scholarly journals Thermodynamics of Generalized Fermi Systems in a Harmonic Trap

2022 ◽  
Vol 2148 (1) ◽  
pp. 012012
Author(s):  
Yushan Li
Keyword(s):  
Heat Capacity ◽  
Thermodynamic Parameters ◽  
Three Dimensional ◽  
Harmonic Trap ◽  
Tsallis Entropy ◽  
Fermi Systems

Abstract Thermodynamics of the generalized ideal Fermi systems in the two-and three-dimensional harmonic traps are respectively calculated by the Tsallis entropy in this paper. The influences of the trap and q-number on the thermodynamic parameters (epically the heat capacity) are analysed in detail. The results yield a well agreement with the classical cases.

scholarly journals ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

2017 ◽  
Vol 126 (1B) ◽  
Author(s):  
PHẠM NGUYỄN THÀNH VINH
Keyword(s):  
Heat Capacity ◽  
Total Energy ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Integral Function ◽  
Harmonic Trap ◽  
Thermodynamic Quantities ◽  
Comprehensive Study ◽  
The Ideal

In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.

scholarly journals ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

2017 ◽  
Vol 126 (1B) ◽  
pp. 117 ◽  
Author(s):  
Pham Nguyen Thanh Vinh
Keyword(s):  
Heat Capacity ◽  
Total Energy ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Integral Function ◽  
Harmonic Trap ◽  
Thermodynamic Quantities ◽  
Comprehensive Study ◽  
The Ideal

In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.

Computational Insights Into Air-Side Flow and Heat Transfer in Compact Heat Exchangers

2005 ◽  
Author(s):  
D. K. Tafti
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Heat Exchangers ◽  
Three Dimensional ◽  
Computer Experiments ◽  
Transfer Coefficients ◽  
Substantial Impact ◽  
Compact Heat Exchangers ◽  
Thermal Phenomena ◽  
Side Flow

The paper describes two- and three-dimensional computer simulations which are used to study fundamental flow and thermal phenomena in multilouvered fins used for air-side heat transfer enhancement in compact heat exchangers. Results pertaining to flow transition, thermal wake interference, and fintube junction effects are presented. It is shown that a Reynolds number based on flow path rather than louver pitch is more appropriate in defining the onset of transition, and characteristic frequencies in the louver bank scale better with a global length scale such as fin pitch than with louver pitch or thickness. With the aid of computer experiments, the effect of thermal wakes is quantified on the heat capacity of the fin as well as the heat transfer coefficient, and it is established that experiments which neglect accounting for thermal wakes can introduce large errors in the measurement of heat transfer coefficients. Further, it is shown that the geometry of the louver in the vicinity of the tube surface has a large effect on tube heat transfer and can have a substantial impact on the overall heat capacity.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

Simulation of Heat Transfer in Bridge-Based Micro Calorimeters

2009 ◽  
Author(s):  
Jun Yu ◽  
Zhen’an Tang ◽  
Zhengxing Huang ◽  
Chong Feng
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Silicon Substrate ◽  
Three Dimensional ◽  
Temperature Response ◽  
Differential Method ◽  
Three Dimensional Finite Element ◽  
Micro Calorimeter

Previous studies of bridge-based micro calorimeters have shown that these devices can measure heat capacity and melting point of ultra thin films with pulse scan calorimetry. The bridge-based micro calorimeters consist of a sample region and several beams that connecting the sample region with silicon substrate. Both the sample region and the beams are suspending on the silicon substrate for thermal isolation. The temperature distribution of the micro calorimeter during a heating pulse depends on the joule-heating of the heating resistor, the heat absorption and heat conduct of the bridge. The heat transfer through the beams during a pulse scan measurement is complex because there is heat generation on some beams and the temperature distribution along the beams is not uniform. Using three dimensional finite element analyses (FEA), the thermal-electrical simulations of the heat transfer in the bridge-based micro calorimeters have been performed. The heat consumption and temperature distribution at steady state analyses, the temperature response of the bridge and the heat generation of the heater at transient analyses have been calculated for the bridge-based micro calorimeter with different sample thermal conductivities and heat capacities. The simulation results indicate that for the bridge-based microcalorimeter using pulse calorimetry, when the heat capacity of the sample film is close to or larger than the heat capacity of an empty calorimeter, the differential method of getting the sample heat capacity from the difference between a micro calorimeter with and without the sample is no longer suitable because the heat transfer and temperature distributions of the two calorimeters are no longer comparable to each other.

scholarly journals Magnetic and Electronic Properties of π-d Interacting Molecular Magnetic Superconductor κ-(BETS)2FeX4 (X = Cl, Br) Studied by Angle-Resolved Heat Capacity Measurements

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 66 ◽  
Author(s):  
Shuhei Fukuoka ◽  
Sotarou Fukuchi ◽  
Hiroki Akutsu ◽  
Atsushi Kawamoto ◽  
Yasuhiro Nakazawa
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Magnetic Fields ◽  
Temperature Dependence ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Spin Configuration ◽  
Magnetic Superconductor ◽  
Heat Capacity Measurements ◽  
Long Range Ordering

Thermodynamic picture induced by π-d interaction in a molecular magnetic superconductor κ-(BETS)2FeX4 (X = Cl, Br), where BETS is bis(ethylenedithio)tetraselenafulvalene, studied by single crystal calorimetry is reviewed. Although the S = 5/2 spins of Fe3+ in the anion layers form a three-dimensional long-range ordering with nearly full entropy of Rln6, a broad hump structure appears in the temperature dependence of the magnetic heat capacity only when the magnetic field is applied parallel to the a axis, which is considered as the magnetic easy axis. The scaling of the temperature dependence of the magnetic heat capacity of the two salts is possible using the parameter of |Jdd|/kB and therefore the origin of the hump structure is related to the direct magnetic interaction, Jdd, that is dominant in the system. Quite unusual crossover from a three-dimensional ordering to a one-dimensional magnet occurs when magnetic fields are applied parallel to the a axis. A notable anisotropic field-direction dependence against the in-plane magnetic field was also observed in the transition temperature of the bulk superconductivity by the angle-resolved heat capacity measurements. We discuss the origin of this in-plane anisotropy in terms of the 3d electron spin configuration change induced by magnetic fields.

Studies in Solvolysis. Part VII. The Neutral Hydrolysis of Methyl Perchlorate

1975 ◽  
Vol 53 (20) ◽  
pp. 3106-3115 ◽  
Author(s):  
Ross Elmore Robertson ◽  
Adrianna Annesa ◽  
John Marshall William Scott
Keyword(s):  
Heat Capacity ◽  
Carbon Atom ◽  
Temperature Dependence ◽  
Thermodynamic Parameters ◽  
Isotope Effect ◽  
Perchlorate Ion ◽  
Rate Of Hydrolysis ◽  
Leaving Groups ◽  
Hydrolysis Of

The temperature dependence of the rate of hydrolysis of methyl perchlorate has been measured and the entropy (ΔS≠), enthalpy (ΔH≠), and heat capacity (ΔCp≠) of activation calculated. The measurements confirm that the perchlorate ion is superior to all other leaving groups in water. The isotope effect related to the hydrolysis of methyl-d3 perchlorate has been measured at three temperatures and shown to be inverse. The thermodynamic parameters and the isotope effect were examined with respect to the mechanism of substitution at a primary carbon atom.

scholarly journals Magnetic properties and heat capacity of the three-dimensional frustratedS=12antiferromagnetPbCuTe2O6

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
B. Koteswararao ◽  
R. Kumar ◽  
P. Khuntia ◽  
Sayantika Bhowal ◽  
S. K. Panda ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Magnetic Properties ◽  
Three Dimensional

The Hydrolysis of Disubstituted Alkyl Phosphorochloridates and N,N,N′,N′-Tetra-stibstituted Phosphorodiamidic Chlorides in Water and Deuterium Oxide: Heat Capacity of Activation and Kinetic Solvent Isotope Effects

1973 ◽  
Vol 51 (4) ◽  
pp. 597-603 ◽  
Author(s):  
E. C. F. Ko ◽  
R. E. Robertson
Keyword(s):  
Heat Capacity ◽  
Thermodynamic Parameters ◽  
Alkyl Group ◽  
Deuterium Oxide ◽  
Isotope Effects ◽  
Potential Relationship ◽  
Mechanism Of Reaction ◽  
Solvent Isotope ◽  
Hydrolysis Of ◽  
Solvent Isotope Effects

The pseudo-thermodynamic parameters, ΔH≠, ΔS≠, and ΔCp≠ and the kinetic solvent isotope effects have been determined for the three alkyl-phosphorochloridates, where the alkyl group is ethylisopropyl and n-propyl; for tetra-methyl and tetra-ethyl phosphorodiamidic chlorides; the di-n-propyl and di-isopropyl analog, the di(isopropylmethylcarbinyl)phosphorochloridate and the tetra-ethylthiophosphorodiamidic chloride. These compounds have a potential relationship to compounds used as insecticides and as polymers. The mechanism of reaction is discussed on the basis of these data.

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