ON THE SPECIFIC HEAT OF SOLIDS AT LOW TEMPERATURES

1957 ◽  
Vol 35 (7) ◽  
pp. 799-810 ◽  
Author(s):  
T. H. K. Barron ◽  
J. A. Morrison
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Noble Metals ◽  
Theoretical Models ◽  
Experimental Results ◽  
Continuum Approximation ◽  
Low Frequencies ◽  
Specific Heats ◽  
Additional Information ◽  
The Continuum

The temperature dependence of the specific heat of solids at very low temperatures is examined, using theoretical models and certain recent experimental results. The temperature region over which the continuum approximation (Cν = aT3) is strictly reliable is shorter than has often been supposed, and the series expansion Cν = aT3 + bT5 + cT7 + … is needed for the analysis of accurate experimental results. For insulators θ0 can best be estimated from measured specific heats by plotting Cν/T3 versus T2; the result is a curve whose intercept at T2 = 0 gives the coefficient of T3 (and hence θ0), and whose slopeand curvature give additional information about the vibrational spectrum at low frequencies. For metals the usual plot of Cν/T versus T2 can be used, but here again neglect of curvature may lead to errors in the estimates of γ and θ0. A brief discussion is given of the low temperature specific heats of a number of solids for which suitable data are available: potassium chloride, lithium fluoride, white tin, tungsten, the noble metals, and elements of diamond structure.

TEMPERATURE DEPENDENCE BEHAVIOR OF ELECTRICAL RESISTIVITY IN NOBLE METALS AT LOW TEMPERATURES

2014 ◽  
Vol 5 (3) ◽  
pp. 982-992 ◽  
Author(s):  
M AL-Jalali
Keyword(s):  
Experimental Data ◽  
Electrical Resistivity ◽  
Temperature Dependence ◽  
Concentration Dependence ◽  
Low Temperatures ◽  
Noble Metals ◽  
Phonon Scattering ◽  
Theoretical Models ◽  
Residual Resistivity ◽  
Electron Phonon Scattering

Resistivity temperature – dependence and residual resistivity concentration-dependence in pure noble metals(Cu, Ag, Au) have been studied at low temperatures. Dominations of electron – dislocation and impurity, electron-electron, and electron-phonon scattering were analyzed, contribution of these mechanisms to resistivity were discussed, taking into consideration existing theoretical models and available experimental data, where some new results and ideas were investigated.

The Specific Heat of Carbon Dioxide—Correction

1928 ◽  
Vol 24 (2) ◽  
pp. 290-290
Author(s):  
W. H. McCrea
Keyword(s):  
Carbon Dioxide ◽  
Specific Heat ◽  
Low Temperatures ◽  
Molecular Form ◽  
Specific Heats ◽  
Heat Curve

In a recent paper in these Proceedings the writer suggested the possibility of a transition from one molecular form to another in CO2. The suggestion is embodied in the equation (10) and the resulting specific heats for low temperatures given. He greatly regrets that it was not till after those results were published that he found they gave a high and altogether impossible maximum in the specific heat curve for higher temperatures before it returns to the neighbourhood of the unmodified curve Cv′.

scholarly journals Atomic specific heats between the boiling points of liquid nitrogen and hydrogen. I.—The mean atomic specific heats at 50° absolute of the elements a periodic function of the atomic weights

1913 ◽  
Vol 89 (609) ◽  
pp. 158-169 ◽  
Keyword(s):  
Periodic Function ◽  
Specific Heat ◽  
Liquid Nitrogen ◽  
Low Temperatures ◽  
Liquid Hydrogen ◽  
Specific Heats ◽  
Boiling Points ◽  
Royal Institution ◽  
Series Of Experiments ◽  
The Mean

A method of determining the specific heat of substances at low temperatures was described in a paper on “Studies with the Liquid Hydrogen and Air Calorimeter,” also in the abstract of a lecture delivered at the Royal Institution entitled“ Liquid Hydrogen Calorimetry,” where the apparatus then used is illustrated. Continuing the use of the same method, but with some modification of the apparatus, the investigation has been extended to a large number of inorganic and organic bodies. In this later series of experiments, the measurements of the specific heats of materials by the liquid hydrogen calorimeter were made over a range of temperature from boiling nitrogen to boiling hydrogen, a fall of temperature of some 57° Abs.

THE RESONANCE METHOD OF MEASURING THE RATIO OF THE SPECIFIC HEATS OF A GAS, Cp/Cv: PART V: SECTION A: AN IMPROVED APPARATUS FOR MEASURING THE RATIO OF THE SPECIFIC HEATS OF A GAS: SECTION B: THE USE OF ELECTRONIC COUNTER CIRCUITS TO MEASURE LOW FREQUENCIES AND A VARIABLE LOW FREQUENCY OSCILLATOR

1949 ◽  
Vol 27a (3) ◽  
pp. 27-38 ◽  
Author(s):  
L. Katz ◽  
S. B. Woods ◽  
W. F. Leverton
Keyword(s):  
Specific Heat ◽  
Low Frequency ◽  
Resonance Method ◽  
Time Interval ◽  
Low Frequencies ◽  
Specific Heats ◽  
Wide Range ◽  
New Apparatus ◽  
The Stability ◽  
Number Of Cycles

This paper describes an improved apparatus for the determination of γ = Cp/Cv, the ratio of the specific heat at constant pressure to the specific heat at constant volume for a gas. With this apparatus, γ is determined by the resonance method of Clark and Katz. The new apparatus is constructed of stainless steel and is designed to withstand pressures up to 100 atm. This new apparatus is more compact and can be used with corrosive gases. Provision is made for the control and accurate measurement of the temperature of the enclosed gas over a wide range of temperatures. An electronic counter which will measure time intervals, in units of 10 μsec., from 100 μsec. to several seconds in length is described in Section B. An unknown frequency may be determined by measuring the time interval in which a preselected number of cycles occurs. The accuracy is such that frequencies may be measured to within approximately 1 part in 105. The circuit for a variable frequency transitron oscillator with an output of 30 w. in a range of 15 to 250 c.p.s. is shown. The stability of the oscillator is such that the frequency may easily be maintained within 1 part in 10,000 for long periods, and with care in temperature control and choice of electrode voltages much greater stabilities may be obtained.

scholarly journals SUPERFLUID BEHAVIOUR OF A QUANTUM q-GAS

1996 ◽  
Vol 10 (01n02) ◽  
pp. 41-46 ◽  
Author(s):  
M. R-MONTEIRO ◽  
L.M.C.S. RODRIGUES
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Continuum Limit ◽  
Deformation Parameter ◽  
Constant Volume ◽  
Oscillator Algebra ◽  
Inequivalent Representations ◽  
Λ Point ◽  
The Continuum

We explore some consequences of the inequivalent representations of a q-oscillator algebra on a highly deformed quantum q-gas. By a simple choice of the continuum limit of the background ν0, the constant volume specific heat per mass C shows a λ-point transition and has a T3 dependence for low temperatures. Choosing a particular value of the deformation parameter q, we are able to reproduce the experimental value of the He II specific heat for T<0.5° K .

SPECIFIC HEATS AND DISPERSION CURVES FOR CsCl ON THE BASIS OF THE SHELL MODEL

1967 ◽  
Vol 45 (10) ◽  
pp. 3339-3346 ◽  
Author(s):  
G. P. Srivastava ◽  
B. Dayal
Keyword(s):  
Specific Heat ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Cesium Chloride ◽  
Dispersion Curves ◽  
Experimental Results ◽  
Fair Agreement ◽  
Chloride Crystal ◽  
Specific Heats ◽  
Positive Ions

The shell model of Dick and Overhauser as developed by Cochran and Woods el al. has been applied to study theoretically the lattice dynamics of a cesium chloride crystal. The polarizabilities of both negative and positive ions have been taken into account in this treatment. The charges on the shells of the two ions come out to be of different magnitude. It is seen that the theoretical specific-heat variation with temperature based on this model is in fair agreement with experimental results in the range for which they have been obtained. The theoretical dispersion curves in the three symmetry directions are also given.

Surface specific heats of metal nanocrystals at low temperatures

Nanoscale ◽  
2015 ◽  
Vol 7 (15) ◽  
pp. 6762-6766 ◽  
Author(s):  
Haile Lei ◽  
Jun Li ◽  
Jiangshan Luo
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Spatial Dimension ◽  
Analytical Expression ◽  
Metal Nanocrystals ◽  
Specific Heats ◽  
The Core ◽  
2D And 3D

In order to quantitatively explain the enhanced specific heat of metal nanocrystals measured from 4.2 K to 80 K, an analytical expression has been deduced to determine the surface specific heat in nanocrystals, which is proportional to T2.5 at low temperatures. The effectively spatial dimension of surfaces should be neither pure 2D nor 3D, but between 2D and 3D, due to the effect of atoms in the core of nanocrystals.

The measurement of lattice specific heats at low temperatures using a heat switch

1955 ◽  
Vol 230 (1183) ◽  
pp. 549-559 ◽  
Keyword(s):  
Specific Heat ◽  
Potassium Chloride ◽  
Thermal Insulation ◽  
Low Temperatures ◽  
Lattice Structure ◽  
Specific Heats ◽  
Simple Lattice ◽  
Order Of Magnitude

The accuracy of the measurement of small specific heats at low temperatures is often limited by the difficulty of achieving adequate thermal insulation of the specimen, especially when exchange gas has been used to cool it down. The paper describes a make-and-break contact which makes possible a degree of thermal insulation an order of magnitude higher than is usually obtained. This ‘heat switch’ has been used to measure the specific heats of three substances with a simple lattice structure. It has been verified that the temperature varia­tion of the specific heats of potassium chloride and grey tin is very close to a T 3 relation at temperatures below about θ D /60. The specific heat of graphite is more complex because of the anisotrophy of the lattice.

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