L.D.P.E.S., University Denis Diderot, (Paris7), France
In the large number of studies about learners' conceptions that have been conducted during the last twenty years, the topics of interest were first defined in terms of the traditional topics of accepted theory. Heat and temperature were among the first topics documented by researchers, followed by pressure in gases and the particulate structure of matter. It soon appeared that similar features of reasoning were involved in pupils' answers concerning very different topics, and more recent research at the university level was focused on these transferable aspects of reasoning. After an outline of the results concerning children's ideas about heat and temperature, these general ways of reasoning will be illustrated with examples in thermodynamics, and some implications for the choice of teaching goals will be discussed.
PHENOMENA INVOLVING HEAT AND TEMPERATURE: A FRAMEWORK FROM A PHYSICIST'S POINT OF VIEW
In the accepted theory of physics, "heat" refers to a type of transfer of energy between two systems, for instance by conduction, and designates the energy transferred in that way. The other way of transferring energy from one system to another is work: for instance, mechanical or electrical work. Processes such as convection or radiation can be referred to these two fundamental types of transfer - heat and work - although in a non trivial way. In fact, in considering energy transfers, we need a proper distinction between heat and work only when entropy is considered. This will not be the case in this chapter, therefore I will not analyze in detail the actual processes of transfer. I will only say "transfer of heat " (although it would be less ambiguous to say: "transfer of heat-type"), or "work".
Temperature is one of the quantities that characterize the state of a system. Its theoretical definition is somewhat complex. But in situations where classical thermodynamics holds, this intensive quantity is simply related to - in fact is proportional to - the mean particulate kinetic energy.
Since energy can be transferred simultaneously by several means, and since particulate energy is not only kinetic, a transfer of heat to a system does not necessarily entail an increase in temperature of this system. For instance, a transfer of heat may cause a change of state, and this occurs without any change in temperature (then it is the potential energy of particles that changes), or a change in temperature may occur during an adiabatic expansion of a gas, i.e. an expansion without any transfer of heat. A transfer of heat may even occur from a "cold" source to a "hot" source (which means, respectively, "colder", or "hotter", than the other source), as in refrigerators.
In this complex domain, a restricted category of phenomena allows simpler predictions : those in which only a transfer of heat occurs, with only the mean particulate kinetic energy varying in each system. Then, it is correct to claim that energy goes from the hotter system to the colder one, until these systems finally reach the same temperature. It is worth noting that in this "restricted category", one might without any trouble identify "heat" with "thermal energy", transferred as well as stored. Then, the difference between heat and temperature would be only that temperature is an intensive quantity, while in the case of energy it is not. In fact, as shown above, the conceptual gap between the two quantities is much more important. In this very brief summary, two conceptual fields are encountered, which extend beyond the topics of heat and temperature: the particulate structure of matter (see chapter E3 of Meheut, and Lijnse and al., 1990), and the concept of energy. These two very important topics cannot be dealt with as such in the limited scope of this chapter. What follows is focused on learners' ways of reasoning about physical phenomena which involve heat and temperature.
CHILDREN'S IDEAS ON SOME THERMODYNAMIC PHENOMENA
It is now widely accepted that a knowledge of learners' common conceptions and ways of reasoning is of crucial importance in designing teaching strategies.
This section describes conceptions held by 10 to 16 year-old adolescents before, during or after teaching, with a particular stress, in the latter case, upon the difficulties that remain after teaching. The findings reported here are mainly drawn from review articles (Erickson 1985; Tiberghien 1985; see also Tiberghien 1984), in which more detail can be found.
-What heat and temperature are said to be
In most pupils' comments, heat seems to be simply something hot that heats other things. As Erickson (1985) wrote, this "something" is equated either with a hot body or with a kind of substance given off by a heat source.
These responses have been obtained during an investigation concerning 12-16 year-olds asked to "say in a couple of sentences what heat is" (Engels 1982):
"Heat is warm air";
"Heat is a warming fluid or solid...when you touch it it feels hot-if anything has got the heat in it".
Still a third of the older pupils in this study gave these types of responses, in contrast with others where "heat" is defined in terms of energy and transfer: "Heat is energy; when it heats something up it will transfer the heat energy to what is heating up.
According to Erickson (ibid.), "up to the age of 12-13 pupils are familiar with the term temperature and are able to use a thermometer to assess the temperature of objects, but they actually have a fairly limited concept of the term and rarely use it spontaneously to describe the condition of an object".
As for the difference between heat and temperature, when children were asked directly about this point, "the most common type of response (accounting for more than 25% at all age levels) is that there is no difference between them". Erickson quotes other typical responses (Engels 1982) in which temperature seems to be either "a measurement of heat" or "the effect of heat":
"Temperature is the amount of heat in that space...it tells you the hotness of the water".
-How are phenomena analyzed?
This being said, researchers agree on focusing their attention on children's comments and predictions concerning phenomena involving heat and temperature, rather than on purely declarative aspects of knowledge.
From a physicists' point of view, the phenomena put into play in these studies can be classified in two types: the "restricted category" defined above ( i.e. with only a transfer of heat and only mean particulate kinetic energy varying) on the one hand, and changes of state on the other.
-Phenomena of the "restricted category"
In the "restricted" category is the experimental fact that all objects in prolonged contact reach the same final temperature. This idea is not obvious to pupils. Researchers report on some answers that seem to deny the existence of a thermodynamic equilibrium between the objects involved.
For instance, when asked if two plates situated in the same room, one of metal and one of plastic, are at the same temperature, most of pupils even after teaching think that this is not the case (Engels & Driver 1985). Tiberghien (1985) also reports that "different materials (flour, nails, water) placed for several hours in an oven at 60oC are at different temperature for the majority of pupils. Typically, flour is at less than 60 oC because flour does not heat up very much, nails are at more than 60 oC because iron heats faster, and water is at 60 oC because it takes the temperature of the surroundings".
Along the same lines, it is not obvious to adolescents that heating any material will result in an increase of this material's temperature. Thus, still quoting Tiberghien, "before teaching, only about a third of the pupils think that the temperature of sand, sugar and water increases when they are heated. Many of them predict that sand will not be hot "because sand cannot heat", whereas water can heat up. For them, the ability to be heated is a "natural" property of particular substances. After teaching, more than 50 per cent of the pupils recognized that the temperature of these three substances increases when they are heated, but it remains a difficult concept for them."
All these difficulties do not appear in the case of homogeneous mixtures of liquids. The existence of a unique final temperature is well accepted by pupils. The focus is a qualitative or quantitative prediction about this final value. Various investigations (Stavy & Berkovitz 1980, Driver & Russel 1981, Strauss 1981, Engels 1982) used mixing experiments with amounts of water at same or different initial temperature. In both cases, qualitative and quantitative predictions were asked. The case of identical initial temperatures are seen as easier to cope with, and quantitative questions are more difficult than qualitative ones. Strategies consisting of adding or subtracting the initial temperatures are still observed at the age of 16 (Engels 1982).
Finally, still in the "restricted" category (only heat transfer occurring and only kinetic energy varying), some questions bear on which materials are good for the thermal insulation of different objects. To produce a correct answer in this case, one needs to consider a property of a given material -being a good or a bad conductor - with a focus on the idea of transfer between two other systems. This idea of transfer also enters into the difficult issue of tactile sensations produced by various materials at same temperature.
Not surprisingly, most of pupils' explanations for such problems rely on a property of the material. But in many of these, the property of the object is asymmetrically linked to one or the other of the categories "hot" or "cold", as if a particular situation had been used to ascribe an intrinsic link between the material and one particular end of the hot-cold continuum.
Most of these explanations seem to take into account the material under consideration and only one of the other involved systems: the body to be insulated or ambient air, with or without the mediation of "heat". Tiberghien (1985) quotes some examples of such explanations:
(to insulate a cold ball bearing), "the aluminum keeps cold better" (11 year-old);
(to insulate a hot drink), "the glass wrapped in cloth will be hotter than the others since it is wrapped in cloth" (11 year-old);
"metal cools things, metal is cool" (12 year-old);
"I think that (metal) will keep (the ice) frozen most easily, because that (cotton) is hotter and keeps the heat better" (12 year-old).
These explanations are predominant before teaching and can be gradually replaced, after teaching, by others which suggest no asymmetry with respect to "hot" and "cold", such as (Tiberghien ibid.): "The material transmits heat more or less quickly; heat propagates, moves in the material, more or less quickly." Saying simply "the material is a conductor or an insulator"" doesn't guarantee that the problem of transfer is properly understood. For instance, the following comment was given by a pupil who had chosen aluminum foil to keep a ball-bearing cold (Tiberghien ibid.):
"because the metal keep the cold, the aluminum is a conductor.
Yes because it will take the temperature of the marble... and it will keep it for a long time." (12 year-old).
The question of symmetry of role between the interacting systems (the "hot" and the "cold" source) is one of the most critical, a point that will be discussed below.
Changes of state
Turning now to changes of state, it appears that the stability of temperature during a change of state is not known before teaching, and that it causes a real surprise when observed. After teaching, this point seems to be widely accepted, although such a stability over time is often considered as affected by the rate of heating, as shown in two studies (Driver & Russel, 1981, Andersson 1979).
It also seems difficult for students to accept that, once the change of state is over, the new phase will behave normally, i.e. will have its temperature increased when heated. Tiberghien (1984, 1985) reports that, asked to explain why a piece of zinc placed in an oven at 1000 oC had successive values of temperature 30o, 70o, 200o, 420o, 420o, 420o, about 20% of a group of pupils answered, after teaching about changes of state, that "it is the highest possible temperature for zinc". Concerning the values of temperature to be expected later on, 70 per cent of the pupils said that "the temperature always stays at 420o ". Swedish students also often think that 100o C is "the maximum temperature of water" (Andersson 1979).
I propose the following hypotheses:
This reluctance to admit a normal behaviour for the phase resulting from a change of state might be phenomenon-dependent. In particular, children would probably admit that heating an ice cube results first in its melting, then in an increase of the temperature of the resulting water.
It might be partly due to the fact that very high and very low temperatures are difficult to imagine. Extreme values, indeed, cannot be connected with ordinary personal experience of a range of temperatures.
It might also be due to a rupture in a way of reasoning. The change of state forces one to leave aside the rule that holds in the "restricted category" of phenomena, i.e.: if a body is heated, its temperature increases. This may seem arbitrary to children and discourage them from coming back to this rule when they consider the phase resulting after the change of state.
In the absence of any experimental support, it is not possible to say much more about these hypotheses. But, from a teaching-learning perspective, the last remark suggests that we take all the more seriously Erikson's plea (Erikson 1985) for presenting pupils with explanations - for instance concerning the boiling point of water:
"...This understanding would seem to require some explanation of what is happening to the liquid, at the molecular level, in order for temperature invariance to make sense."
Thus, concerning simple heat transfers as well as changes of state, simply "learning the facts" seems insufficient to reach a coherent understanding of the concepts involved. This idea consistently leads one to analyze the types of reasoning that commonly appear in this domain.
COMMON WAYS OF REASONING CONCERNING SYSTEMS
-Transferable aspects of reasoning: first hints
One of the main results concerning children's ideas about heat and temperature is that when they analyze a heat transfer children have difficulty in taking into account both the hot and the cold source. Somewhat similar is the reluctance of children to consider both sides of a moving piston when they analyze the forces due to pressures which are acting on this object (Séré 1985, Méheut 1997). It seems as if two causes were too much for a given effect. At the end of their book on children's ideas in science, Driver et al. (1985) conclude that: "These recurring ideas....tend to derive from a linear causal reasoning with a single action producing an effect". Andersson (1986), and Gutierrez & Ogborn (1992) also pinpointed the simple causal structure commonly observed in learners' reasoning.
Transferable with respect to specific content as it is, this trend of reasoning is likely to be all the more resistant to teaching (Viennot 1993a). Indeed, concerning heat transfer along a metallic rod, university students were found (Rozier 1987, Viennot 1996) to use a "sequential reasoning" - which is also extremely common in electricity (see chapter C2 of Duit and v.Rhöneck) i.e. they reason as if heat was something starting from the hot source along the rod, irrespective of what is situated downstream. Like children, they have the greatest difficulties in taking into account on the same footing both the "starting" (hot) area and the "arrival" (cold) area of heat in a transfer.
In fact, Rozier (ibid.) observed, at the university level, the enormous resistance to instruction of common trends of reasoning that she referred to as "linear causal reasoning" and that she analyzed as follows.
The quasistatic analysis of systems
It is useful to recall first some major features of the accepted theory. The analysis of systems, indeed, puts into play several physical quantities. When multivariable systems are transformed, they can, under certain conditions, be analyzed in a quasistatic way. This means that the quantities that characterize the state of the system evolve simultaneously under the permanent constraint of simple laws. "Simple" excludes laws of propagation from one side of the system to another. In other words, "quasistatic" and "propagative" are two exclusive adjectives. For instance, in thermodynamics, a quasistatic transformation of a perfect gas is such that, at any time, the relation pV = NRT (with classical notations) holds as if the system was permanently in thermodynamic equilibrium. This type of analysis can be contrasted with the trends of reasoning described below, with instances in thermodynamics.
Reducing the number of variables
A most general and well known tendency in coping with multivariable problems is to ignore some relevant variables. This is illustrated in particular by a test given to university students (Rozier, 1987, Rozier & Viennot, 1991). An adiabatic compression of a perfect gas is presented. It is said that "pressure and temperature both increase". The question is "can you explain why in terms of particles?" About half of the students in various levels at university gave answers such as:
"The volume decreases; therefore there are more molecules per unit volume and the pressure increases"
"The volume decreases, therefore the molecules are closer to each other; therefore there are more collisions and the pressure increases"
These responses may be outlined in the following way:
V decreases > n increases > p increases
Concerning pressure, they mirror an exclusive link of this quantity with particle density (n). The other relevant factor, namely the mean square speed of particles is ignored. This constitutes a preferential association between pressure and particle density, at the expense of the kinetic aspect. In this way, the role of temperature is ignored. Méheut (1996) also observed that students have more difficulty in understanding the relation between pressure and "force of collisions" than between pressure and particle density.
Reasoning with such linear chains about multivariable problems leads in fact to ad hoc arguments and to inconsistencies. For instance, one cannot "explain" at the same time the lower pressure at higher altitudes by the implication "particle density (n) decreases > pressure p decreases" and the way a hot air balloon works by the link "hot air inside the balloon > particle density (n) decreases", without a contradiction concerning the pressure inside the hot air balloon, which obviously is not lower than the external one. In both cases, when using the pV = NRT relationship (holding for perfect gases), it is necessary to specify what happens to the third relevant variable, i.e. the absolute temperature T. The implication - "particle density (n) decreases > pressure p decreases" - only holds at constant temperature. At a higher altitude, both n and T are lower than at sea level, whilst in a hot air balloon, n is lower but T is higher than in the external air, which explains why the internal pressure p is not lower than outside the balloon.
Another common way of reducing the number of variables actually considered is to combine two variables as if they were only two facets of the same notion. "Thermal motion" is one of these notions often used by learners as well as by textbooks' writers as a kind of conglomerate of the speed of particles and mean distance between them. Statements such as "particles need more room to move faster", "in solids particles cannot move", "thermal motion is more intense in gases", are very commonly found (Rozier & Viennot, 1991). In fact, "thermal motion", if intended as the mean particulate kinetic energy, is only a function of temperature (when classical thermodynamics holds), and therefore the mean distance between particles is not a relevant parameter in that respect. At thermodynamic equilibrium between gas and liquid, for instance, temperature and therefore "thermal motion" are the same in the two phases.
Causality and chronology: the linear causal reasoning
Another aspect of common reasoning is presented by Rozier (ibid.). Students were asked to "explain" the increase in volume resulting from the (quasistatic) isobaric heating of a gas. About 40% of various samples of university students gave answers of the following type:
"The temperature of the gas increases. Knowing that pV = NRT, therefore at constant volume, pressure increases: the piston is free to slide, therefore it moves and volume increases."
The linear structure of this response is manifest: supply of heat > T increases > p increases > V increases
More surprising is the contradiction apparent between this answer and the statement of the problem, where pressure is said to be constant.
This seemingly contradictory statement can be understood if the described events are not supposed to be simultaneous (as in a quasistatic analysis).
Some students, indeed, clearly stipulate that there are two steps in this argument:
First step: supply of heat > T increases > p increases, with the volume being kept constant.
Second step: p increases > V increases, the piston being now released.
This suggests a reconsideration of the status of arrows in linear arguments such as those outlined above. These arrows do not mean only "therefore", but also "later". The totally ambivalent word "then" (or equivalently the words "alors" in French, "entonces" in Spanish) favors this melding of these logical and chronological levels.
To sum up Rozier's findings, a "linear causal reasoning" is often observed. Its structure is that of a chain: F1 > F2 > ...> Fn , in which each phenomenon F is specified by only one quantity, and where the causality referred to by an arrow has both a logical and a chronological content. As a whole, such arguments look like stories with simple events and successive episodes.
Permanence: a forgotten case
Understanding phenomena as successive consistently leads one to seeing them as temporary, or at least it obscures reasoning in terms of permanence. This is indeed what is observed by Rozier. An argument commonly observed to explain an increase of temperature in adiabatically compressed gases, "collisions between molecules produce heat", is almost never spontaneously confronted, neither by students nor by teachers, with the long term outcome of this assumed phenomenon, i.e. an explosion. Steady states of disequilibrium, for instance in a green-house or in a bolometer, often raise comments such as : "more energy gets in than out, so the temperature is higher". The result from unbalanced flows in the long term, again an explosion, is not envisaged. This implicit focus on a aspect of change hinders a check of validity which relies on an analysis of the long term evolution of the system (see also Viennot 1993b).
The importance of rates of change in learners' reasoning is also emphasized by Kesidou & al. (1995). They report the case of 15- to 16-year-old students who deny temperature equalization for a piece of metal at 20oC placed into water at 80oC, arguing that the rates of temperature changes are different for the two bodies in contact. This shows how difficult it may be to reconcile views on changes and the idea of a final permanent state.
In brief, it is common to explain steady states with arguments implicitly focused on a particular aspect of change, or to focus on an aspect of change without consistently considering the end of the story. Consequently, the part played by time often seems to be totally blurred in learners' arguments. We can, for instance, review the comment quoted above: (in an oven at 60 oC) "nails are at more than 60oC because the metal heats faster".
Clearly (in the authors' opinion), the pupil who gave this answer focused on a rate of change with no clear distinction between this topic and that of a final (permanent) state of equilibrium.
CONCLUDING REMARKS: SOME GUIDELINES FOR THE CHOICE OF TEACHING GOALS
The main features of "linear common reasoning" analyzed above seem to be widely shared by university students and children. However, reasoning consistently with accepted thermodynamics requires two essential components that are opposed to these common trends of reasoning.
1- identify the relevant systems as well their relevant characteristics in order to predict transfers of heat, instead of simply ascribing to objects a property intrinsically linked with only one of the categories "hot" or "cold"; more generally consider several causes for one effect, contrary to the linear causal reasoning.
2- clearly sort out what concerns changes on the one hand, permanent states on the other.
It is all the more important, when designing a teaching sequence, to specify very precisely the corresponding conceptual goals.
Of course, these goals should be compatible with the analysis of phenomena implied in accepted physics. But this compatibility is to be looked for at a level which remains to be defined. Teachers are therefore confronted with making choices.
The question of the explanations to be proposed to learners is a crucial problem. Given the complexity of the thermodynamic phenomena, we suggest that the following attitudes be adopted. (Rozier & Viennot 1991):
One has to be extremely careful with the degree of "explanation" actually expected, and to specify what the proposed argument fails to explain. For instance:
"Solids expand when heated (or contract when cooled), but we cannot (yet) explain why. Knowing that "thermal motion" (mean particulate kinetic energy) increases (or decreases) in such a case is not enough to explain why this makes the solid expand. Indeed the particles might vibrate more intensely, and stay around the same place without drifting."
One can also work with "soft" explanations which are focused on one predominant variable, but without hiding the dangers of their careless extension to other cases. For instance, the idea that "at high altitude, there are fewer molecules, therefore pressure is lower" requires the addition: "This reasoning works only if the molecules have (more or less, admittedly) the same mean speed in the two situations being compared."
This "harder" qualitative reasoning may be considered too demanding for a given population, but in fact the required degree of consistency can be chosen from a continuum which ranges from factual knowledge to accepted theory. For instance, it may be considered appropriate, for a given population of children, to teach the fact that at sea level, water boils at 100 oC, and this without the least explanation. But if one clearly introduces some factors which do not affect the boiling temperature, such as the amount of water and the rate of heating, this already constitutes the beginning of a multivariable reasoning.
In the same perspective of a realistic adaptation to learners, the goal of aiming at a clear distinction between heat and temperature may be debatable. But if one decides to take this challenge, it is useful to decide which of the following conceptual targets are aimed at: the intensive character of temperature and the extensive character of heat, the identification of relevant systems and parameters, the distinction between phenomena of "restricted category" (only heat transfer and only kinetic energy varying) and others (for instance, changes of state).
Moreover, the attitudes suggested above concerning explanations and corresponding reservations are intrinsic components of scientific modeling.
When selecting the goals for teaching, it may be decided, or not, to make explicit the question of modeling. The reader will find in chapters E3 (Méheut) and E4 (Psillos) of this book some reports on experiments concerning teaching sequences explicitly focused on modeling. They constitute a necessary complement to the present chapter.
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and ways of reasoning in thermodynamics: learner's common approach
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