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

1933 ◽  
Vol 9 (1) ◽  
pp. 84-93 ◽  
Author(s):  
S. M. Dockerty

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.

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.


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.


1865 ◽  
Vol 155 ◽  
pp. 71-202 ◽  

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.


1982 ◽  
Vol 60 (14) ◽  
pp. 1853-1856 ◽  
Author(s):  
Eva I. Vargha-Butler ◽  
A. Wilhelm Neumann ◽  
Hassan A. Hamza

The specific heats of five polymers were determined by differential scanning calorimetry (DSC) in the temperature range of 300 to 360 K. The measurements were performed with polymers in the form of films, powders, and granules to clarify whether or not DSC specific heat values are dependent on the diminution of the sample. It was found that the specific heats for the bulk and powdered form of the polymer samples are indistinguishable within the error limits, justifying the determination of specific heats of powders by means of DSC.


1845 ◽  
Vol 1 ◽  
pp. 373-374
Author(s):  
M. Regnault

Professor Forbes observed that, in his communication to the Royal Society on the Conductivity of Soils for Heat, on the 20th December last (see Proceedings, page 343*), he had referred to the separation of the conductivity and specific heat, which are involved in the results of the thermometric experiments on subterranean temperature. In order to eliminate the effect of specific heat, M. Regnault of Paris (well known by his experiments on this subject) undertook, at the request of M. Elie de Beaumont, to ascertain the specific heats of the soils in which the different sets of thermometers are sunk.


1987 ◽  
Vol 65 (9) ◽  
pp. 1104-1110 ◽  
Author(s):  
Douglas L. Martin

Specific-heat measurements on silver and gold in the 15–320 K range are reported and compared with earlier measurements on these metals. The present results together with recent measurements on copper (D. L. Martin, Rev. Sci. Instrum. 58, 639 (1987)) are analyzed in terms of the Debye temperature. The results suggest a negative anharmonic contribution to specific heat for silver and gold. Structure in the results for all three metals below 60 K is consistent with known imperfections in the International Practical Temperature Scale of 1968.


Author(s):  
Alamir Hassan ◽  
Mohamed Hassan ◽  
Mohamed Shedid

Abstract Specific heat is a vital characteristic of nanofluids. The present work is an experimental assessment for the isobaric specific heat measurements for the Al2O3 nanoparticle dispersed in a base fluid of different mixture ratio of ethylene glycol and water at 30, 40, 50, and 60 vol%. The experiments were conducted over temperature range from 35 to 105 °C with nanoparticle concentrations of 0.5 to 2.5 vol%. The results indicated that the specific heat of nanofluid decreases as the nanoparticle volume increases and EG ratio increases but increases as the temperature increases. This characteristic demonstrates that the use of nanofluids should be at as high temperature as possible to fulfill a good beneficial effect. A new correlation from the measurements with maximum deviation of 2.2% was found to estimate the specific heat for these nanofluids.


The present paper is occupied with an experimental investigation into the variation of the specific heat at constant volume of carbon dioxide attending change of absolute density. The investigation is in continuation of a previous one, in which Carbon Dioxide, Air, and Hydrogen were the subjects of a similar enquiry over low ranges of density. It appeared to me desirable to extend the observations more especially in the case of carbon dioxide, because of the extended knowledge we already possess of its isothermals, and the fact that its critical temperature is within convenient reach. Other physical properties of the gas have also received much attention of recent years. It is also readily procured in a nearly pure state. The observations recorded in this paper extend, in the one direction, to densities, such that liquid is present at the lower temperature; and in the other, to a junction with the highest densities of the former paper. A plotting of the new observations is in satisfactory agreement with the record of the old. It reveals, however, the fact that the linear nature of the variation of the specific heat with density, deduced from the former results, is not truly applicable over the new, much more extended range observation. For convenience the chart at the end of this paper embraces the former results, and the present paper is extended to include the entire results on the variation of specific heat with density where the range of temperature, obtaining at each experiment, is approximately the same: that from air temperature to 100° C.


Thermodynamic measurements have been made at temperatures below 1°K, obtained by the method of magnetic cooling, on copper potassium sulphate and on a diluted copper Tutton salt. A study has been made of the field- dependence (for small fields) of the adiabatic susceptibility of the cooled and thermally isolated salt, the measurements covering the range of temperature from 1°K down to 0.05°K for copper potassium sulphate, and to 0.025° K for the dilute salt. From these measurements the entropy and magnetic susceptibility are determined as functions of the absolute temperature. It is concluded that for both salts the susceptibility follows a Curie-Weiss law, the values of ∆ being 0.034 and 0.0048º K respectively; the specific heats are of the form ∆ / T 2 , the values found for A being 6.1x10 -4 R for copper potassium sulphate and 1.98x10 -4 R for the dilute salt.Deviations from this behaviour in a ferromagnetic direction are found for copper potassium sulphate below 0.07° K.


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