scholarly journals Contributions to the theory of specific heat IV—On the calculation of the specific heat of crystals from elastic data

1935 ◽  
Vol 149 (866) ◽  
pp. 126-130 ◽  
Keyword(s):  
Specific Heat ◽  
Elastic Constants ◽  
General Problem ◽  
Elastic Waves ◽  
Low Temperatures ◽  
Equation Of Motion ◽  
Mean Value ◽  
Elastic Data ◽  
The Mean ◽  
The Waves

This paper contains a development of a method of calculating θ D values from elastic data (at low temperatures) originally given in Part II. 1—The general problem is that one is given the equation of motion of a continuum, and hence the velocity of the elastic waves as a function of the direction of the waves in a crystal and of the elastic constants; for specific heat purposes it is necessary to obtain from this equation the mean value of the velocity, and this is correlated fairly easily with the Debye θ D value.

scholarly journals Bakerian Lecture :─On the variation of the specific heat of water, with experiments by a new method

1912 ◽  
Vol 86 (587) ◽  
pp. 254-257 ◽  
Keyword(s):  
Specific Heat ◽  
Experimental Evidence ◽  
Electric Current ◽  
Heat Loss ◽  
Mean Value ◽  
Mechanical Method ◽  
Order Of Accuracy ◽  
Steady Current ◽  
Differential Pair ◽  
The Mean

The question of the variation of the specific heat of water is so fundamental in calorimetry, and the results of different observers and different methods are still so discordant, that no apology is needed for the publication of fresh experimental evidence. The continuous electric method, which I carried out in conjunction with Prof. Barnes, was specially designed to avoid the main sources of error of the older methods in which mercury thermometers and open calorimeters were employed. In this method. the rise of temperature of a steady current of water, heated by a steady electric current in its passage through a fine tube hermetically scaled in a vaccumjacket, was observed with a differential pair of platinum thermometers. Errors due to lag, or to uncertainty of water-equivalent, or to evaporation or heat-loss in transference, were thus eliminated, and a higher order of accuracy was secured in the temperature measurements. The results of the continuous electric method in the case of water showed a variation of specific heat amounting to less than one half of 1 per cent. between 10° and 80°C., with a minimum at 37.6°C., followed by a very slow and steady rise. The mean value from 0° to 100°C. agreed to 1 in 2000 with the experiments of Reynolds and Moorby by the mechanical method, and the values from 5° to 35° C. agreed to a similar order of accuracy with the experiments of Rowland. But the value at 80°C. was 1 per cent. lower than that found by Lüdin's (Zürich, 1895), employing the ordinary method of mixture with an open calorimeter and mercury thermometers. Lüdin's results for the variation over the range 30° to 100°C. agreed more closely with the continuous electric method than those of any previous observers; but showed a minimum at 25°C., and a maximum at 87°C., which could not be reconciled with the experiments of Reynolds and Moorby on the mean specific heat from 0° to 100°C., or with the most probable reduction of Regnault's experiments between 110° and 190°C.

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.

scholarly journals III. On the specific heats of gases at constant volume. Part I. Air, carbon dioxide, and hydrogen

1891 ◽  
Vol 48 (292-295) ◽  
pp. 440-441 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Specific Heat ◽  
Mean Value ◽  
Constant Volume ◽  
Specific Heats ◽  
Absolute Density ◽  
The Mean ◽  
The Absolute

In this first notice the specific heats, at constant volumes, of air, carbon dioxide, and hydrogen are treated over pressures ranging from 7 to 25 atmospheres. The range of temperature is not sensibly varied. It is found that the specific heats of these gases are not constant, but are variable with the density. In the case of air the departure from constancy is small and positive; that is, the specific heat increases with increase of the density. The experiments afford directly the mean value 0·1721 for the specific heat of air at the absolute density of 0·0205, corresponding to the pressure of 19·51 atmospheres. A formula based on the variation of the specific heat with density observed in the experiments ascribes the value 0·1715 for the specific heat at the pressure of one atmosphere.

Specific Heat and Elastic Constants of Sodium Iodide at Low Temperatures

1960 ◽  
Vol 120 (2) ◽  
pp. 332-334 ◽  
Author(s):  
Richard N. Claytor ◽  
Billy J. Marshall
Keyword(s):  
Specific Heat ◽  
Elastic Constants ◽  
Low Temperatures ◽  
Sodium Iodide

scholarly journals Proposal for determining changes in entropy of semi ideal gas using mean values of temperature functions

2014 ◽  
Vol 68 (5) ◽  
pp. 615-628 ◽  
Author(s):  
Branko Pejovic ◽  
Vladan Micic ◽  
Mitar Perusic ◽  
Goran Tadic ◽  
Ljubica Vasiljevic ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Specific Heat ◽  
Internal Energy ◽  
Temperature Interval ◽  
Specific Heat Capacity ◽  
Mean Value ◽  
Ideal Gas ◽  
Mean Values ◽  
Arbitrary Temperature ◽  
The Mean

In a semi-ideal gas, entropy changes cannot be determined through the medium specific heat capacity in a manner as determined by the change of internal energy and enthalpy, i.e. the amount of heat exchanged. Taking this into account, the authors conducted two models through which it is possible to determine the change in the specific entropy of a semi-ideal gas for arbitrary temperature interval using the spread sheet method, using the mean values of the appropriate functions. The idea is to replace integration, which occurs here in evitably, with mean values of the previous functions. The models are derived based on the functional dependence of the actual specific heat capacity on the temperature. The theorem used is that of the mean value of a function as well as the mathematical properties of the definite integral. The mean value of a fractional function is determined via its integrand while the logarithmic functions were performed by applying a suitable transformation of the differential calculus. The relations derived relation, using the computer program, have enabled the design of appropriate thermodynamic tables through which it is possible to determine the change in entropy of arbitrary state changes in an efficient and rational manner, without the use of calculus or finished forms. In this way, the change in the entropy of a semi-ideal gas is determined for an arbitrary temperature interval using the method which is analogous to that applied in determining the change of internal energy and enthalpy or the amount of heat exchanged, which was the goal of the work. Verification of the proposed method for both the above functions was performed for a a few characteristic semi-ideal gases where change c(T) is significant, for the three adopted temperature intervals, for the characteristic change of state. This was compared to the results of the classical integral and the proposed method through the prepared tables. In certain or special cases, it is possible to apply the presented method also in determining the change in entropy of the real gas. Apart from that, the paper shows that the change in entropy for the observed characteristic case can be represented or graphically determined using the planimetric method of diagrams with suitably selected coordinates.

Interpretation of elastic properties of ionic crystals. Validity of a quasi-additivity rule?

1993 ◽  
Vol 205 (2) ◽  
Author(s):  
S. Haussühl
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Mean Value ◽  
Molecular Volume ◽  
Ionic Crystals ◽  
Additivity Rule ◽  
The Mean

AbstractIn groups of isotypic ionic crystals the product of the mean value of the principal elastic constants and of the molecular volume, the

scholarly journals The variation with temperature of the specific heat of sodium in the solid and the liquid state; also a determination of its latent heat of fusion

1914 ◽  
Vol 89 (614) ◽  
pp. 561-574 ◽  
Keyword(s):  
Melting Point ◽  
Specific Heat ◽  
Latent Heat ◽  
Liquid State ◽  
Mean Value ◽  
Heat Of Fusion ◽  
Latent Heat Of Fusion ◽  
The Mean ◽  
Considerable Range

The present paper contains the results of an investigation into the variation, with temperature, of the specific heat of sodium in the solid and the liquid state; also, some determinations of its latent heat of fusion. Our knowledge of the variations of the specific heat of metals in the region of their melting point is extremely vague and hypothetical, since the methods of investigation commonly employed are only capable of giving the mean value of the specific heat over a considerable range of temperature.

scholarly journals Contributions to the theory of specific heat III—On the existence of pseudo-T 3 regions in the specific heat curve of a crystal

1935 ◽  
Vol 149 (866) ◽  
pp. 117-125 ◽  
Keyword(s):  
Vibrational Spectrum ◽  
Specific Heat ◽  
Low Temperatures ◽  
Previous Investigation ◽  
Lattice Structure ◽  
Dimensional Case ◽  
One Dimensional ◽  
Heat Curve ◽  
Elastic Data ◽  
The One

This paper is a continuation of the previous investigation (Part II) on the vibrational spectrum of a crystal. The influence of the maxima of the density of the vibrations on the form of the θ D — T diagram is discussed in some detail. The main result is the discovery that more than one region of constant θ D value is possible—which is equivalent to the possibility of pseudo-T 3 regions in the specific heat curve. A further result is an explanation of the discrepancies hitherto found between the θ D values derived from thermal and from elastic data at low temperatures. 1—We shall start with an examination of the one-dimensional case which is important because it provides a striking example of the influence of the lattice structure on the specific heat curve.

scholarly journals The Brownian movement of a galvanometer coil and the influence of the temperature of the outer circuit

1927 ◽  
Vol 115 (771) ◽  
pp. 391-406 ◽  
Keyword(s):  
Experimental Verification ◽  
Low Temperatures ◽  
Mean Value ◽  
Brownian Movement ◽  
Theoretical Methods ◽  
Different Temperatures ◽  
The Mean ◽  
Galvanometer Coil

Some time ago, in connection with certain curves published from this Institute, and illustrative of the thermo-relay method for the magnification of galvanometer deflections, Ising pointed out* that the current irregularities superposed upon the baseline-current, as traced out photographically, could be interpreted as due to the Brownian movement of the suspended coil of the galvanometer, and indeed were of the order required theoretically. To prove definitely that these small variations are really due to the Brownian movements, it is evidently necessary to show that the temperature of the galvanometer system has an influence upon the mean value of the movement. The difficulties involved in maintaining the galvanometer itself at sufficiently low temperatures are great, and it is much more convenient to cool a series-connected coil in the outer circuit. This introduces the problem of the Brownian movement in a system at two different temperatures, and this has not, until recently, been investigated theoretically. The purpose of the present work is, then, to develop the necessary theoretical methods for such problems, and to obtain an expression for the Brownian movement which can be subjected to direct experimental verification.

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