Entropy (energy dispersal)
Encyclopedia
The description of entropy as energy dispersal provides an introductory method of teaching the thermodynamic
concept of entropy
. In physics
and physical chemistry
, entropy has commonly been defined as a scalar
measure of the disorder of a thermodynamic system
. This newer approach sets out a variant approach to entropy, namely as a measure of energy
dispersal or distribution at a specific temperature
. Under this approach, changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature
.
The energy dispersal approach to teaching entropy was developed to facilitate teaching entropy to students beginning university chemistry
and biology
. This new approach also avoids ambiguous terms such as disorder and chaos, which have multiple everyday meanings.
, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.
Such descriptions have tended to be used together with commonly used terms such as disorder and chaos which are ambiguous, and whose everyday meaning is the opposite of what they are intended to mean in thermodynamics. Not only does this situation cause confusion, but it also hampers the teaching of thermodynamics. Students were being asked to grasp meanings directly contradicting their normal usage, with equilibrium
being equated to "perfect internal disorder" and the mixing of milk in coffee from apparent chaos to uniformity being described as a transition from an ordered state into a disordered state.
The description of entropy as the amount of "mixedupness" or "disorder," as well as the abstract nature of the statistical mechanics
grounding this notion, can lead to confusion and considerable difficulty for those beginning the subject. Even though courses emphasised microstate
s and energy level
s, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.
In this approach, the second law of thermodynamics
is introduced as "Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so." in the context of common experiences such as a rock falling, a hot frying pan cooling down, iron rusting, air leaving a punctured tyre and ice melting in a warm room. Entropy is then depicted as a sophisticated kind of "before and after" yardstick — measuring how much energy is spread out over time as a result of a process such as heating a system, or how widely spread out the energy is after something happens in comparison with its previous state, in a process such as gas expansion or fluids mixing (at a constant temperature). The equations are explored with reference to the common experiences, with emphasis that in chemistry the energy that entropy measures as dispersing is the internal energy of molecules.
The statistical interpretation is related to quantum mechanics in describing the way that energy is distributed (quantized) amongst molecules on specific energy levels, with all the energy of the macrostate always in only one microstate at one instant. Entropy is described as measuring the energy dispersal for a system by the number of accessible microstates, the number of different arrangements of all its energy at the next instant. Thus, an increase in entropy means a greater number of microstates for the final state than for the initial state, and hence more possible arrangements of a system's total energy at any one instant. Here, the greater 'dispersal of the total energy of a system' means the existence of many possibilities.
Continuous movement and molecular collisions visualised as being like bouncing balls blown by air as used in a lottery can then lead on to showing the possibilities of many Boltzmann distribution
s and continually changing "distribution of the instant", and on to the idea that when the system changes, dynamic molecules will have a greater number of accessible microstates. In this approach, all everyday spontaneous physical happenings and chemical reactions are depicted as involving some type of energy flows from being localized or concentrated to becoming spread out to a larger space, always to a state with a greater number of microstates.
This approach provides a good basis for understanding the conventional approach, except in very complex cases where the qualitative relation of energy dispersal to entropy change can be so inextricably obscured that it is moot. Thus in situations such as the entropy of mixing
when the two or more different substances being mixed are at the same temperature and pressure so there will be no net exchange of heat or work, the entropy increase will be due to the literal spreading out of the motional energy of each substance in the larger combined final volume. Each component’s energetic molecules become more separated from one another than they would be in the pure state, when in the pure state they were colliding only with identical adjacent molecules, leading to an increase in its number of accessible microstates.
Variants of the energy dispersal approach have been adopted in number of undergraduate chemistry texts, mainly in the United States. An advanced text, Physical Chemistry by Peter Atkins
of Oxford University and Julio De Paula, has followed suit. Starting with the 8th edition, Atkins and De Paula describe entropy in terms of dispersal of energy, without mentioning "disorder."
Websites have made the energy dispersal approach accessible not only to all students of chemistry, but also to the lay public seeking a basic intuitive understanding of thermodynamic entropy. For example, here is a page setting out the qualitative simplicity of the notion of entropy.
is created by any irreversible process (such as friction), or when heat is diffused by conduction, mechanical energy is dissipated, and it is impossible to restore the initial state.
In the mid-1950s, with the development of quantum theory
, researchers began speaking about entropy changes in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels, such as by the reactants and product
s of a chemical reaction
.
In 1984, the Oxford physical chemist Peter Atkins, in a book The Second Law, written for laypersons, presented a nonmathematical interpretation of what he called the "infinitely incomprehensible entropy" in simple terms, describing the Second Law of thermodynamics as "energy tends to disperse". His analogies included an imaginary intelligent being called "Boltzmann's Demon," who runs around reorganizing and dispersing energy, in order to show how the W in Boltzmann's equation relates to energy dispersion. This dispersion is transmitted via atomic vibrations and collisions. Atkins wrote: "each atom carries kinetic energy
, and the spreading of the atoms spreads the energy…the Boltzmann equation
therefore captures the aspect of dispersal: the dispersal of the entities that are carrying the energy."
Stanley Sandler, in his 1989 Chemical and Engineering Thermodynamics, described how given any thermodynamic process, a quantity TS can be interpreted as the amount of mechanical energy
that has been converted into thermal energy
by viscous dissipation, dispersion, and other system irreversibilities. In 1997, John Wrigglesworth described spatial particle distributions as represented by distributions of energy states. According to the second law of thermodynamics, isolated systems will tend to redistribute the energy of the system into a more probable arrangement or a maximum probability energy distribution, i.e. from that of being concentrated to that of being spread out. By virtue of the First law of thermodynamics
, the total energy does not change; instead, the energy tends to disperse from a coherent to a more incoherent state. In his 1999 Statistical Thermodynamics, M.C. Gupta defined entropy as a function that measures how energy disperses when a system changes from one state to another. Other authors defining entropy in a way that embodies energy dispersal are Cecie Starr and Andrew Scott.
In a 1996 article, the physicist Harvey S. Leff set out what he called "the spreading and sharing of energy." Another physicist, Daniel F. Styer, published an article in 2000 showing that "entropy as disorder" was inadequate. In an article published in the 2002 Journal of Chemical Education, Frank L. Lambert
argued that portraying entropy as "disorder" is confusing and should be abandoned. He has gone on to develop detailed resources for chemistry instructors, equating entropy increase as the spontaneous dispersal of energy, namely how much energy is spread out in a process, or how widely dispersed it becomes – at a specific temperature.
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
concept of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
. In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and physical chemistry
Physical chemistry
Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...
, entropy has commonly been defined as a scalar
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
measure of the disorder of a thermodynamic system
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....
. This newer approach sets out a variant approach to entropy, namely as a measure of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
dispersal or distribution at a specific temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
. Under this approach, changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature
Thermodynamic temperature
Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...
.
The energy dispersal approach to teaching entropy was developed to facilitate teaching entropy to students beginning university chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
and biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
. This new approach also avoids ambiguous terms such as disorder and chaos, which have multiple everyday meanings.
Problem: entropy as disorder is hard to teach
The term "entropy" has been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theoryQuantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.
Such descriptions have tended to be used together with commonly used terms such as disorder and chaos which are ambiguous, and whose everyday meaning is the opposite of what they are intended to mean in thermodynamics. Not only does this situation cause confusion, but it also hampers the teaching of thermodynamics. Students were being asked to grasp meanings directly contradicting their normal usage, with equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
being equated to "perfect internal disorder" and the mixing of milk in coffee from apparent chaos to uniformity being described as a transition from an ordered state into a disordered state.
The description of entropy as the amount of "mixedupness" or "disorder," as well as the abstract nature of the statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
grounding this notion, can lead to confusion and considerable difficulty for those beginning the subject. Even though courses emphasised microstate
Microstate (statistical mechanics)
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations...
s and energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.
Solution: entropy as energy dispersal
Entropy can be described in terms of "energy dispersal" and the "spreading of energy," while avoiding all mention of "disorder" and "chaos" except when explaining misconceptions. All explanations of where and how energy is dispersing or spreading have been recast in terms of energy disperal, so as to emphasise the underlying qualitative meaning.In this approach, the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
is introduced as "Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so." in the context of common experiences such as a rock falling, a hot frying pan cooling down, iron rusting, air leaving a punctured tyre and ice melting in a warm room. Entropy is then depicted as a sophisticated kind of "before and after" yardstick — measuring how much energy is spread out over time as a result of a process such as heating a system, or how widely spread out the energy is after something happens in comparison with its previous state, in a process such as gas expansion or fluids mixing (at a constant temperature). The equations are explored with reference to the common experiences, with emphasis that in chemistry the energy that entropy measures as dispersing is the internal energy of molecules.
The statistical interpretation is related to quantum mechanics in describing the way that energy is distributed (quantized) amongst molecules on specific energy levels, with all the energy of the macrostate always in only one microstate at one instant. Entropy is described as measuring the energy dispersal for a system by the number of accessible microstates, the number of different arrangements of all its energy at the next instant. Thus, an increase in entropy means a greater number of microstates for the final state than for the initial state, and hence more possible arrangements of a system's total energy at any one instant. Here, the greater 'dispersal of the total energy of a system' means the existence of many possibilities.
Continuous movement and molecular collisions visualised as being like bouncing balls blown by air as used in a lottery can then lead on to showing the possibilities of many Boltzmann distribution
Boltzmann distribution
In chemistry, physics, and mathematics, the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution...
s and continually changing "distribution of the instant", and on to the idea that when the system changes, dynamic molecules will have a greater number of accessible microstates. In this approach, all everyday spontaneous physical happenings and chemical reactions are depicted as involving some type of energy flows from being localized or concentrated to becoming spread out to a larger space, always to a state with a greater number of microstates.
This approach provides a good basis for understanding the conventional approach, except in very complex cases where the qualitative relation of energy dispersal to entropy change can be so inextricably obscured that it is moot. Thus in situations such as the entropy of mixing
Entropy of mixing
In thermodynamics the entropy of mixing is the increase in the total entropy of a compound system, when different and chemically non-reacting chemical substances or material components are mixed by removing partition between the system's initially separate volumes...
when the two or more different substances being mixed are at the same temperature and pressure so there will be no net exchange of heat or work, the entropy increase will be due to the literal spreading out of the motional energy of each substance in the larger combined final volume. Each component’s energetic molecules become more separated from one another than they would be in the pure state, when in the pure state they were colliding only with identical adjacent molecules, leading to an increase in its number of accessible microstates.
Variants of the energy dispersal approach have been adopted in number of undergraduate chemistry texts, mainly in the United States. An advanced text, Physical Chemistry by Peter Atkins
Peter Atkins
Peter William Atkins is a British chemist and former Professor of Chemistry at the University of Oxford and a Fellow of Lincoln College. He is a prolific writer of popular chemistry textbooks, including Physical Chemistry, Inorganic Chemistry, and Molecular Quantum Mechanics...
of Oxford University and Julio De Paula, has followed suit. Starting with the 8th edition, Atkins and De Paula describe entropy in terms of dispersal of energy, without mentioning "disorder."
Websites have made the energy dispersal approach accessible not only to all students of chemistry, but also to the lay public seeking a basic intuitive understanding of thermodynamic entropy. For example, here is a page setting out the qualitative simplicity of the notion of entropy.
History of energy dispersal
The exact origin of "energy dispersal" as a description of entropy change is not certain. Its first appearance is believed to have been in William Thomson's (Lord Kelvin) 1852 article "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy." Thomson distinguished between two types or "stores" of mechanical energy: "statical" and "dynamical." He discussed how these two types of energy can change from one form to the other during a thermodynamic transformation. When heatHeat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
is created by any irreversible process (such as friction), or when heat is diffused by conduction, mechanical energy is dissipated, and it is impossible to restore the initial state.
In the mid-1950s, with the development of quantum theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, researchers began speaking about entropy changes in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels, such as by the reactants and product
Product (chemistry)
Product are formed during chemical reactions as reagents are consumed. Products have lower energy than the reagents and are produced during the reaction according to the second law of thermodynamics. The released energy comes from changes in chemical bonds between atoms in reagent molecules and...
s of a chemical reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
.
In 1984, the Oxford physical chemist Peter Atkins, in a book The Second Law, written for laypersons, presented a nonmathematical interpretation of what he called the "infinitely incomprehensible entropy" in simple terms, describing the Second Law of thermodynamics as "energy tends to disperse". His analogies included an imaginary intelligent being called "Boltzmann's Demon," who runs around reorganizing and dispersing energy, in order to show how the W in Boltzmann's equation relates to energy dispersion. This dispersion is transmitted via atomic vibrations and collisions. Atkins wrote: "each atom carries kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
, and the spreading of the atoms spreads the energy…the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
therefore captures the aspect of dispersal: the dispersal of the entities that are carrying the energy."
Stanley Sandler, in his 1989 Chemical and Engineering Thermodynamics, described how given any thermodynamic process, a quantity TS can be interpreted as the amount of mechanical energy
Mechanical energy
In physics, mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system. It is the energy associated with the motion and position of an object. The law of conservation of energy states that in an isolated system that is only subject to...
that has been converted into thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....
by viscous dissipation, dispersion, and other system irreversibilities. In 1997, John Wrigglesworth described spatial particle distributions as represented by distributions of energy states. According to the second law of thermodynamics, isolated systems will tend to redistribute the energy of the system into a more probable arrangement or a maximum probability energy distribution, i.e. from that of being concentrated to that of being spread out. By virtue of the First law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
, the total energy does not change; instead, the energy tends to disperse from a coherent to a more incoherent state. In his 1999 Statistical Thermodynamics, M.C. Gupta defined entropy as a function that measures how energy disperses when a system changes from one state to another. Other authors defining entropy in a way that embodies energy dispersal are Cecie Starr and Andrew Scott.
In a 1996 article, the physicist Harvey S. Leff set out what he called "the spreading and sharing of energy." Another physicist, Daniel F. Styer, published an article in 2000 showing that "entropy as disorder" was inadequate. In an article published in the 2002 Journal of Chemical Education, Frank L. Lambert
Frank L. Lambert
Frank L. Lambert is a Professor Emeritus of Chemistry at Occidental College, Los Angeles. He is known for his advocacy of changing the definition of thermodynamic entropy as “disorder” in US general chemistry texts to its replacement by viewing entropy as a measure of energy dispersal.-Teaching...
argued that portraying entropy as "disorder" is confusing and should be abandoned. He has gone on to develop detailed resources for chemistry instructors, equating entropy increase as the spontaneous dispersal of energy, namely how much energy is spread out in a process, or how widely dispersed it becomes – at a specific temperature.
Further reading
- Carson, E. M., and Watson, J. R., (Department of Educational and Professional Studies, Kings College, London), 2002, "Undergraduate students' understandings of entropy and Gibbs Free energy," University Chemistry Education - 2002 Papers, Royal Society of Chemistry.
- Frank L. Lambert, 2002, "Disorder - A Cracked Crutch For Supporting Entropy Discussions," Journal of Chemical Education 79: 187-92. Updated version here.
- Leff, Harvey S., 2007, "Entropy, Its Language and Interpretation," Foundations of Physics 37(12): 1744-66.
Texts using the energy dispersal approach
- Atkins, P. W., Physical Chemistry for the Life Sciences. Oxford University Press, ISBN 0-19-928095-9; W. H. Freeman, ISBN 0-7167-8628-1
- Benjamin Gal-Or, "Cosmology, Physics and Philosophy", Springer-Verlag, New York, 1981, 1983, 1987 ISBN 0-387-90581-2, W. H. Freeman ISBN 0-7167-8759-8
- Bell, J., et al., 2005. Chemistry: A General Chemistry Project of the American Chemical Society, 1st ed. W. H. Freeman, 820pp, ISBN 0-7167-3126-6
- Brady, J.E., and F. Senese, 2004. Chemistry, Matter and Its Changes, 4th ed. John Wiley, 1256pp, ISBN 0-471-21517-1
- Brown, T. L., H. E. LeMay, and B. E. Bursten, 2006. Chemistry: The Central Science, 10th ed. Prentice Hall, 1248pp, ISBN 0-13-109686-9
- Ebbing, D.D., and S. D. Gammon, 2005. General Chemistry, 8th ed. Houghton-Mifflin, 1200pp, ISBN 0-618-39941-0
- Ebbing, Gammon, and Ragsdale. Essentials of General Chemistry, 2nd ed.
- Hill, Petrucci, McCreary and Perry. General Chemistry, 4th ed.
- Kotz, Treichel, and Weaver. Chemistry and Chemical Reactivity, 6th ed.
- Moog, Spencer, and Farrell. Thermodynamics, A Guided Inquiry.
- Moore, J. W., C. L. Stanistski, P. C. Jurs, 2005. Chemistry, The Molecular Science, 2nd ed. Thompson Learning. 1248pp, ISBN 0-534-42201-2
- Olmsted and Williams, Chemistry, 4th ed.
- Petrucci, Harwood, and Herring. General Chemistry, 9th ed.
- Silberberg, M.S., 2006. Chemistry, The Molecular Nature of Matter and Change, 4th ed. McGraw-Hill, 1183pp, ISBN 0-07-255820-2
- Suchocki, J., 2004. Conceptual Chemistry 2nd ed. Benjamin Cummings, 706pp, ISBN 0-8053-3228-6
External links
- Entropy Sites: A Guide. A large website, maintained by Frank L. Lambert, with links to work on the energy disperal approach to entropy.
- "The Second Law of Thermodynamics (6)."