Excursus on the Carnot-Kelvin aspect of Thermodynamics

1937 ◽  
Vol 32 (5) ◽  
pp. 748-750
Keyword(s):  
Specific Heat ◽  
Work Function ◽  
Physical System ◽  
Thermal Capacity ◽  
General Function ◽  
Available Energy ◽  
Universal Space ◽  
Different Temperatures ◽  
Lower Temperature ◽  
Image Position

According to Carnot's postulate heat can give rise to work only by falling to lower temperature. This negation ensures that at each temperature a definite physical system possesses a work-function A, named by W. Thomson its available, energy at that temperature. This aspect of Carnot's postulate was enforced especially in Thomson and Tait's Nat. Phil. (1867). These available energies at different temperatures combine into one more general function, the isothermal available energy, which is a function of temperature θ as well as configuration. (Cf. the Minkowski condensation of personal spaces and times into a single universal space-time.) Thus we are entitled to assert the equationwhere Ψ1r is the force exerted by the coordinate ψr of configuration. The final term in δA though regular has not to do with ostensible work: and −η, as yet arbitrary, here equal to A/θ, may be described as the thermal capacity or specific heat of available energy.

scholarly journals On the capacity for heat of water between the freezing and boiling points, together with a determination of the mechanical equivalent of heat in terms of the international electrical units.―Experiments by the continuous-flow method of calorimetry performed in the Macdonald Physical Laboratory of McGill University, Montreal

1901 ◽  
Vol 67 (435-441) ◽  
pp. 238-244 ◽  
Keyword(s):  
Specific Heat ◽  
Continuous Flow ◽  
Thermal Capacity ◽  
Boiling Points ◽  
Physical Laboratory ◽  
Complete Work ◽  
Different Temperatures ◽  
Mcgill University ◽  
Continuous Flow Method

At the Toronto meeting of the British Association in 1897, a new method of calorimetry was proposed by Professor Callendar and the author for the determination of the specific heat of a liquid in term of the international electrical units. At the Dover meeting ii September, 1899, some of the general results obtained with the method for water over a part of the range between 0° and 100 were communicated, with a general discussion of the bearing of the experiments to the work of other observers. In the present paper the author gives a summary of the complete work, in the case of water, to determine the thermal capacity at different temperatures between the freezing and boiling points.

scholarly journals The thermal capacity of pure iron

1940 ◽  
Vol 174 (956) ◽  
pp. 1-15 ◽  
Keyword(s):  
Heat Capacity ◽  
Specific Heat ◽  
Thermal Capacity ◽  
Total Heat ◽  
Large Temperature ◽  
Specific Heats ◽  
The Past ◽  
Heat Curve ◽  
Different Temperatures ◽  
The Subject

Although the heat capacity of iron at different temperatures has been the subject of a number of investigations in the past, it is only recently that iron of purity greater than 99.9 % has been available. Furthermore, in most previous determinations the property actually measured has been the total heat over a relatively large temperature range. Specific heats deduced from such measurements are liable to appreciable error, since if the total heat curve is smoothed, small fluctuations in the specific heat will be concealed, whereas if the actual observations are retained without smoothing, fluctuations which have no physical existence may appear in the result. Thus, suppose that the total heat is measured from 50 to 145 and from 50 to 155° C, the former being in error by 1 part in 1000 in excess and the latter the same amount in defect, the error in the specific heat over the range 145-155° C will be almost 2%. Evidently a real variation of 1 or 2% would be liable to pass unnoticed if any smoothing is undertaken, and conversely, fluctuations of this order may be introduced spuriously if the observations are used without smoothing. In general, calorimetry from high temperatures cannot be carried out to an accuracy of 1 part in 1000, and in any case, even this accuracy is insufficient at temperatures of the order of 1000° C.

XXXI.—On Thermodynamic Motivity

1878 ◽  
Vol 28 (3) ◽  
pp. 741-744
Author(s):  
W. Thomson
Keyword(s):  
Mechanical Energy ◽  
Thermal Capacity ◽  
The Body ◽  
Philosophical Magazine ◽  
Different Temperatures ◽  
Image Position ◽  
Different Parts

After having for many years felt with Professor Tait the want of a word “to express the Availability for work of the heat in a given magazine, a term for that possession the waste of which is called Dissipation” I now suggest the word Motivity to supply this want.In my paper on the “Restoration of Energy from an Unequally Heated Space,” published in the Philosophical Magazine for January 1853, I gave the following expression for the amount of “mechanical energy” derivable from a body B, given with its different parts at different temperatures, by the equalisation of its temperature throughout to one common temperature T, by means of perfect thermodynamic engines,—where t denotes the temperature of any point x, y, z of the body; c the thermal capacity of the body's substance at that point and that temperature; J, Joule's equivalent; and μ, Carnot's function of the temperature t.

Silicon Tetrachloride Synthesis from Rice Hulls: Transmission and Scanning Electron Microscope Study

1972 ◽  
Vol 30 ◽  
pp. 236-237 ◽  
Author(s):  
Richard S. Thomas ◽  
Prabir K. Basu ◽  
Francis T. Jones
Keyword(s):  
Silicon Tetrachloride ◽  
Silica Sand ◽  
Mineral Matter ◽  
Chemical Heterogeneity ◽  
Scanning Electron Microscope Study ◽  
Rice Hulls ◽  
Hull Structure ◽  
Lower Temperature ◽  
Image Position ◽  
Disposal Problem

Silicon tetrachloride, used in industry for the production of highest purity silicon and silica, is customarily manufactured from silica-sand and charcoal.SiCl4 can also be made from rice hulls, which contain up to 20 percent silica and only traces of other mineral matter. Hulls, after carbonization, actually prove superior as a starting material since they react at lower temperature. This use of rice hulls may offer a new, profitable solution for a rice mill byproduct disposal problem.In studies of the reaction kinetics with carbonized hulls, conversion of SiO2 to SiCl4 was found to proceed within a few minutes to a constant, limited yield which depended reproducibly on the ambient temperature of the reactor. See Fig. 1. This suggested that physical or chemical heterogeneity of the silica in the hull structure might be involved.

Thermal Properties of an Incompletely Degenerate Fermi Gas

1936 ◽  
Vol 32 (1) ◽  
pp. 108-111 ◽  
Author(s):  
N. F. Mott
Keyword(s):  
Thermal Properties ◽  
Specific Heat ◽  
Electron Gas ◽  
Electronic States ◽  
Fermi Gas ◽  
Paramagnetic Susceptibility ◽  
Free Electrons ◽  
Periodic Field ◽  
Degenerate Fermi Gas ◽  
Image Position

The purpose of this note is to calculate the specific heat and paramagnetic susceptibility of an electron gas obeying the Fermi-Dirac statistics for all temperatures, including those temperatures for which the gas is partially degenerate. The results are applicable to the electrons in a metal, whether free or moving in a periodic field, provided only that the number of electronic states per gram atom with energy between E and E + dE can be expressed in the formas for free electrons.

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.

scholarly journals Maximally Reliable Markov Chains Under Energy Constraints

2009 ◽  
Vol 21 (7) ◽  
pp. 1863-1912 ◽  
Author(s):  
Sean Escola ◽  
Michael Eisele ◽  
Kenneth Miller ◽  
Liam Paninski
Keyword(s):  
Physical System ◽  
Infinite Length ◽  
Energy Functions ◽  
Available Energy ◽  
Energy Demands ◽  
Multistate System ◽  
Linear Chains ◽  
Energy Constraints ◽  
Cascade Structure ◽  
Reliable Solution

Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.

scholarly journals Effects of light intensity and temperature on Cylindrospermopsis raciborskii (Cyanobacteria) with straight and coiled trichomes: growth rate and morphology

2012 ◽  
Vol 72 (2) ◽  
pp. 343-351 ◽  
Author(s):  
MC. Bittencourt-Oliveira ◽  
B. Buch ◽  
TC. Hereman ◽  
JDT. Arruda-Neto ◽  
AN. Moura ◽  
...  
Keyword(s):  
Growth Rate ◽  
Light Intensity ◽  
Morphological Changes ◽  
Population Control ◽  
Distinct Species ◽  
Cylindrospermopsis Raciborskii ◽  
Climatic Chamber ◽  
Light Intensities ◽  
Different Temperatures ◽  
Lower Temperature

Cylindrospermopsis raciborskii (Woloszynska) Seenayya et Subba Raju (Ordem Nostocales) is one of the most troublesome bloom-forming species in Brazil. Understanding the population dynamics of the different morphotypes of C. raciborskii (straight and coiled) could assist in the prediction of favourable conditions for the proliferation of this potentially toxin-producing species. The aim of the present study was to assess the effects of two different light intensities and temperatures on the growth rate and morphology of the trichomes of the straight and coiled morphotypes. For such, two non-toxin producing strains of C. raciborskii were used - one with a coiled trichome (ITEP31) and another with a straight trichome (ITEP28). The strains were cultured in BG-11 medium in a climatic chamber under controlled conditions. Two light intensities (30 and 90 µmol.m-2.s-1 ) were combined at temperatures of 21 and 31 °C and the growth rate and morphological changes were analysed. The morphotypes responded differently to the different temperatures and light intensities. Both strains exhibited faster growth velocities when submitted to higher light intensity and temperature. The lower temperature and higher luminosity hampered the development of both strains. Variations in cellular morphology and an absence of akinetes in both strains were related to the lower temperature (21 °C). The coiled morphotype demonstrated considerable phenotype plasticity, changing the morphology of trichome throughout its growth curve. Although molecular analysis does not sustain the separation of the morphotypes as distinct species, their different eco-physiological responses should be considered further knowledge of extreme importance for the population control of these potentially toxic organisms.

scholarly journals Creep behaviour and life assessment of a cast nickel – base superalloy MAR – M247

2019 ◽  
Vol 38 (2019) ◽  
pp. 590-600
Author(s):  
Marie Kvapilova ◽  
Jiri Dvorak ◽  
Petr Kral ◽  
Karel Hrbacek ◽  
Vaclav Sklenicka
Keyword(s):  
Creep Behaviour ◽  
Life Assessment ◽  
Dislocation Creep ◽  
Nickel Base Superalloy ◽  
Creep Characteristics ◽  
Different Temperatures ◽  
High Temperature Components ◽  
Lower Temperature ◽  
Nickel Base ◽  
Different Grain Size

AbstractThe cast nickel-base MAR-M247 superalloy has been widely used for high-temperature components. In this work, the creep behaviour of two alternates of MAR-M247 superalloy with different grain size processed at different temperatures of casting are compared. Under the creep testing conditions used in this study, only negligible differences of creep behaviour of the alternate alloys were found and the evaluated creep characteristics correspond to the power-law or dislocation creep. The microstructure of the alloys consists of a𝛾matrix with a eutectic,𝛾'strengthening cubic precipitates, and M6C and M23C6carbides. Increasing the temperature induces the dissolution of some M23C6carbides. Fractures of both variants of alloys exhibit a more ductile character at higher temperatures, while at lower temperature a mixture of brittle and ductile fracture modes was observed, which changes the creep fracture ductility.

Analytic functions of finite dimensional linear transformations

1959 ◽  
Vol 55 (1) ◽  
pp. 51-61 ◽  
Author(s):  
S. N. Afriat
Keyword(s):  
Power Series ◽  
Integral Formula ◽  
Characteristic Root ◽  
Interpolation Formula ◽  
General Function ◽  
Linear Transformations ◽  
Multiple Characteristic ◽  
Characteristic Roots ◽  
Image Position ◽  
Necessary And Sufficient

Since the first introduction of the concept of a matrix, questions about functions of matrices have had the attention of many writers, starting with Cayley(i) in 1858, and Laguerre(2) in 1867. In 1883, Sylvester(3) defined a general function φ(a) of a matrix a with simple characteristic roots, by use of Lagrange's interpolation formula, and Buchheim (4), in 1886, extended his definition to the case of multiple characteristic roots. Then Weyr(5) showed in 1887 that, for a matrix a with characteristic roots lying inside the circle of convergence of a power series φ(ζ), the power series φ(a) is convergent; and in 1900 Poincaré (6) obtained the formulaefor the sum, where C is a circle lying in and concentric with the circle of convergence, and containing all the characteristic roots in its ulterior, such a formula having effectively been suggested by Frobenius(7) in 1896 for defining a general function of a matrix. Phillips (8), in 1919, discovered the analogue, for power series in matrices, of Taylor's theorem. In 1926 Hensel(9) completed the result of Weyr by showing that a necessary and sufficient condition for the convergence of φ(a) is the convergence of the derived series φ(r)(α) (0 ≼ r < mα; α) at each characteristic root α of a, of order r at most the multiplicity mα of α. In 1928 Giorgi(10) gave a definition, depending on the classical canonical decomposition of a matrix, which is equivalent to the contour integral formula, and Fantappie (11) developed the theory of this formula, and obtained the expressionfor the characteristic projectors.

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