach is to define a closed system which contains all the energy for the duration of the event. When this is done, the constant height of each bar is confirmation of the First Law (conservation of energy). The concept of closed systems is usually inappropriate for middle years students in which case care needs to be taken that all the energy involved in the event is accounted for at the start if conclusions using the First Law are to be drawn.

(4) Energy Changes: One of complicating features of drawing useful diagrams representing energy is that we are often interested in changes in energy rather than total energies. For example, in the ball bounce, we are interested in the change in gravitational potential energy between the drop position and the bounce surface rather than the total potential energy the with respect to the centre of the Earth. Usually, in middle schooling, the issue can be treated lightly, without explicit instruction, but some students are likely to appreciate a more rigorous treatment.

Tony Wright works at the School of Education, The University of Queensland.
Figure 4. The diagrams are more useful
if the event is quantified. Students
can then explore the consequences of
change on a spread sheet.

Quntifying a single bounce

                Before   After
                bounce   bounce

mass (kg)       0.050    0.050

height (m)      1.20     0.85

energy (J)      0.60     0.43

heat & sound
(J)                      0.17
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Author:Wright, Tony
Publication:Teaching Science
Article Type:Report
Geographic Code:8AUST
Date:Dec 22, 2007
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