Mustafa Sozbilir

Ataturk University Kazim Karabekir Education Faculty Department of Secondary Science and Mathematics Education, 25240 – Erzurum, Turkey




This study is intended to review some of the selected researches carried out on students’ understandings of entropy, Gibbs free energy and spontaneity.  The review puts together the important findings of the researches, summarises the misunderstanings identified together with the possible sources of these misunderstandings.  Therefore, this study would be beneficial for the researchers and lecturers in science and chemistry education area.


Key Words: Misunderstandings, entropy, Gibbs free energy, spontaneity.


1. Introduction

Ever since the classical studies of Piaget, there has been an interest in the conceptions of physical science held by young children (Osborne, 1983).  Even a casual observer of the field of science education over the last two decades knows that this has been a period of unprecedented exposure of the ideas held by children, adolescents, and to a lesser extent adults, about a wide range of scientific phenomena (Griffiths, 1994).  Research in this domain has attempted to answer questions such as which misunderstandings occur, what are their origins, how extensive are they and, of course, what can be done about them? (Gil-Perez and Carrascosa, 1990).  It is quite understandable why students’ ideas concerning chemical phenomena have become a research focus.  Many students from secondary level to university struggle to learn chemistry and many do not succeed (Nakleh, 1992).  Research now shows that many students do not correctly understand fundamental concepts (Griffiths, 1994) and also many of the scientifically incorrect ideas held by the students go unchanged from the early years of the schooling to university, even up to adulthood (Gil-Perez and Carrascosa, 1990).  By not fully and appropriately understanding fundamental concepts, many students have trouble understanding the more advanced concepts that build upon these fundamental concepts (Thomas, 1997).


Many high school and university students experience difficulties with fundamental thermodynamic ideas in chemistry (Banerjee, 1995).  Despite the importance of thermodynamics as the foundation of chemistry, most students emerge from introductory courses with only very limited understanding of this subject (Ochs, 1996).


Entropy and Gibbs free energy are fundamental concepts in chemical thermodynamics that helps to explain the natural tendency of matter and energy in the universe to become less ordered (Tomanek, 1994).  This is an explanation of the Second Law of Thermodynamics which states that entropy increases when a chemical reaction occurs spontaneously.  In general, students seem to have not problem with the second law, because it does not run against students’ everyday experiments and it is in accordance with the requirements of the school science curricula. 


This study intended to review some of the key research studies about students’ understandings of entropy, Gibbs free energy and spontaneity.  The benefits of this study to the science education would be two folds.  Firstly, it would serve a starting point for the researchers in this area and secondly, the common misunderstandings would be available to lecturers as a ready to use material.


1.1 The Review of the Selected Literature on Entropy

Students generally interpret entropy as a measure of disorder (Johnstone et al, 1977; Sozbilir, 2001).  Although the recent research studies (Selepe and Bradley, 1997; Ribeiro, 1992) support this finding, there are evidences that students misunderstood the second law.  Some of the misunderstandings identified are given in Table 1 and discussed below.


Table 1. The identified misunderstandings about entropy and spontaneity


Misunderstandings Identified

Students’ Age

Revealed By

When the entropy is increased, the temperature is also increased

17 years old

Johnstone et al. (1977)

When a released rubber band contracts entropy decreases

According to the Second Law, the entropy of the system must increase for a spontaneous change


Thomas (1997)

Entropy equals to the disorder of the system


Sozbilir (2001), Selepe and Bardley (1997)

CO2 has bigger entropy than C3H8 at the same temperature

Entropy is the cause for the disorder in the system


Selepe and Bardley (1997)

Entropy shows that work has been done on the system

A micro state is a little state, it is not related with entropy


Sozbilir (2001),

Ribeiro (1992)

In an isolated system the change of entropy is greater or equal to zero


Entropy of the universe does not change or decrease


Ribeiro (1992)

A system always goes to maximum entropy

The change of entropy of a reaction is always positive

Inaccurate connection of entropy to the number of collisions and intra-molecular interactions


Sozbilir (2001)

Inaccurate connection of the entropy of a system and the entropy changes accompanying in the surroundings

Entropy of the whole system decreases or does not change when a spontaneous change occurs in an isolated system


It was reported that there was some tendency to confuse entropy with kinetic energy (Johnstone et al, 1977).  They explored this confusion from an easy rubber band experiment in which a rubber band at room temperature has more entropy value than when it is released.  Their study showed that nearly half of the students considered that the entropy value of released rubber band was more than its initial state, and also that its temperature must increase when it contracts in contrast to the scientific view.  They concluded that “increase in entropy, therefore, seems to equate with increase in temperature, perhaps through some misconceptual notion of disorder (Johnstone et al., 1977; p.250)”.  Similar results were also identified by Sozbilir (2001) and (Selepe and Bradley, 1997).  They concluded that there seemed to be a strong relationship between entropy and kinetic energy of the particles.  Another misunderstanding explored by Johnstone et al (1977), Sozbilir (2001), Selepe and Bradley (1997) resulted from a misinterpretation of the term ‘disorder’ as ‘chaos’.  The source of this misunderstanding was the point taught where a haphazard array of tumbled building bricks was accorded ‘greater entropy’ than the original ordered array.  It was also found that the students’ understanding of the word ‘disorder’ is different from its scientific meaning (Ribeiro, 1992).  Students used disorder in the sense of chaos or randomness.  It was also reported that the majority of the students considered that disorder was larger when the energy increased.  Moreover, it was found that students perceived entropy and disorder as equal or that entropy was the cause for the disorder in the system (Selepe and Bradley, 1997).  The study revealed that students perceived that entropy shows that work has been done on the system.  Finally, university chemistry students were asked to compare the entropy values of carbon dioxide and propane at the same temperature.  The results indicate that students thought that carbon dioxide had bigger entropy than propane at the same temperature (Ribeiro, 1992).  


In another study Ribeiro (1992) interviewed 14 Portuguese undergraduates in chemistry in their final year.  It was reported that although the majority of the students remembered the term microstate, only a few of them were able to explain it in terms of the possible arrangements of the particles.  It was also found that microstate was perceived as a little state and not related with entropy.  In the same study it was also revealed that students have such misunderstandings as that entropy of the universe does not change, a system always goes to maximum entropy, the change of entropy of a reaction is always positive and finally, in an isolated system, the change of entropy is greater than or equal to zero.  The research suggests that university teachers should determine students’ existing knowledge, lecturers should be careful in the language they use, scientific ideas must be shown to be useful to explain real phenomena and students should be helped to see clearly the contextual differentiation of their knowledge more clearly (Ribeiro, 1992).


In a study carried out in Germany by Duit and Kesidou (1988), 14 students were interviewed in order to discover 10th grade (about 16 years old) high school students’ understanding of the Second Law and irreversibility.  It was explored that most of the students had the correct idea that heat flows from a hot body to a cold body and that temperature differences tend to equalize.  Contrary to this result, there was a considerably number of students who thought that a certain temperature difference might arise after the temperature equalisation.  Their concluding remark was that students’ ideas about the natural processes were mainly based on everyday experiences rather than scientific ones taught in school.  In a subsequent study, Kesidou and Duit (1993) suggested two ways to overcome this misunderstanding.  Firstly, the experiments should be carried out by the students and secondly a framework should be provided that conceptualises the thermal interaction as an exchange of heat that runs spontaneously as long as there is a temperature difference.


A classroom based study conducted by Tomanek (1994) in a secondary environmental science class which explored the idea of entropy in the study of basic ecology.  The data was collected during 9 weeks school time by making audio recordings of all class sessions and by interviewing students.  The study revealed several different understandings of entropy is developed by secondary students during this study.  Some of those ideas are:


·                    Entropy governs matter and energy in such a way that both became less ordered and less useful for human purposes


·                    Increasing the rate of entropy decreases the amount of ‘useful’ matter and energy.


·                    Maintaining living systems increases the entropy.


·                    Highly consumptive life styles accelerate the entropy.


·                    Reducing the amounts of waste matter and waste energy that enter the environment reduce the entropy.


·                    Entropy contributes to the process of ecological succession. (p.79).


Tomanek (1994)’s study shows that students could develop scientifically acceptable ideas if they are taught concisely.  Students involved this research learned entropy as a physical law of nature rather than an idea that matter becomes more mixed up.  It was argued that it would be useful to develop tasks at the beginning of the course leading students to discuss, and confront alternative ways of thinking about entropy.


In a research with the chemistry undergraduates it was found that students were having difficulty in understanding the term ‘disorder’ and ‘spontaneity’ (Sozbilir, 2001).  It appeared that students’ understood ‘disorder’ as chaos, randomness or instability in some cases.  Disorder and entropy were considered as synonymous in other cases. They also thought of ‘spontaneity’ as a random rapid movement or as an undirected action.  It was concluded that students’ tendency to use algorithm to solve the problems associated with conceptual understandings seemed to cause misunderstandings (Sozbilir, 2001).

Students were also found having difficulty in differentiating the visual disorder and entropy.  This most probably comes from the analogies used during teaching and also the definitions made and analogies used in textbooks (Sozbilir, 2001).  Some of the misunderstandings seem to have originated from incorrect transformation of the macro-world to the micro-world of particles in spite of the fact that particles in the micro-world have been introduced for easier understanding at the level of sensation.  Few students were aware of the definition of entropy; that it is the measure of the number of ways that energy can be shared among the particles.  In addition, only a few students were aware of the microstates which are the possible ways of arrangements of particles.  It appears that teaching entropy as ‘a measure of disorder’ is more likely to confuse students and cause misunderstandings as discussed above.  In recent studies Lambert (1999, 2002) argued that teaching entropy by using ‘disorder’ should be avoided as it does not help students to visualise and conceptualize entropy accurately. 


1.2 The Review of Selected Literature Gibbs Free Energy and Spontaneity

The physical chemistry courses, where students tackle more advanced ideas of thermodynamics and kinetics, is perceived by many students to be one of their most difficult courses (Thomas, 1997).  Gibbs (free) energy is one of the key ideas in thermodynamics which is a part of physical chemistry courses.  It is generally thought of as a subtle idea.  In fact, the term ‘free energy’ used by scientists is not so different from the term ‘energy’ used by pupils (Ross, 1988).  Gibbs (free) energy was called by different names such as ‘exergy’ (Ogborn, 1986), ‘fuel value’ or ‘available energy’ (Ross, 1993).  In his theoretical based articles, Ogborn (1986) defined the Gibbs (free) energy as ‘go’ of things or sometimes ‘capacity to do work’.  He wrote that “free energy is generally costly, important not to waste, easily slips through our fingers and gets lost, and is what ‘makes things happen’.  Any process which happens will use some free energy up.  A process which (overall) increases free energy cannot happen.  To make it happen, more free energy must be lost somehow than is gained (Johnstone et al, 1977; p. 83)”.  His idea was that if something makes things happen it has free energy.  For example, ‘a furnace has free energy because it makes things happen’.  Research in this are revealed several misunderstandings that students hold.  Some of them are summarised in Table 2.


Table 2. Some identified misunderstandings about Gibbs free energy and spontaneity


Identified Misunderstandings

Students’ age

Revealed by

If a reaction has large Gibbs energy change, it will occur rapidly.

17 years old

Johnstone et al (1977)

Possibly, the net rate of reaction in a system tends to zero as equilibrium is approached.

High negative value of ΔH and positive value of TΔS, make the right-hand side of the equation negative; hence, ΔG is negative and the reaction is spontaneous.

College (BscEd)


Banerjee (1995)

Gibbs energy would increase or decrease linearly to make the reaction spontaneous either in the direction A B or B A, depending on whether A(reactant) or B(product) had more Gibbs energy to start with.

ΔG is the thermal energy transferred into or out of the system


Thomas and Schwenz (1998)

Confusing ΔG (the change in Gibbs energy between two states) with Gibbs energy itself so that Gibbs energy of the system either asymptotically approaches zero or goes to zero at equilibrium


Thomas (1997)

ΔrGθ is the same as ΔG except that ΔrGθ is measured at standard temperature (298K) and standard pressure (1 bar), whereas, ΔG is measured at any particular temperature and pressure

Free energy is the energy taken out or lost by the system during a reaction


Selepe and Bradley (1997)

Free energy is the energy that has not been used to make the reaction occur

Free energy is the internal energy that makes substance react

Gibbs energy increases in a spontaneous reaction


Sozbilir (2002)

The slower the reaction, the smaller change in Gibbs energy

The bigger the Gibbs energy change, the faster a reaction occurs.

The smaller ΔrGθ, the faster the reaction occurs.

The bigger ΔrGθ, the faster the reaction occurs.

The reaction with bigger ΔrGθ goes towards full completion.

If a reaction occurs fast, it goes towards full completion.


It was observed that A-level students had some serious misunderstandings about the Gibbs energy.  Johnstone et al., (1977) identified that nearly a quarter of the subjects thought that if a reaction had a large Gibbs energy change it would occur rapidly.  They also thought that there was a misunderstanding, which was not tested, that the net rate of the reaction in a system tends to zero as equilibrium is approached.  They suggested that this was because of the fact that the value of ΔG tends to zero.  It was also suggested that misunderstandings of thermodynamic ideas arose among high school students would be because of the fact that they are not mature enough to appreciate the conceptual subtleties of the subject.  The remedies for these kinds of misunderstandings might include the suggestions that students should avoid using too much mathematics during learning the thermodynamic ideas, and also helping the students to make the correct connections with their existing knowledge.


Banerjee (1995) carried out a research with 60 third semester college students’ (BScEd) in order to find out their ideas of chemical equilibrium and thermodynamics.  An achievement test on thermodynamics and equilibrium was developed and given after 12 weeks to assess the conceptual understanding and problem-solving abilities of the students.  Many widespread misunderstandings were revealed.  One of those misunderstandings was that in an equilibrium reaction, a high negative value of ΔH and positive value of TΔS, make the right-hand side of the reaction negative.  Hence, ΔG is negative and the reaction is spontaneous.  This misunderstanding arose from the misinterpretation of the fundamental equation of thermodynamics, ΔG = ΔH – TΔS.  It was argued that students used the logic correctly but the interpretation was wrong.  It is a common misinterpretation which takes place in most school textbooks.  The researcher explains that “the tendency to lower Gibbs energy is solely a tendency toward greater overall entropy.  Systems change spontaneously solely because that increases the entropy of universe, not because they tend to lower energy.  The equation ΔG = ΔH – TΔS gives the impression that systems favour lower energy, but this is misleading. ΔS is entropy of the system and, – ΔH/T is the entropy change of the surroundings.  Total entropy tends toward maximum for spontaneous reaction [6; p. 880-881]”.  It was argued that the driving force was entropy rather than lower energy for the spontaneous processes.


The second misunderstanding was identified from the question: ‘Draw a graph of Gibbs energy versus extent of reaction of A → B’.  Students thought that Gibbs energy would increase or decrease linearly to make the reaction spontaneous either in the direction A → B or B → A depending on whether A (reactant) or B (product) initially had more Gibbs energy.  The researcher comments that students were not able to conceptualise that Gibbs energy has the lowest value at the equilibrium position.  The same researcher also argues that these kinds of misunderstandings should not be thought of being specific to this sample.  They are widespread among students and even teachers (Banerjee, 1995).


In a recent study Thomas (1997) studied students’ misunderstandings in thermodynamic concepts in physical chemistry.  It was reported that students considered that ΔGθ is the same as ΔG except that ΔGθ is measured at a standard temperature (298 K) and standard pressure (1 bar), whereas, ΔG is measured at any particular temperature and pressure.  It was also reported that students confused ΔG (the change in Gibbs energy between two states) with Gibbs energy itself so that Gibbs energy of the system either asymptotically approaches zero or goes to zero at equilibrium.  In another study, it was reported that students perceived Gibbs energy as the thermal energy transferred into or out of the system (Thomas, 1998).


In a study in South Africa with student teachers, it was reported that students’ understanding of free energy was rather superficial.  Six out of ten students said that free energy is the energy taken out or lost by the system during a reaction.  In addition, two out of ten argued that free energy is the energy that has not been used to make the reaction to occur and free energy is the internal energy that makes substances to react (Selepe and Bradley, 1997).


More recently, Sozbilir (2002) carried out a study with Turkish chemistry undergraduates revealed several different misunderstandings.  The most common misunderstandings are given in Table 2.  Moreover, there was a general trend among the undergraduates which was the confusion of thermodynamics data and kinetics data.  Students were found as more likely to use thermodynamics data to make estimation about the kinetics of a reaction.


2. Discussion

The review shows that Entropy, Gibbs free energy and spontaneity are found to be difficult ideas to be grasped by high school students and undergraduates.  In many cases students’ understanding of the basic aspects of these ideas are limited, distorted or wrong.  The difficulties arise from misinterpretation of mathematical equations in thermodynamics and not adequately integrating the new knowledge with students’ existing knowledge.  Students’ explanations are mostly based on the macrophysical world, their thinking on the microphysical world is limited.  The everyday meanings of the scientific terms dominate their interpretations.  Lecturers should check that students have acquired the correct scientific meanings of the concepts and apply them in both everyday and theoretical situations.


Physical chemistry instructors may sometimes overestimate students’ understandings of the key chemical concepts and underestimate their difficulties in acquiring them.  If instructors recognize the possibility of misunderstandings concerning basic concepts and difficulty of learning advanced level concepts on the basis of these misunderstandings they will be better able to teach difficult concepts.


Although there are some studies which reflect the theoretical aspects and students’ understandings, there are few systematic research studies.  Students’ difficulties with these concepts need further study as do the other thermodynamic concepts.  High school and university students’ understanding of the relationships between entropy changes and temperature, entropy and spontaneity, entropy changes in the case of solid and liquid matter and the nature of Gibbs free energy would benefit from further research.  It is also important to make available the findings of the studies reviewed above into the classroom teachers, lecturers and students. Otherwise, the research studies in science education would not reach the ultimate aim.



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