Thermal Equilibrium Between LiquidHe3and Powdered Cerium Magnesium Nitrate at Very Low Temperatures

1966 ◽  
Vol 16 (7) ◽  
pp. 273-275 ◽  
Author(s):  
W. R. Abel ◽  
A. C. Anderson ◽  
W. C. Black ◽  
J. C. Wheatley
Keyword(s):  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Magnesium Nitrate

The thermal conductivity of metals

1938 ◽  
Vol 34 (3) ◽  
pp. 474-497 ◽  
Author(s):  
R. E. B. Makinson
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Major Part ◽  
Lattice Energy ◽  
Conduction Electrons ◽  
Electronic Heat ◽  
Lattice Waves ◽  
Lattice Heat

The methods used to measure separately the electronic and lattice heat conductivities κeand κgin a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κeand for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratioLe= κe/σTas a function ofT, both for the monovalent metals and for a model metal with 1·8 × 10−2conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κeand κgas functions ofTare given in both cases, and these, together with a comparison of the observed Lorentz ratio andLe, show that in the monovalent metals κgis unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.

Thermal field theory

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Statistical Physics ◽  
Thermal Field ◽  
Scalar Fields ◽  
Temperature Dependent ◽  
Scalar Particles ◽  
Debye Mass

After a review of the calculational approaches, the free energy of scalar particles in thermal equilibrium is calculated. The IR behaviour of mass-less scalar fields is examined, finding that a resummation of IR divergent terms is necessary. In general, particles acquire a temperature-dependent (Debye) mass, while symmetries of the Lagrangian may be hidden at low temperatures. In an appendix, the basics of equilibrium statistical physics is reviewe

Thermal contact between cerium magnesium nitrate and liquid3He at very low temperatures

1973 ◽  
Vol 10 (3-4) ◽  
pp. 379-395 ◽  
Author(s):  
J. H. Bishop ◽  
D. W. Cutter ◽  
A. C. Mota ◽  
J. C. Wheatley
Keyword(s):  
Low Temperatures ◽  
Thermal Contact ◽  
Magnesium Nitrate

Heat Capacity of Diluted Cerium Magnesium Nitrate and Its Potential for the Production of Very Low Temperatures

1969 ◽  
Vol 187 (1) ◽  
pp. 273-275 ◽  
Author(s):  
B. M. Abraham ◽  
O. Brandt ◽  
Y. Eckstein ◽  
J. B. Ketterson ◽  
M. Kuchnir ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Low Temperatures ◽  
Magnesium Nitrate

NUCLEAR ORIENTATION EXPERIMENTS WITH Pr142 AND Yb175 NUCLEI

1958 ◽  
Vol 36 (8) ◽  
pp. 997-1009 ◽  
Author(s):  
J. M. Daniels ◽  
J. L. G. Lamarche ◽  
M. A. R. Le Blanc
Keyword(s):  
Magnetic Fields ◽  
External Field ◽  
Magnetic Moment ◽  
Low Temperatures ◽  
Nuclear Orientation ◽  
Magnesium Nitrate ◽  
Spin Hamiltonian ◽  
Crystal Axis ◽  
Γ Ray ◽  
Made In

Pr142 has been oriented as an impurity in cerium magnesium nitrate, and the anisotropy of the 1.57 Mev γ-ray was measured as a function of temperature in the range 0.003° K to 1.0° K, both in zero external field and in a field of 320 gauss parallel to the trigonal crystal axis. The results are not consistent with what has been published about the spin Hamiltonian of Pr+++ in this lattice. The magnetic moment of Pr142 is very small, and it was not possible to see any saturation of the anisotropy at low temperatures. Values for the magnetic moment of Pr142 were found for two different assumed decay schemes, these are 0.11 nuclear magnetons for the spin assignments [Formula: see text], and 0.15 nuclear magnetons for the spin assignments [Formula: see text]. Similar experiments were carried out on Yb175. Measurements were made in a variety of external magnetic fields up to 700 oersted, and at temperatures as low as 0.003° K. No anisotropy was observed for the 396 kev γ-ray, nor for the 282 kev γ-ray. The most likely explanation for this result is that the lifetime of the γ-emitting state is about 10−10 seconds. The relation between the results of this experiment and others on the same isotope (Phil. Mag. 2, 1079 (1952)) is discussed.

Thermal resistance between powdered cerium magnesium nitrate and liquid helium at very low temperatures

1971 ◽  
Vol 4 (4) ◽  
pp. 391-400 ◽  
Author(s):  
W. C. Black ◽  
A. C. Mota ◽  
J. C. Wheatley ◽  
J. H. Bishop ◽  
P. M. Brewster
Keyword(s):  
Thermal Resistance ◽  
Liquid Helium ◽  
Low Temperatures ◽  
Magnesium Nitrate

scholarly journals Evaluation of the thermodynamics of a four level system using canonical density matrix method

2011 ◽  
Vol 33 (4) ◽  
pp. 91-108
Author(s):  
Aladunjoye A. Awoga ◽  
Akpan A. Ikot ◽  
Eno E. Ituen ◽  
Louis E. Akpabio
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Density Matrix ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Kronecker Product ◽  
Entire System ◽  
Level System ◽  
Laws Of Thermodynamics ◽  
Product Method

Abstract We consider a four-level system with two subsystems coupled by weak interaction. The system is in thermal equilibrium. The thermodynamics of the system, namely internal energy, free energy, entropy and heat capacity, are evaluated using the canonical density matrix by two methods. First by Kronecker product method and later by treating the subsystems separately and then adding the evaluated thermodynamic properties of each subsystem. It is discovered that both methods yield the same result, the results obey the laws of thermodynamics and are the same as earlier obtained results. The results also show that each level of the subsystems introduces a new degree of freedom and increases the entropy of the entire system. We also found that the four-level system predicts a linear relationship between heat capacity and temperature at very low temperatures just as in metals. Our numerical results show the same trend.

INTERMEDIATE-STATE REORIENTATION OF ORIENTED NUCLEI

1966 ◽  
Vol 44 (9) ◽  
pp. 1965-1984 ◽  
Author(s):  
J. M. Daniels ◽  
Sushil K. Misra
Keyword(s):  
Angular Distribution ◽  
Intermediate State ◽  
Low Temperatures ◽  
Nuclear Orientation ◽  
Zinc Nitrate ◽  
Magnesium Nitrate ◽  
Experimental Results ◽  
Γ Ray ◽  
Experimental Values ◽  
Reorientation Process

When radioactive nuclei in a paramagnetic ion at low temperatures become oriented (the magnetic h.f.s. method of nuclear orientation) and decay by β emission followed by a delayed γ ray, frequently, these nuclei become reoriented between the emission of the β ray and the γ ray, and this reorientation affects the observed angular distribution of the γ ray. The theory of this reorientation process is presented, assuming a time-independent Hamiltonian during the reorientation period. Numerical calculations of the effects to be expected on this static reorientation model have been made for 175Yb, 147Nd, and 141Ce in cerium magnesium nitrate, 57Co in cerium zinc nitrate, and 147Nd in neodymium ethyl sulphate. These calculations are compared with the reported experimental results. The experimental values for 147Nd in neodymium ethyl sulphate, 141Ce in cerium magnesium nitrate, and 57Co in cerium zinc nitrate could be explained by the static reorientation model; the others could not. The need is stressed for more reliable experimental results, in order to develop the theory of reorientation further.

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