scholarly journals The specific heats of ferromagnetic substances

1928 ◽  
Vol 117 (778) ◽  
pp. 680-691 ◽  
Keyword(s):  
Specific Heat ◽  
Critical Point ◽  
Applied Field ◽  
Close Relation ◽  
Molecular Field ◽  
Curie Constant ◽  
Apparent Increase ◽  
Specific Heats ◽  
The Given ◽  
Ferromagnetic Substance

It is well known that a close relation must exist between the thermal and the magnetic properties of a ferromagnetic substance. On the basis of his theory of the internal molecular field, Weiss predicted a discontinuity in the specific heat of a ferromagnetic substance in the region of its critical point. His reasoning may be briefly summarised as follows. The mutual potential energy, E, of a number of elementary magnets, each of moment μ and making an angle θ with the applied field H, is given by E = —½ Ʃ μ H cos θ; so that when we consider a cubic centimetre of the given substance we may write E = — ½ H. I, where I is the intensity of magnetisation. Since the substance is ferromagnetic, we must suppose, according to Weiss, the existence of a molecular field of considerable magnitude, equal to N I, where N is a constant which is obtainable from a knowledge of the Curie constant and the critical point of the substance. Thus we may further write E = — ½NI 2 , and, since E is negative, we must provide heat in order to demagnetise the substance. The amount of heat necessary to demagnetise 1 gm. of the substance is therefore 1/2J. N/ᵖ. I 2 where ᵖ is the density of the substance. Now I varies with the temperature, so that the heat necessary to demagnetise a substance results in an apparent increase of its specific heat by an amount ∂/∂T (1/2J. N/ᵖ. I 2 ) = 1/2J. N/ᵖ. ∂I 2 /∂T.

ON THE SPECIFIC HEAT OF COPPER FROM −78° TO 0 °C.

1933 ◽  
Vol 9 (1) ◽  
pp. 84-93 ◽  
Author(s):  
S. M. Dockerty
Keyword(s):  
Specific Heat ◽  
Recent Work ◽  
Adiabatic Calorimetry ◽  
Close Relation ◽  
Experimental Curve ◽  
Electrical Heating ◽  
Maximum Deviation ◽  
Specific Heats ◽  
Expected Values

This paper is a continuation of recent work by H. L. Bronson, H. M. Chisholm, and the author (3) on the specific heats of tungsten, molybdenum, and copper from 0° to 500 °C. The "method of electrical heating" and adiabatic calorimetry have been extended to determine the specific heat of copper from −78° to 0 °C.The equation previously given for the specific heat of copper contained only the first two terms of the Debye expansion and was found not to hold below −30 °C. The following equation containing four terms of the Debye expansion fits the experimental curve from −78° to 500 °C. with a maximum deviation of only about 0.05%,[Formula: see text]where the units are joules per gram per °K. The constants of this equation were determined empirically and their close relation to theoretically expected values has been discussed.

scholarly journals On the specific heat of ferromagnetic substances

1926 ◽  
Vol 112 (760) ◽  
pp. 157-176 ◽  
Keyword(s):  
Specific Heat ◽  
Magnetic Energy ◽  
Molecular Field ◽  
Magnetic Contribution ◽  
Intimate Connection ◽  
Mechanical Equivalent ◽  
Ferromagnetic Substance

According to the Weiss theory of ferromagnetism, there is an intimate connection between the specific heat of a body and its magnetisation. Weiss has shown that the magnetic energy per cubic centimetre of a ferromagnetic substance is:- W = -½HI (1) where I is the intensity of magnetisation and H is the molecular field. Further, it is assumed that H = NI (2) where N is a constant depending on the material itself. Thus W = -½NI 2 and d W/ d T = -½N d / d T (I 2 ) where T is the temperature. d W/ d T will contribute to the specific heat of the substance which will become equal to S = s + 1/ρJ d W/ d T, where s = specific heat neglecting magnetic contribution, S = total specific heat, ρ = density, J = mechanical equivalent of heat, Therefore S = s - N/2ρJ d / d T (I 2 ).

Specific Heats of Solids due to Molecular Rotations

1937 ◽  
Vol 33 (4) ◽  
pp. 524-533 ◽  
Author(s):  
T. S. Chang
Keyword(s):  
Critical Temperature ◽  
Potential Energy ◽  
Specific Heat ◽  
Critical Point ◽  
The State ◽  
Boltzmann Constant ◽  
Specific Heats ◽  
Classical Statistics ◽  
Molecular Rotations

Bethe's method, used in the problem of order-disorder transitions in alloys, is applied formally to the problem of molecular rotations in solids. To apply this method, we assume that the solid is entirely homogeneous, and that the state of rotation is the same throughout the solid. Without this assumption, the application of this method is impossible.A particular form of the mutual potential energy between two neighbouring molecules has been chosen, and classical statistics is employed throughout. The calculations are made entirely after the manner of Bethe, and the similarities of the two problems are pointed out. The result is that there is a critical temperature, and also a discontinuity in the specific heat of the magnitude of some ten times the Boltzmann constant per molecule, arising from the sudden setting in of the rotations as the temperature is increased beyond the critical point. Agreement with the experiments is bad, indicating that a more profound theory is necessary.

A Rational Equation of State for Water and Water Vapor in the Critical Region

1964 ◽  
Vol 86 (3) ◽  
pp. 320-326 ◽  
Author(s):  
E. S. Nowak
Keyword(s):  
Water Vapor ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Critical Point ◽  
Critical Region ◽  
Constant Pressure ◽  
Parametric Equation ◽  
Enthalpy And Entropy ◽  
Specific Volumes

A parametric equation of state was derived for water and water vapor in the critical region from experimental P-V-T data. It is valid in that part of the critical region encompassed by pressures from 3000 to 4000 psia, specific volumes from 0.0400 to 0.1100 ft3/lb, and temperatures from 698 to 752 deg F. The equation of state satisfies all of the known conditions at the critical point. It also satisfies the conditions along certain of the boundaries which probably separate “supercritical liquid” from “supercritical vapor.” The equation of state, though quite simple in form, is probably superior to any equation heretofore derived for water and water vapor in the critical region. Specifically, the deviations between the measured and computed values of pressure in the large majority of the cases were within three parts in one thousand. This coincides approximately with the overall uncertainty in P-V-T measurements. In view of these factors, the author recommends that the equation be used to derive values for such thermodynamic properties as specific heat at constant pressure, enthalpy, and entropy in the critical region.

The specific heats of three paramagnetic salts at very low temperatures

1956 ◽  
Vol 237 (1210) ◽  
pp. 395-403 ◽  
Keyword(s):  
Specific Heat ◽  
Absolute Temperature ◽  
Magnesium Nitrate ◽  
Paramagnetic Resonance ◽  
Specific Heats ◽  
Ammonium Alum ◽  
Relaxation Measurements ◽  
Ferric Ammonium ◽  
The Absolute ◽  
Measured Specific Heat

The specific heats of three paramagnetic salts, neodymium magnesium nitrate, manganous ammonium sulphate and ferric ammonium alum, have been measured at temperatures below 1°K using the method of γ -ray heating. The temperature measurements were made in the first instance in terms of the magnetic susceptibilities of the salts, the relation of the susceptibility to the absolute temperature having been determined for each salt in earlier experiments. The γ -ray heatings gave the specific heat in arbitrary units. The absolute values of the specific heats were found by extrapolating the results of paramagnetic relaxation measurements at higher temperatures. The measured specific heat of neodymium magnesium nitrate is compared with the value calculated from paramagnetic resonance data, and good agreement is found.

Study of the Specific-Heat Singularity ofHe3near Its Critical Point

1972 ◽  
Vol 6 (1) ◽  
pp. 364-377 ◽  
Author(s):  
G. Raymond Brown ◽  
Horst Meyer
Keyword(s):  
Specific Heat ◽  
Critical Point

scholarly journals III. Investigations of the specific heat of solid bodies

1865 ◽  
Vol 155 ◽  
pp. 71-202 ◽  
Keyword(s):  
Specific Heat ◽  
Thermal Action ◽  
General View ◽  
Specific Heats ◽  
General Law ◽  
Different Temperatures ◽  
The Times ◽  
The Individual ◽  
Solid Bodies

I. About the year 1780 it was distinctly proved that the same weights of different bodies require unequal quantities of heat to raise them through the same temperature, or on cooling through the same number of thermometric degrees, give out unequal quantities of heat. It was recognized that for different bodies the unequal quantities of heat, by which the same weights of different bodies are heated through the same range, must be determined as special constants, and considered as characteristic of the individual bodies. This newly discovered property of bodies Wilke designated as their specific heat , while Crawford described it as the comparative heat, or as the capacity of bodies for heat . I will not enter upon the earliest investigations of Black, Irvine, Crawford, and Wilke, with reference to which it may merely be mentioned that they depend essentially on the thermal action produced when bodies of different temperatures are mixed, and that Irvine appears to have been the first to state definitely and correctly in what manner this thermal action (that is, the temperature resulting from the mixture) depends on the original temperature, the weights, and the specific heats of the bodies used for the mixture. Lavoisier and Laplace soon introduced the use of the ice-calorimeter as a method for determining the specific heat of bodies; and J. T. Mayer showed subsequently that this determination can be based on the observation of the times in which different bodies placed under comparable conditions cool to the same extent by radiation. The knowledge of the specific heats of solid and liquid bodies gained during the last century, and in the first sixteen years of the present one, by these various methods, may be left unmentioned. The individual determinations then made were not so accurate that they could be compared with the present ones, nor was any general conclusion drawn in reference to the specific heats of the various bodies. 2. Dulong and Petit’s investigations, the publication of which commenced in 1818, brought into the field more accurate determinations, and a general law. The investigations of the relations between the specific heats of the elements and their atomic weights date from this time, and were afterwards followed by similar investigations into the relations of the specific heats of compound bodies to their composition. In order to give a general view of the results of these investigations, it is desirable to present, for the elements mentioned in the sequel, a synopsis of the atomic weights assumed at different times, and of certain numbers which stand in the closest connexion with these atomic weights.

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