Volume 67, Issue 12, December 1999
 GUEST COMMENT
 PAPERS


Bringing atoms into firstyear physics
View Description Hide DescriptionWe argue that thermal physics should not be treated as a separate topic in introductory physics. The firstyear calculusbased college physics should offer a modern, unified view of physics representative of the contemporary scientific enterprise. It should focus on the consequences of the central fact that matter is composed of atoms, and on the process of modeling physical systems. Such a focus is more interesting and relevant to students than a repetition of a purely classical treatment. We give an example of a course that emphasizes physical modeling of phenomena in terms of the atomic nature of matter. Thermal physics is woven into the entire course and is fully integrated with classical and semiclassical mechanics.

Thermal physics in the introductory physics course: Why and how to teach it from a unified atomic perspective
View Description Hide DescriptionHeat and thermodynamics are traditionally taught in the introductory physics course from a predominantly macroscopic point of view. However, it is advantageous to adopt a more modern approach that systematically builds on students’ knowledge of the atomic structure of matter and of elementary mechanics. By focusing on the essential physics without requiring more than elementary classical mechanics, this approach can be made sufficiently simple to be readily teachable during five or six weeks of an ordinary calculusbased introductory physics course. This approach can be highly unified, using atomic considerations to infer the properties of macroscopic systems while also enabling thermodynamicanalyses independent of specific atomic models. Furthermore, this integrated point of view provides a deeper physical understanding of basic concepts (such as internal energy, heat, entropy, and absolute temperature) and of important phenomena (such as equilibrium, fluctuations, and irreversibility).

Development of energy concepts in introductory physics courses
View Description Hide DescriptionThe workenergy theorem, derived from Newton’s second law, applies to the displacement of a particle or the center of mass of an extended body treated as a particle. Because work, as a quantity of energy transferred in accordance with the First Law of Thermodynamics, cannot be calculated in general as an applied force times the displacement of center of mass, the workenergy theorem is not a valid statement about energy transformations when work is done against a frictional force or actions on or by deformable bodies. To use work in conservation of energy calculations, work must be calculated as the sum of the products of forces and their corresponding displacements at locations where the forces are applied at the periphery of the system under consideration. Failure to make this conceptual distinction results in various errors and misleading statements widely prevalent in textbooks, thus reinforcing confusion about energy transformations associated with the action in everyday experience of zerowork forces such as those present in walking, running, jumping, or accelerating a car. Without a thermodynamically valid definition of work, it is also impossible to give a correct description of the connection between mechanical and thermal energy changes and of dissipative effects. The situation can be simply corrected and student understanding of the energy concepts greatly enhanced by introducing and using the concept of internal energy, that is, articulating the First Law of Thermodynamics in a simple, phenomenological form without unnecessary mathematical encumbrances.

Entropy and time
View Description Hide DescriptionThe emergence of a direction of time in statistical mechanics from an underlying timereversalinvariant dynamics is explained by examining a simple model. The manner in which timereversal symmetry is preserved and the role of initial conditions are emphasized. An extension of the model to finite temperatures also is discussed.

Entropy, information, and computation
View Description Hide DescriptionThe relation between entropy, information, and randomness is discussed. Algorithmic information theory is introduced and used to provide a fundamental definition of entropy. The relation between algorithmic entropy and the usual Shannon–Gibbs entropy is discussed.

Incomplete descriptions and relevant entropies
View Description Hide DescriptionStatistical mechanics relies on the complete although probabilistic description of a system in terms of all its microscopic variables. Its object is to derive from this microscopic description the static and dynamic properties for some reduced set of variables. The elimination of the irrelevant variables is guided by the maximum entropy criterion, which produces the least biased probability law consistent with the available information about the relevant variables. This approach defines relevant entropies which measure the missing information associated with the variables retained in the incomplete description. The relevant entropies depend not only on the state, but also on the coarseness of the reduced description of the system. Their use sheds light on questions such as the second law, both in equilibrium and in irreversible thermodynamics, the projection operator method of statistical mechanics, Boltzmann’s theorem, and spinecho experiments.

An invertibility paradox
View Description Hide DescriptionThe chaotic volumepreserving standard map is used to illustrate the invertibility paradox, which is related to the reversibility paradox of the microscopic foundations of thermodynamics. The new paradox, whose resolution relies exclusively on phasespace arguments, gives insight into Boltzmann’s original resolution of the reversibility paradox.

A thermodynamic derivative means an experiment
View Description Hide DescriptionAll too often, courses in thermodynamics and statistical mechanics barrage their students with numerous equations that are left unexamined and uninvestigated. This note explains how to pause, examine a thermodynamic equation, and render it more meaningful. Three techniques are discussed: (1) design two experiments that would measure the quantities on either side of the equality; (2) examine special cases; (3) consider the consequences if the equality failed to hold.

Thermodynamics of mixtures: Functions of mixing and excess functions
View Description Hide DescriptionApplying thermodynamics to realistic systems requires a knowledge of the thermodynamic properties of mixtures. Functions of mixing and excess functions provide a useful approach. The concepts are simple and their application straightforward, but students often fail to apply them correctly when they are given only a theoretical explanation. We discuss some typical mistakes and some problems we have found useful for overcoming them.

Thermodynamics at work: The pressure derivative of the specific heat
View Description Hide DescriptionThermodynamics relates measurable quantities such as thermal coefficients and specific heats. The first law, which implies that the enthalpy is a function of state, yields a relation for the pressure derivative of the specific heat The second law gives a simpler and wellknown relation for this pressure derivative. We compare the values of the pressure derivative of obtained from the first and second laws to the values obtained from measurements for water at different pressures. The comparison illustrates the scope and methodology of thermodynamics.

Thermodynamics of high temperature, Mie–Gruneisen solids
View Description Hide DescriptionWe construct a set of equations of state for condensed matter at temperatures well above the Debye temperature. These equations incorporate the Mie–Gruneisen equation of state and generic properties of high temperature solids. They are simple enough to provide an alternative to the ideal gas and the van der Waals equations of state for illustrating thermodynamic concepts.

A simple demonstration of a metastable state
View Description Hide DescriptionA system whose macroscopic properties appear to be unchanging in time may not be in a state of minimum free energy. A common example of such a metastable state is a supercooled liquid.Liquidsodium acetate is a system in which the passage of a supercooled liquid into its stable, crystalline form is readily demonstrated.

The thermodynamic cube: A mnemonic and learning device for students of classical thermodynamics
View Description Hide DescriptionThe “thermodynamic cube,” a mnemonic device for learning and recalling thermodynamic relations, is introduced. The cube is an extension of the familiar “thermodynamic square” seen in many textbooks. The cube reproduces the functions of the usual thermodynamic squares and incorporates the Euler relations which are not as well known.

What if entropy were dimensionless?
View Description Hide DescriptionOne of entropy’s puzzling aspects is its dimensions of energy/temperature. A review of thermodynamics and statistical mechanics leads to six conclusions: (1) Entropy’s dimensions are linked to the definition of the Kelvin temperature scale. (2) Entropy can be defined to be dimensionless when temperature T is defined as an energy (dubbed tempergy). (3) Dimensionless entropy per particle typically is between 0 and ∼80. Its value facilitates comparisons among materials and estimates of the number of accessible states. (4) Using dimensionless entropy and tempergy, Boltzmann’s constant k is unnecessary. (5) Tempergy, kT, does not generally represent a stored system energy. (6) When the (extensive) heat capacity tempergy is the energy transfer required to increase the dimensionless entropy by unity.

The art of statistical mechanics: Looking at microscopic spectra and seeing macroscopic phenomena
View Description Hide DescriptionSimple graphical spectra are presented as visual paradigms for the basic ideas of statistical mechanics. Each spectrum is designed so that the mechanical information can be readily converted into thermal and statistical properties.

An experiment to demonstrate the canonical distribution
View Description Hide DescriptionWe describe a simple experiment, suitable for an undergraduate laboratory, in which the collector current in a transistor is measured as a function of the base–emitter voltage at various temperatures. The experiment gives a very convincing demonstration of the canonical distribution of statistical mechanics, in which the probability of occupancy of a state of energy is proportional to

Detailed balance, quantum distribution functions, and equilibrium of mixtures
View Description Hide DescriptionWe consider systems of nearly free particles (or quasiparticles) interacting by scattering, emission and absorption of radiation, or by physical or chemical transformation. The condition of detailed balance yields the appropriate distribution function for each species, the equality of their temperatures, and a relation for their chemical potentials associated with particle transformations. For example, antiparticles coexisting in equilibrium have opposite chemical potentials, and excitations above the Bose–Einstein condensate have zero chemical potential. For mixtures of classical ideal gases, the law of mass action is obtained.

Three interesting problems in statistical mechanics
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A walk in phase space: Solidification into crystalline and amorphous states
View Description Hide DescriptionThe formation of crystalline and amorphous solids is described using a simple glass bead demonstration and a discussion of annealing and rapid quenching on a computer.
