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A New Perspective of How to Understand Entropy in Thermodynamics 2 B.Sc IOP Physics Education Phys. Educ. 55 P A P ER Phys. Educ. 55 (2020) 015005 (6pp) iopscience.org/ped 2020 A new perspective of how © 2019 IOP Publishing Ltd to understand entropy PHEDA7 in thermodynamics 015005 Guobin Wu1 and Amy Yimin Wu2 G Wu and A Yimin Wu 1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, People’s Republic of China A new perspective of how to understand entropy in thermodynamics 2 B.Sc. (Mathematics), University of Manitoba, Winnipeg, Canada E-mail: [email protected] Printed in the UK Abstract PED Using the analogy between thermodynamics and electricity, two new concepts of thermal charge and quantity of thermal charge are introduced. A simple 10.1088/1361-6552/ab4de6 yet explicit definition of entropy is then derived—entropy is the quantity of thermal charge. As a result, quantity of thermal charge (entropy) and quantity of heat (energy) are now clearly distinguishable from each other. The former 1361-6552 is an energy carrier while the latter is energy itself. This largely eliminates the difficulties in learning and applying thermodynamics, and therefore will be of considerable assistance to those who work, teach and study in the fields Published associated with thermodynamics. This also leads us to re-examine the validity of caloric theory and make a brief comment on it. 1 1. Introduction fairly independent and a bit arbitrary. It shared 1 Being a branch of physics, thermodynamics is little commonalities with the better-developed one of the most important fundamental theo- branches at that time: mechanics and electric- ries in modern science and technology. When it ity. Therefore, it was challenging to clarify the comes to explaining phenomena in nature, con- concepts in thermodynamics by analogizing to ducting scientific experiments and theoretical similar concepts in other subjects. As a result, research, developing new technology, designing thermodynamics developed much slower than and manufacturing new products, etc., thermody- other branches and experienced more twists and namics does have a wide application as the other turns. Since the misconceptions or misinterpreta- branches of physics do. However, in compariso n tions were not corrected or clarified over time, it to the others, thermodynamics is commonly resulted in this subject becoming even more com- viewed as a difficult subject to study. A number plex and difficult to study. of abstract concepts such as entropy, enthalpy, Scottish chemist Black [1] (1728–1799) free energy, state function, reversibility and made a significant contribution to the theory cycles, etc. make it even more obscure. Among of heat. He was one of the first to state that the concepts, entropy is no doubt one of the most two physical quantities—intensity of heat and difficult physical quantities to understand in con- quanti ty of heat, were required to describe ther- ventional thermodynamics. mal phenomena. The former was already known The history of science tells us the develop- as temper ature at that time, the latter, however, ment of thermodynamics at its early stage was was not given a specific name or term. In 1865, 1361-6552/ 20 /015005+6$33.00 1 © 2019 IOP Publishing Ltd G Wu and A Yimin Wu the concept of entropy with its mathematical defi- introduced into physics by Clausius was, contrary nition was put forwarded by the German physi- to general belief, not a new physical quantity but cist Clausius. As Truesdell [2] pointed out, the the reconstruction of the ‘quanti ty of heat’ con- term ‘entropy’ means nothing to ordinary per- ceived about one hundred years earlier by Scottish sons and only intense headaches to those who chemist Black’. In his opinion, Black’s concept of have studied thermodynamics. Or, let us quote ‘quantity of heat’ coincided perfectly with what Callendar’s words [3], ‘…Clausius gave it the was called entropy [4, 7]. To use Callendar’s words name of ‘entropy’ and defined it as the integral [3], ‘In justice to Carnot, it (entropy) should be of dQ/T. Such a definition appeals to the math- called caloric’. In addition to the previous attempts, ematicians only’. As a matter of fact, the major- Der Karlsruher Physikkurs [8] (the Karlsruhe ity of today’s physics teachers still believe that Physics Course, or KPC for short), based on Job’s entropy is quite difficult to teach [4], and many idea, suggested at the very beginning that entropy engineers and technologists confess that although is what in everyday language we call ‘quantity of they have been working in the fields related to heat’ or simply ‘heat’ with the symbol S and its thermodynamics for many years, they never feel unit of measurement Carnot, abbreviated Ct. they have fully grasped the concept of entropy. It should be mentioned that the German This reality obviously has a negative impact on Physical Society (DPG) published a report3 in teaching and applying thermodynamics in various 2013, in which KPC’s approach was questioned areas. Therefore, in order to update its concepts and its definition of entropy as‘ colloquially and structure to make it easier to study and apply, called heat’ was rejected. Herrmann and Pohlig a reform in thermodynamics is urgently needed. from KPC responded4 about two weeks later. The above-mentioned attempts all have cer- tain things in common. They try to provide tan- 2. Attempts to reform thermodynamics gible explanations to Clausius’ mathematical Several attempts have been made to reform the definition of entropy in order to make it easier traditional thermodynamics since 1911 when to understand by employing such terms like Callendar, the president of the British Physical ‘quanti ty of heat’ or simply ‘heat’, ‘caloric’ and Society at that time pointed out that entropy was ‘calory’ [2]; they use temperature and the rede- basically what had already been introduced by fined entropy as the two core physical quantities Carnot and had been called caloric. It was defined in thermodynamics. To conventional thermody- directly by his equation W = AQ (T − T0), where namics, redefining entropy and reorganizing the W is the work done by a quantity of caloric Q structure of the subject was no doubt very innova- falling from a temperature T to T0; A is a conver- tive. The new concepts of entropy directly related sion factor for units. This means entropy could be to ‘heat’ or ‘caloric’ are more intuitive and could introduced in a way ‘which any schoolboy could therefore be regarded as a great improvement understand’ [3]. In 1972, Job [5] proposed to base over Clausius’ abstract concept. However, the the teaching of thermodynamics on the concept new ideas must be convincing and scientifically of entropy and pointed out that our everyday correct, as indicated in DPG’s report. usage of the word ‘heat’ which was explained as It is worth of notice that what is called ‘heat’ a physical quantity could be equated to entropy in by Black is fundamentally different from the conventional thermodynamics. interpretation of heat in conventional thermody- About one decade later, Falk et al [6] intro- namics, where the word ‘heat’ denotes a specific duced a concept of teaching physics based on form of energy. It is unambiguous that Black’s ‘substance-like’ quantities that can be treated as a ‘heat’ is an extensive quantity of a substance- ‘fluid’, such as mass, electric charge, momentum, like nature, a state variable with no possibility of amount of substance, etc. as the carriers of energy being a form of energy. Thus we have a conflict. in physical processes. Entropy was just the energy carrier in thermal phenomena. This idea was really 3 www.dpg-physik.de/veroeffentlichungen/publikationen/stel- helpful in visualizing the relationships between lungnahmen-der-dpg/bildung-wissenschaftlicher-nachwuchs/ kpk/stellungnahme_kpk.pdf. abstract physical quantities and making analogies 4 www1.unipa.it/girep2014/accepted-papers-proceedings/16_ between them. Falk also wrote [7], ‘The entropy Herrmann.pdf. January 2020 2 Phys. Educ. 55 (2020) 015005 A new perspective of how to understand entropy in thermodynamics That is, the new concept of entropy and the tradi- (3) Majority rules. We agree with DPG’s view- tional concept of energy are both called ‘quanti ty point: Heat is energy. Hence, it is much easier of heat’ or simply ‘heat’. In other words, the to change the concept of entropy in KPC same term ‘heat’ is used to express two differ- thermodynamics as opposed to changing the ent concepts and/or interpreted in two different concept of energy in conventional thermody- ways. This results in confusion. As pointed out in namics. As a matter of fact, this change will DPG’s report, ‘…entropy is by far not the same as cause no harm to KPC itself, rather will make heat, and cannot be referred to as such, not even it easier to study and master. colloquially . For the sake of further discussion, ‘ ’ Our next thought was how to find a new term let the new interpretation of heat be called Falk s ’ to change the concept of entropy. On the one interpretation and the other one conventional hand, it seems to us that the word thermal would interpretation. ‘ ’ be the best substitute for ‘heat’. But we need an 3. A few thoughts on entropy answer to the question ‘thermal what?’ On the other hand, the word ‘caloric’ does not seem Is it possible to resolve the conflict or eliminate the suitable because it was not only banished from confusion? G. Job suggested that the word ‘heat’ physics as an invalid concept for many years, but and its combinations be denoted with an asterisk also has the meaning ‘thermal substance’ or ‘heat (*) when Falk s interpretation is used, and with ’ substance’ in English with its Chinese translation a dot ( ) when the conventional interpretation is · ‘热质’, in which the first character means‘ heat’ used [5].
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