<i>An Introduction to Thermal Physics</i>

Schroeder, Daniel V.; Gould, Harvey

doi:10.1063/1.2405696

Cited by 146 publications

(96 citation statements)

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“…When the working medium of the Otto cycle is classical ideal gas, the efficiency of the system is written as η = 1 − (V 1 /V 2 ) γ−1 , where V 1 and V 2 are initial and final volumes (V 1 < V 2 ) of the adiabatic expansion process and γ = C p /C v , is the ratio of the specific heats [33]. Similar to the classical cycle, the quantum Otto cycle consists of two adiabatic processes and two thermalization processes [34,35].…”

Section: Quantum Otto Cyclementioning

confidence: 99%

Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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Abstract:We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples; coupled spin-1/2 systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-1/2 systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus, the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.

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Section: Quantum Otto Cyclementioning

confidence: 99%

Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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“…The probability of photon creation is expressed by a weighting factor that is a function of the temperature of the cavity and the wavelength of the photon. By combining my derivation of the temperature-independent prefactor with Planck's temperature-dependent probability distribution, I will show that the major equations [17][18][19][20] that describe blackbody radiation can be derived from the assumption that the photon is an extended body in 3-dimensional Euclidean space.…”

Section: Resultsmentioning

confidence: 99%

Evidence that photons have extension in space

Wayne¹

2014

Turk J Phys

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Satyendra Nath Bose realized that there was a logical inconsistency in the derivation of Planck's radiation law since the derivation used to obtain the temperature-independent prefactor in the blackbody radiation law had been based in part on classical wave hypotheses, such as the number of degrees of freedom of the ether. Bose worked out a strictly quantum derivation by combining the quantum hypothesis with statistical mechanics to determine the number of states of each mode that would occupy a 6-dimensional phase space. Here I use the model of an extended photon to show that the temperature-independent prefactor of Planck's radiation law can be derived in an alternative manner by calculating how many extended photons of each mode would fill a 3-dimensional Euclidean space. By combining my derivation of the temperature-independent prefactor with Planck's temperature-dependent probability distribution, I show that all of the major equations that describe blackbody radiation can be derived from the assumption that the photon is an extended body in 3-dimensional Euclidean space. This derivation provides evidence for the suggestion that photons are neither mathematical points nor groups of infinite plane waves, but quantized and finite volume elements.

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“…This work showed that even after instruction students often struggle to distinguish microstates of a system from macrostates and to appropriately relate the two. The fundamental assumption of statistical mechanics states that all accessible microstates of a system (microscopic arrangements of a system's particles in phase space) are equally probable [23]. Microstates that share common macroscopic properties (system volume, internal energy, etc.)…”

Section: Introductionmentioning

confidence: 99%

“…for the binomial distribution. Some students took this idea to the extreme on the coin toss question by stating that the most probable result of flipping 6 × 10 23 coins is 3 × 10 23 AE 1 heads. The distinction between a single discrete macrostate and an equilibrium thermodynamic "state" (consisting of a range of virtually indistinguishable macrostates) is subtle and requires careful attention by both students and instructors.…”

Section: Introductionmentioning

confidence: 99%

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Student understanding of the Boltzmann factor

Smith

Mountcastle

Thompson

2015

Phys. Rev. ST Phys. Educ. Res.

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[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.

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An Introduction to Thermal Physics

Cited by 146 publications

References 0 publications

Implications of Coupling in Quantum Thermodynamic Machines

Implications of Coupling in Quantum Thermodynamic Machines

Evidence that photons have extension in space

Student understanding of the Boltzmann factor

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