A Complementary Relation of Fluctuations between Energy and Temperature in a Small Specimen

2020 ◽  
pp. 2150026
Author(s):  
Shoichi Nagata
Keyword(s):  
Simple Formula ◽  
Heat Bath ◽  
Temperature Fluctuations ◽  
Physical Models ◽  
Small Specimen ◽  
Amount Of Substance ◽  
Complementary Relation ◽  
Avogadro’S Number ◽  
Number Formula ◽  
Quantitative Analyses

Research on fluctuations in energy and temperature is presented for a small specimen. The small specimen in contact with a heat bath shows energy fluctuations, [Formula: see text], at the constant temperature. On the other hand, when this small specimen is isolated from the reservoir and adiabatic isolation is kept, it exhibits temperature fluctuations, [Formula: see text], at the constant energy. This means that the temperature is unsharp if a sharp energy is assigned. A complementary relation between [Formula: see text] and [Formula: see text] is proposed in a simple formula. The connection between [Formula: see text] and [Formula: see text] is mediated by the heat capacity [Formula: see text]. This complementary relation is valid in general and it does not depend on the amount of substance. If the constituent number[Formula: see text] of the system is of the order of Avogadro’s number, then the fluctuations have been masked by large [Formula: see text]and we cannot see the influence of the fluctuations. However, when the number [Formula: see text] decreases, the intrinsic features of fluctuations come out gradually. This paper presents the quantitative analyses of the fluctuations in the energy and temperature for several physical models. Typical characteristics in the fluctuations can be clearly seen only in a small specimen, which are shown in the graphical representations. It is stressed that the values of [Formula: see text] and [Formula: see text] are defined for the different prescribed conditions specified above.

Temperature fluctuations in a heat bath

1993 ◽  
Vol 61 (1) ◽  
pp. 54-58 ◽  
Author(s):  
Harrison Bertrand Prosper
Keyword(s):  
Heat Bath ◽  
Temperature Fluctuations

A relationship between the Avogadro’s number NA and the transition frequency of the caesium 133 atom ΔνCs

2021 ◽  
Vol 34 (1) ◽  
pp. 12-16
Author(s):  
Teodor Ognean
Keyword(s):  
Ground State ◽  
International System ◽  
Transition Frequency ◽  
Amount Of Substance ◽  
Weights And Measures ◽  
Avogadro’S Number ◽  
System Of Units ◽  
Measurement Units ◽  
Definition Of ◽  
New Si

At the 26th meeting of the General Conference on Weights and Measures (CGPM) held on 13‐16 November 2018 at Versailles, France, the new International System of Units (SI) was established. Following the CGPM’s decision, the new SI units were established based upon a set of seven defining constants. This set of constants is the most fundamental feature in the definition of the entire system of units. What is truly remarkable about the new SI is the fact that all measurement units, except the amount of substance mole and Avogadro’s number NA , are defined based on the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Cs</mml:mi> </mml:mrow> </mml:msub> </mml:math> equal to 9 192 631 770 Hz. This article, based on dimensional analysis, presents the possibility of connecting the Avogadro’s number NA and the mole, to the transition frequency <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mo>Δν</mml:mo> </mml:mrow> <mml:mrow> <mml:mtext>Cs</mml:mtext> </mml:mrow> </mml:msub> </mml:math> .

Temperature Fluctuations for a System in Contact with a Heat Bath

2013 ◽  
Vol 153 (6) ◽  
pp. 1132-1142 ◽  
Author(s):  
J. Leo van Hemmen ◽  
André Longtin
Keyword(s):  
Heat Bath ◽  
Temperature Fluctuations

scholarly journals Temperature Fluctuations and Mixtures of Equilibrium States in the Canonical Ensemble

2004 ◽  
Author(s):  
Hugo Touchette
Keyword(s):  
Thermodynamic Limit ◽  
Particle Physics ◽  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Thermal Contact ◽  
Heat Bath ◽  
Temperature Fluctuations ◽  
Thermodynamic Quantities ◽  
Inverse Temperature ◽  
Nuclear Scattering

It has been suggested recently that "Q-exponential" distributions, which form the basis of Tsallis' nonextensive thermostatistical formalism, may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. In this chapter, we revisit this idea in connection with a detailed microscopic calculation of the energy and temperature fluctuations present in a finite vessel of perfect gas thermally coupled to a heat bath. We find that the probability density related to the inverse temperature of the gas has a form similar to a x<sup>2</sup> density, and that the "mixed" Gibbs distribution inferred from this density is non-Gibbsian. These findings are compared with those obtained by a number of researchers who worked on mixtures of Gibbsian distributions in the context of velocity difference measurements in turbulent fluids as well as secondary distributions in nuclear scattering experiments…. Most, if not all, textbooks on thermodynamics and statistical physics define temperature as being a quantity which, contrary to other thermodynamic observables like energy or pressure, does not admit fluctuations. Because of that, it is somewhat surprising to see papers with the expression "temperature fluctuations" in their titles appearing from time to time in serious scientific journals on subjects as various as particle physics and fluid dynamics (see, e.g., Ashkenazi and Steinberg [3], Ching [9], Chiu et al. [10], and Stodolsky [24]). Indeed, how can the temperature of a system, however small, fluctuate if one defines it "as equal to the temperature of a very large heat reservoir with which the system is in equilibrium and in thermal contact" [18]? Also, in the case of the reservoir, how can temperature be a fluctuating parameter if its definition requires one to assume the thermodynamic limit, in other words, to assume that the system acting as a reservoir is composed of an infinite number of particles or degrees of freedom? Presumably, the thermodynamic limit should rule out any fluctuations of thermodynamic quantities like the mean energy or the pressure, so that if temperature is related to these quantities, how can it fluctuate?

The Mole and Avogadro’s Number

2021 ◽  
pp. 13-18
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Amount Of Substance ◽  
Avogadro’S Number

Measuring Chemical Quantities: The Mole introduces the mole as the chemist’s unit for the amount of substance and discusses its relationship with Avogadro’s number of chemical entities including atoms, ions, molecules and formula units. Calculations demonstrate the use of the mole to convert between mass and the number of chemical entities.

scholarly journals More 1-cocycles for classical knots

2021 ◽  
pp. 2150032
Author(s):  
Thomas Fiedler
Keyword(s):  
Natural Number ◽  
Moduli Space ◽  
Lagrange Interpolation ◽  
Simple Formula ◽  
Solid Torus ◽  
Interpolation Polynomial ◽  
Lagrange Interpolation Polynomial ◽  
Vassiliev Invariant ◽  
Number Formula

Let [Formula: see text] be the topological moduli space of long knots up to regular isotopy, and for any natural number [Formula: see text] let [Formula: see text] be the moduli space of all [Formula: see text]-cables of framed long knots which are twisted by a string link to a knot in the solid torus [Formula: see text]. We upgrade the Vassiliev invariant [Formula: see text] of a knot to an integer valued combinatorial 1-cocycle for [Formula: see text] by a very simple formula. This 1-cocycle depends on a natural number [Formula: see text] with [Formula: see text] as a parameter and we obtain a polynomial-valued 1-cocycle by taking the Lagrange interpolation polynomial with respect to the parameter. We show that it induces a non-trivial pairing on [Formula: see text] already for [Formula: see text].

Quantitative Analysis of Powder Mixtures by Diffuse Reflectance

1980 ◽  
Vol 34 (2) ◽  
pp. 161-164 ◽  
Author(s):  
Harry G. Hecht
Keyword(s):  
Quantitative Analysis ◽  
Simple Formula ◽  
Diffuse Reflectance ◽  
The Other ◽  
Model Systems ◽  
Large Concentration ◽  
Initial Estimate ◽  
Powder Mixtures ◽  
Fitting Procedure ◽  
Quantitative Analyses

Previous tests of continuum diffuse reflectance models are extended in the current study to include powder mixtures in which one component is an intense absorbant and the other is a nonabsorbing scatterer. For model systems of this type, the Pitts-Giovanelli formula gives a very good fit over a large concentration range. However, the fitting procedure is very sensitive to the initial estimate of parameters, and it failed to converge in several cases. The Rozenberg formula, on the other hand, was very stable and gave a moderately good fit to the data, particularly for low reflectances. A simplified version of the Rozenberg formula, Ro/ R = 1 + β, was almost as good, and represents a very simple formula which should be quite useful for quantitative analyses.

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

In situ microprobe quantitation of inorganic particle burden in paraffin sections of lung tissue

1988 ◽  
Vol 46 ◽  
pp. 990-991
Author(s):  
Jerrold L. Abraham
Keyword(s):  
Lung Tissue ◽  
Quantitative Information ◽  
Particulate Material ◽  
Paraffin Sections ◽  
Tissue Samples ◽  
Qualitative And Quantitative ◽  
The Past ◽  
Quantitative Analyses ◽  
Data Result

Inorganic particulate material of diverse types is present in the ambient and occupational environment, and exposure to such materials is a well recognized cause of some lung disease. To investigate the interaction of inhaled inorganic particulates with the lung it is necessary to obtain quantitative information on the particulate burden of lung tissue in a wide variety of situations. The vast majority of diagnostic and experimental tissue samples (biopsies and autopsies) are fixed with formaldehyde solutions, dehydrated with organic solvents and embedded in paraffin wax. Over the past 16 years, I have attempted to obtain maximal analytical use of such tissue with minimal preparative steps. Unique diagnostic and research data result from both qualitative and quantitative analyses of sections. Most of the data has been related to inhaled inorganic particulates in lungs, but the basic methods are applicable to any tissues. The preparations are primarily designed for SEM use, but they are stable for storage and transport to other laboratories and several other instruments (e.g., for SIMS techniques).

A New Detector System For The HB5 Stem Instrument

1985 ◽  
Vol 43 ◽  
pp. 134-135
Author(s):  
J.M. Cowley
Keyword(s):  
Dark Field ◽  
Detector System ◽  
Electron Holography ◽  
Small Specimen ◽  
Bright Field ◽  
Multiple Images ◽  
Practical Applications ◽  
Wide Range ◽  
Diffraction Patterns ◽  
Operational Modes

The HB5 STEM instrument at ASU has been modified previously to include an efficient two-dimensional detector incorporating an optical analyser device and also a digital system for the recording of multiple images. The detector system was built to explore a wide range of possibilities including in-line electron holography, the observation and recording of diffraction patterns from very small specimen regions (having diameters as small as 3Å) and the formation of both bright field and dark field images by detection of various portions of the diffraction pattern. Experience in the use of this system has shown that sane of its capabilities are unique and valuable. For other purposes it appears that, while the principles of the operational modes may be verified, the practical applications are limited by the details of the initial design.

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