scholarly journals Fractional differentiability of the non-smooth heat curve

2012 ◽  
Vol 61 (19) ◽  
pp. 190502
Author(s):  
Wu Guo-Cheng ◽  
Shi Xiang-Chao
Keyword(s):  
Heat Curve ◽  
Fractional Differentiability

THE ENTHALPY-POROSITY METHOD WITH A RECTANGULAR SPECIFIC HEAT CURVE

2018 ◽  
Author(s):  
Wim Beyne ◽  
Bernd Ameel ◽  
Alvaro de Gracia ◽  
Gabriel Zsembinszki ◽  
Luisa F Cabeza ◽  
...  
Keyword(s):  
Specific Heat ◽  
Heat Curve

An anomaly in the specific heat below 3 °K of copper containing hydrogen

1969 ◽  
Vol 47 (14) ◽  
pp. 1485-1491 ◽  
Author(s):  
Neil Waterhouse
Keyword(s):  
Specific Heat ◽  
Molecular Hydrogen ◽  
Pure Copper ◽  
Solid Hydrogen ◽  
Rotational State ◽  
Experimental Results ◽  
Ortho Hydrogen ◽  
Temperature Range ◽  
A Value ◽  
Heat Curve

The specific heat of copper heated in hydrogen at 1040 °C has been measured over the temperature range 0.4 to 3.0 °K and found to be anomalous. The anomaly occurs in the same temperature range as the solid hydrogen λ anomaly which, in conjunction with evidence of ortho to para conversion of hydrogen in the sample, suggests the presence of molecular hydrogen in the copper. The anomaly reported by Martin for "as-received" American Smelting and Refining Company (ASARCO) 99.999+ % pure copper has been briefly compared with the present results. The form of the anomaly produced by the copper-hydrogen specimen has been compared with Schottky curves using the simplest possible model, that for two level splitting of the degenerate J = 1 rotational state of the ortho-hydrogen molecule.Maintenance of the copper-hydrogen sample at ~20 °K for approximately 1 week removed the "hump" in the specific heat curve. An equation of the form Cp = γT + (464.34/(θ0c)3)T3 was found to fit these experimental results and produced a value for γ which had increased over that for vacuumannealed pure copper by ~2%.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

Computer Simulation Study of Adsorption, Isosteric Heat and Phase Transitions of Methane on Graphite

1992 ◽  
Vol 290 ◽  
Author(s):  
Shaoyi Jiang ◽  
Keith E. Gubbins
Keyword(s):  
Isosteric Heat ◽  
Graphite Substrate ◽  
Ensemble Monte Carlo ◽  
Adsorbed Films ◽  
Heat Curve ◽  
First Time ◽  
Grand Canonical ◽  
Adsorption Of Methane ◽  
Incommensurate Phases ◽  
Good Agreement

AbstractWe report Canonical (NVTMC), Grand Canonical (GOMC) and Gibbs Ensemble Monte Carlo (GEMC) simulations for adsorption of methane on graphite. Lennard-Jones (LJ) potentials are used for the intermolecular interactions, and both structured and structureless (10–4–3) solid-fluid potentials are considered. Several sets of methane-methane L.I parameters have been used in the literature, and we compare results obtained with these sets throughout our simulations. The adsorption isotherm and isosteric heat curve are obtained at 77.5 K and found in good agreement with experiments. The commensurateincommensurate transition (CIT) of methane on a graphite substrate with periodically varying adsorbate-adsorbent potential at 40.0 K is studied and is in qualitative agreement with experiment. The effect of varying the corrugation of the fluid-wall potential on the commensurate and incommensurate phases is explored. The GEMC simulations have been carried out to study the vapor-liquid equilibrium (VLE) of a two-dimensional (2D) LJ fluid with system sizes up to 3000 particles. The effect of system sizes on the critical behavior is investigated. The GEMC method has also been successfully applied to study the VLE in 2D adsorbed films for the first time.

On metastable approximations in co-operative assemblies

1956 ◽  
Vol 235 (1201) ◽  
pp. 247-259 ◽  
Keyword(s):  
Exact Solution ◽  
Specific Heat ◽  
Curie Point ◽  
Lattice Structure ◽  
Three Dimensional ◽  
Entropy Change ◽  
Successive Approximations ◽  
Series Expansions ◽  
Temperature Expansion ◽  
Heat Curve

The exact solution of the three-dimensional Ising model of a ferromagnetic presents diffi­culties of a very fundamental nature. It therefore seems that the most reliable information on the behaviour of the model is provided by exact series expansions of the partition func­tion at low and high temperatures. However, the usual low -temperature expansion fails to converge in the neighbourhood of the critical point. By rearranging the terms of the series on the basis of physical considerations, it is possible to obtain a systematic set of successive approximations, each approximation taking exact account of clusters of a given size or less (metastable approximations). By extrapolation accurate estimates can be derived of the Curie point and critical values of the energy and entropy. It is found that there is a marked difference in behaviour between two- and three-dimensional lattices, a far larger proportion of the entropy change taking place in the temperature region below the Curie point in the latter case. The corre­sponding specific heat curves are therefore much closer to those observed experimentally. Finally, a brief discussion is given of the dependence of the specific heat curve on lattice structure.

scholarly journals A note on the specific heat of the hydrogen molecule

1927 ◽  
Vol 115 (771) ◽  
pp. 483-486 ◽  
Keyword(s):  
Specific Heat ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Wave Mechanics ◽  
Nuclear Spins ◽  
Rotational States ◽  
Heat Curve ◽  
Symmetrical Group ◽  
The Moment ◽  
The One

In a recent article F. Hund has treated the problem of the specific heat of the hydrogen molecule on the basis of the wave mechanics. The total number of rotational states are divided due to the homopolar character of the molecule into two groups, to the one of which belong wave functions symmetrical in the two nuclei, and to the other wave functions which are antisymmetrical in the nuclei. Hund has suggested that the presence of both groups in hydrogen may be accounted for by assuming that the nuclei possess a spin, in which case transitions between symmetrical or between antisymmetrical states will have their usual intensity but transitions between symmetrical and antisymmetrical states will be very weak, of the order of the coupling of the nuclear spins. He then writes the following expression for the rotational specific heat, C r /R = σ 2 d 2 / d σ 2 log Q, Q = β [1 + 5 e -6σ + 9 e -20σ + ...] + 3 e -2σ + 7 e -12σ + 11 e -30σ +...., (1) where σ = h 2 /8π 2 I k T and β is the ratio of the weights of the symmetrical group of states to the antisymmetrical group. Hund has found that he obtains a close agreement between (1) and the observed specific heat curve only when β has about the value 2, that is when the symmetrical states have twice the weight of the antisymmetrical. He further obtains for this case I = 1·54 × 10 -41 gm. cm. 2 , the moment of inertia of the H 2 molecule.

Adsorption on evaporated tungsten films - II. The chemisorption of hydrogen and the catalytic parahydrogen conversion

1951 ◽  
Vol 206 (1084) ◽  
pp. 39-50 ◽  
Keyword(s):  
Air Temperatures ◽  
Reaction Proceeds ◽  
Heat Curve ◽  
Kinetics Of

The chemisorption of hydrogen in densely packed layers on tungsten is reversible even at liquid-air temperatures. Values for the fraction of surface atoms covered, θ, are obtained for various temperatures and pressures and the combination of isothermal heats for high θ values with previously published calorimetric heats for low θ values gives the heat curve for the whole chemisorption from θ = 0 to 1. The results are applied to the kinetics of the parahydrogen conversion, and it is claimed that reaction proceeds according to the equation 2W + H 2 ⇌ 2WH .

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