Thermodynamics

“ It follows, in fact, from the
second law of thermodynamics, that whenever work is derived from
heat, a certain quantity of heat falls in potential without doing
work or, in short, is dissipated. On the other hand, work may be
entirely converted into heat. The result is the heat-tendency of
the universe. Heat, being an undirected form of energy, seeks, as
it were, its own level, so that the result of this heat-tendency
is continual approach to uniformity of potential. ”

“ Thus, ordinary statics teaches us that a liquid with its vapour on the top forms a system in equilibrium, if we apply to the two fluids a pressure depending on temperature alone. Thermodynamics will furnish us, in addition, with the expression of the heat of vaporization and of, the specific heats of the two saturated fluids. ”

“ The corresponding cases in thermodynamics would be bodies which could absorb or give out an infinite amount of heat without passing certain limits of temperature, when no external work is done in the positive or negative sense. Such infinite values present no analytical difficulties, and do not contradict the general laws of mechanics or of thermodynamics, but they are quite foreign to our ordinary experience of nature. ”

“ Other transformations of heat are often included under the same title (see Energetics) . An historical account of the development of thermodynamics is given in the article Heat. The object of the present article is to illustrate the practical application of the two general principles— (1) Joule’s law of the equivalence of heat and work, and (2) Carnot's principle, that the efficiency of a reversible engine depends only on the temperatures between which it works; these principles are commonly known as the first and second laws of thermodynamics. ”

“ The same substance may be able to exist in two different states at the same temperature and pressure, as when water and its saturated vapour are contained in the same vessel. The conditions under which the thermal and mechanical equilibrium of two fluids, two mixtures, or the same substance in two physical states in contact with each other, is possible belong to thermodynamics. All that we have to observe at present is that, in the cases in which the fluids do not mix of themselves, the potential energy of the system must be greater when the fluids are mixed than when they are separate. ”

“ This equation expresses, in symbols, the two laws of thermodynamics. For it states that the gain of energy is the excess of the heat supplied over the work done, which is an expression of the first law. And it expresses the heat supplied as the product of the absolute temperature by the gain of entropy, which is a statement of the second law in terms of Thomson's mode of measuring absolute temperature. ”

“ Through the science of thermodynamics, heat has a place in many of the industrial processes that bring us the conveniences of modern life. But as recently as 200 years ago, the true nature of heat was not understood. In the early days of science the phenomena associated with heat were ascribed to a mystical and intangible fluid called "caloric." This fluid was believed to have the power of penetrating and expanding materials, sometimes melting or dissolving them, and converting some substances to vapor. ”

“ Another idea, that of thermodynamic motivity, on which Thomson suggested might be founded a fruitful presentation of the subject of thermodynamics, may be mentioned here. It was set forth in a letter written to Professor Tait in May 1879. If a system of bodies be given, all at different temperatures, it is possible to reduce them to a common temperature, and by doing so to extract a certain amount of mechanical energy from them. ”

“ The Laws of Thermodynamics.—I. When equal quantities of mechanical effect are produced by any means whatever from purely thermal sources, or lost in purely thermal effects, equal quantities of heat are put out of existence, or are generated. [To this we may add, after Joule, that in the latitude of Manchester 772 foot-pounds of work are capable of raising the temperature of a pound of water from 50°F. to 51°F. This corresponds to 1390 foot-pounds per centigrade degree, and in metrical units to 425 kilogramme-metres per calorie (see Heat) .] ”

“ This definite quantity belonging to a material system, its entropy φ, is thus concomitant with its energy E, which is also a definite function of its actual state by the law of conservation of energy; these, along with its temperature T, and the various co-ordinates expressing its geometrical configuration and its physical and chemical constitution, are the quantities with which the thermodynamics of the system deals. That branch of science develops the consequences involved in just two principles: (i.) that the energy of every isolated system is constant, and (ii.) ”

“ In his last work, Elementary Principles in Statistical Mechanics, Professor Gibbs returned to a theme closely connected with the subjects of his earliest publications. In these he had been concerned with the development of the consequences of the laws of thermodynamics which are accepted as given by experience; in this empirical form of the science, heat and mechanical energy are regarded as two distinct entities, mutually convertible of course with certain limitations, but essentially different in many important ways. ”

“ Changes of entropy must be calculated in terms of quantities of heat, and must be interpreted in a similar manner. The majority of thermodynamical problems may be treated without any reference to entropy, but it affords a convenient method of expression in abstract thermodynamics, especially in the consideration of irreversible processes and in reference to the conditions of equilibrium of heterogeneous systems. ”

“ If there is neither heating nor cooling ∂w = 0, and we obtain by integration T = Cv, where C is a constant.
138 Elaborate discussions of the theory of this experiment will be found in modern treatises on thermodynamics, and in various recent memoirs, and the differential equation has been modified in various ways, and integrated on various suppositions, which it would be out of place to discuss here.
The cooling effect of passing a gas such as air or oxygen through a narrow orifice has been used to liquefy the gas. ”

“ Thus, when a gas is absorbed by water, much heat is evolved, and we may suppose the result to be due in part to chemical combination, and in part to the condensation of the gas into a liquid, by which means its latent heat is rendered sensible. On the other hand, when a liquid unites with a solid, or when two solids unite with one another, and the product is a liquid, we have very often the absorption of heat, the heat rendered latent by the dissolution of the solid being more than that generated by combination. ”

“ The other gases through a similar compression should also rise in temperature. They should rise, but not equally, in inverse ratio with their specific heat at constant volume. In fact, the reduction of volume being by hypothesis always the same, the quantity of heat due to this reduction should likewise be always the same, and consequently should produce an elevation of temperature dependent only on the specific heat acquired by the gas after its compression, and evidently in inverse ratio with this specific heat. ”

“ The distinction of Formal Thermotics and Physical Thermotics,—of the discovery of the mere Laws of Phenomena, and the discovery of their causes,—is applicable here, as in other departments of our knowledge. But we cannot exhibit, in any prominent manner, the latter division of the science now before us; since no general theory of heat has yet been propounded, which affords the means of calculating the circumstances of the phenomena of conduction, radiation, expansion, and change of solid, liquid, and gaseous form. ”

“ According to the kinetic theory of gases an elevation of temperature consists in an increase of the kinetic energy of the translatory motion of the gaseous particles; and no doubt there actually is, from time to time, a passage of some more quickly moving particles from a portion of a gas in which the average kinetic energy is low, to a region in which the average kinetic energy is high, and thus a transference of heat from a region of low temperature to one of higher temperature. ”

“ According to the theory developed here, we therefore have to imagine an energy store in the interior of each body, whose amount is so enormous that the usually observed heating and cooling processes, and even quite deep invasive chemical transformations associated with considerable heat effects, changes it by only an imperceptible fraction. This is valid down to the lowest attainable temperatures: for both the specific heat of a body as well as the reaction enthalpy of chemical processes keep up their magnitude close to absolute zero. ”

“ In short, although the laws which govern the relations of molar energy to heat are in the abstract positively known, yet in endeavoring to trace the distribution and precise condition of energy when it becomes absorbed within a body, or vice versa, the mode and minutest detail of its transformation into gross mechanical effect, the most consistent theories have heretofore depended on the hypothesis that actual or real heat is a condition of molecular kinetic energy, and that the various latent heats are due to potentialities of molecular arrangement. ”

“ When a gas passes without change of temperature from one definite volume and pressure to another volume and another pressure equally definite, the quantity of caloric absorbed or relinquished is always the same, whatever may be the nature of the gas chosen as the subject of the experiment.
Take, for example, 1 litre of air at the temperature of 100° and under the pressure of one atmosphere. If we double the volume of this air and wish to maintain it at the temperature of 100°, a certain quantity of heat must be supplied to it. ”

“ When a body passes from a state of solidity to that of fluidity, it absorbs a quantity of heat, which becomes chemically combined with it, and insensible to the touch or the thermometer; in the same manner, when it passes from a fluid state to that of vapour or gas, it combines with a still larger quantity of heat, which remains latent in it, so long as it continues in the state of gas, but when it returns to the liquid or solid state, it gives out the heat which was combined with it, which, being set at liberty, flows into the surrounding bodies, and augments their temperature. ”

“ These molecules that have been slowed down are then cold; they will absorb heat from the air about them, and since the molecule of hydrogen gas at room temperature is moving at about seven miles a second, when the molecules of the confined gas in our car, or the molecules of the metal bar are slowed down to but a few hundred miles an hour, their temperature drops to some hundreds of degrees below zero, and they absorb energy very rapidly, for the greater the difference in temperature, the greater the rate of heat absorption. ”

“ Let us assume, as is commonly the case, that the intrinsic energy of the initial system is greater than that of the final system. When the first system then is transformed into the second, the excess of energy which the former possesses must appear in the shape of heat, light, electrical energy, mechanical energy, &c. It is for the most part a simple matter to obtain the excess of energy entirely in the form of heat, the amount of which is easily susceptible of measurement, and thus the existence of thermochemistry as a practical science is rendered possible. ”

“ We need not consider the formula that we have just given as applicable to very great changes in the volume of gases. We have regarded the elevation of temperature as being in inverse ratio to the specific heat; which tacitly supposes the specific heat to be constant at all temperatures. Great changes of volume lead to great changes of temperature in the gas, and nothing proves the constancy of specific heat at different temperatures, especially at temperatures widely separated. ”

“ From thermodynamic theory it is concluded that cold is produced whenever a solid is strained by opposing, and heat when it is strained by yielding to, any elastic force of its own, the strength of which would diminish if the temperature were raised; but that, on the contrary, heat is produced when a solid is strained against, and cold when it is strained by yielding to, any elastic force of its own, the strength of which would increase if the temperature were raised. When the strain is a condensation or dilatation, uniform in all directions, a fluid may be included in the statement. ”

“ In our demonstrations we tacitly assume that after a body has experienced a certain number of transformations, if it be brought identically to its primitive physical state as to density, temperature, and molecular constitution, it must contain the same quantity of heat as that which it initially possessed; or, in other words, we suppose that the quantities of heat lost by the body under one set of operations are precisely compensated by those which are absorbed in the others. ”

“ Heat changes solids to liquids, and liquids to gases; it resolves compounds, or it aids chemical union. In every chemical combination heat is developed; in every case of dissociation heat is absorbed. Properly written, every equation should be: a + b = c + heat; e.g. 2 H + 0 = H2O + heat; or, c - a = b - heat; e.g. H2O - 2 H = 0 - heat. Another illustration is the combination of C and O, and the dissociation of CO2, as given on page 82. C + O2 = CO2 + energy. CO2 - O2 = C - energy. ”