Volume 70, Issue 2, February 2002
 LETTERS TO THE EDITOR



Spinstatistics theorem
View Description Hide Description  Top

 QUESTIONS AND ANSWERS


Answer to Question #78. A question about the Maxwell relations in thermodynamics
View Description Hide Description 
Answer to Question #78. A question about the Maxwell relations in thermodynamics
View Description Hide Description 
Answer to Question #78. A question about the Maxwell relations in thermodynamics
View Description Hide Description 
Answer to Question #78. A question about the Maxwell relations in thermodynamics
View Description Hide Description 
Answer to Question #78. A question about the Maxwell relations in thermodynamics
View Description Hide Description 
Question #81. The equipartition theorem and rotational instability
View Description Hide Description  Top

 PAPERS


Resource Letter: TACMB1: The theory of anisotropies in the cosmic microwave background
View Description Hide DescriptionThis Resource Letter provides a guide to the literature on the theory of anisotropies in the cosmic microwave background. Journal articles, web pages, and books are cited for the following topics: discovery, cosmological origin, early work, recombination, general CMBanisotropy references, primary CMBanisotropies (numerical, analytical work), secondary effects, SunyaevZel’dovich effect(s), lensing, reionization, polarization,gravity waves, defects, topology, origin of fluctuations, development of fluctuations, inflation and other ties to particle physics, parameter estimation, recent constraints, web resources, foregrounds, observations and observational issues, and Gaussianity.

Cautious revolutionaries: Maxwell, Planck, Hubble
View Description Hide DescriptionThree scientists exemplified the cautious behavior that we might like all scientists to display: indeed, they were so critical of their own ideas that they risked losing credit for them. Nevertheless, they finally earned at least as much fame as they deserved, leaving historians to wonder about what they really believed. Maxwell initially rejected the kinetic theory of gases because two of its predictions disagreed with experiments; later he revived the theory, showed that one of those experiments had been misinterpreted, and eventually became known as one of the founders of the modern theory. Planck seems to have intended his 1900 quantum hypothesis as a mathematical device, not a physical discontinuity; later he limited it to the emission (not absorption) of radiation, thereby discovering “zeropoint energy.” Eventually he accepted the physical quantum hypothesis and became known as its discoverer. Hubble (with Humason) established the distance–velocity law, which others used as a basis for the expanding universe theory; later he suggested that redshifts may not be due to motion and appeared to lean toward a static model in place of the expanding universe.

A statistical development of entropy for the introductory physics course
View Description Hide DescriptionMany introductory physics texts introduce the statistical basis for the definition of entropy in addition to the Clausius definition, We use a model based on equally spaced energy levels to present a way that the statistical definition of entropy can be developed at the introductory level. In addition to motivating the statistical definition of entropy, we also develop statistical arguments to answer the following questions: (i) Why does a system approach a state of maximum number of microstates? (ii) What is the equilibrium distribution of particles? (iii) What is the statistical basis of temperature? (iv) What is the statistical basis for the direction of spontaneous energy transfer? Finally, a correspondence between the statistical and the classical Clausius definitions of entropy is made.

Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas
View Description Hide DescriptionWe report on an investigation of student understanding of the first law of thermodynamics. The students involved were drawn from firstyear university physics courses and a secondyear thermal physics course. The emphasis was on the ability of the students to relate the first law to the adiabatic compression of an ideal gas. Although they had studied the first law, few students recognized its relevance. Fewer still were able to apply the concept of work to account for a change in temperature in an adiabatic process. Instead most of the students based their predictions and explanations on a misinterpretation of the ideal gas law. Even when ideas of energy and work were suggested, many students were unable to give a correct analysis. They frequently failed to differentiate the concepts of heat, temperature, work, and internal energy. Some of the difficulties that students had in applying the concept of work in a thermal process seemed to be related to difficulties with mechanics. Our findings also suggest that a misinterpretation of simple microscopic models may interfere with student ability to understand macroscopic phenomena. Implications for instruction in thermal physics and in mechanics are discussed.

A calculation of the timeofflight distribution of trapped atoms
View Description Hide DescriptionWe consider the ballistic expansion of a cloud of trapped atoms falling under the influence of gravity. Using a simple coordinate transformation, we derive an analytical expression for the timeofflight signal. The properties of the signal can be used to infer the initial temperature of the cloud. We first assume a point size cloud with an isotropic velocity distribution to explain the physical basis of the calculation. The treatment is then generalized to include a finitesize cloud with an anisotropic velocity distribution, and an exact result for the signal is derived. The properties of the signal are discussed, and an intuitive picture is presented to explain how initial conditions determine the features of the signal.

Perturbation of infinite networks of resistors
View Description Hide DescriptionThe resistance between arbitrary nodes of an infinite network of resistors is calculated when the network is perturbed by removing one bond from the perfect lattice. A relation is given between the resistance and the lattice Green’s function of the perturbed resistor network. By solving the Dyson equation, the Green’s function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results are presented for a square lattice.

The shape of the Eiffel Tower
View Description Hide DescriptionThe distinctive shape of the Eiffel Tower is based on simple physics and is designed so that the maximum torque created by the wind is balanced by the torque due to the Tower’s weight. We use this idea to generate an equation for the shape of the Tower. The solution depends only on the width of the base and the maximum wind pressure. We parametrize the wind pressure and reproduce the shape of the Tower. We also discuss some of the Tower’s interesting history and characteristics.

Forces on permeable conductors in magnetic fields
View Description Hide DescriptionIt is often implied that the force density formula is all that is required to calculate the force that would be experienced by any stationary currentcarrying medium in a region of space containing a magnetic field. However, representations of this formula are not all compatible, and the methods of applying such formulas when the conductor or surrounding medium have permeabilities different from vacuum are not widely known. The simplest case that one might consider is that of a currentcarrying wire in an otherwise uniform field. It appears that the experimental measurements corresponding to such a situation have not been carried out for permeable media, and these results are reported here. The permeability and current can cause substantial changes in the field distribution from its background form, but the total force per unit length on the wire remains compatible with the formula with I being the conduction current and being the flux density that was present before the permeable currentcarrying wire was introduced.

An experimental apparatus for white light imaging by means of a spherical obstacle
View Description Hide DescriptionWe discuss the use of a spherical obstacle as an imaging device for white light illumination. A brief description of the phenomenon is given and then a simple, compact experimental apparatus is described in detail. The experimental results underline the importance of the spatial incoherence of light used in the imaging arrangement. The superiority of incoherent over coherent illumination is demonstrated and some interesting features of imaging by a spherical obstacle are discussed.

Understanding wave characteristics via linear superposition of retarded fields
View Description Hide DescriptionThe Feynman–Schwartz method of linearly superposing retarded fields to understand the origin of the refractive index is generalized to an obliquely incident electromagnetic wave interacting with a planar medium. Different integral equations for the wave field in the medium are obtained for the state and the state of wave polarization. The two states of polarization are shown to satisfy the same differential equation for the spatial variation of the fields and thus they have the same dispersion relation (or the index of refraction) and change of phase velocity upon penetration into the medium. The integral equations are also used to deduce the wellknown reflection and transmission coefficients in various cases.

δ function converging sequences
View Description Hide DescriptionWe discuss the usefulness and physical interpretation of a simple and general way of constructing sequences of functions that converge to the Dirac delta function. The main result, which seems to have been largely overlooked, includes most of the δfunction converging sequences found in textbooks, is easily extended, and can be used to introduce many useful generalized functions to physics students with little mathematical background. We show that some interesting deltafunction identities are simple consequences of the one discussed here. An illustrative example in electrodynamics is also analyzed, with the surprising result that the formalism allows as a limit an uncharged massless particle which creates no electromagnetic field, but has a nonzero electromagnetic energy–momentum tensor.
 Top
