Thermal equilibrium

“ For we can by mere geometrical displacement change the order of the bodies so as to bring different ones into direct contact. If this disturbed the thermal equilibrium, we could construct cyclic processes to take advantage of the resulting flow of heat to do mechanical work, and such processes might be carried on without limit. Thus it is proved that if a body A is in temperature-equilibrium with B, and B with C, then A must be in equilibrium with C directly. ”

“ If the external influences which act upon a fluid in thermal equilibrium are made to change very slowly, causing the pressure, volume and temperature of the fluid to pass very slowly through a continuous series of values and in general involving the doing of work upon or by the fluid and the giving of heat to or taking of heat from the fluid, then the fluid will pass slowly through a process consisting of a continuous series of states of thermal equilibrium. ”

“ In the settled state there is an equal distribution of density throughout all the elementary spaces, there are no different streams (whirls or eddies) present, and an equal partition of energy exists for all the elementary spaces. For it thermal equilibrium exists, the entropy is a maximum, and temperature of the state has now a definite meaning, because temperature is the mean energy of the molecules for this state of equilibrium. ”

“ 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. ”

“ In gases at atmospheric pressure, the commercially available thermal sources induce transition rates between quantum energy states which are small compared to those of the competing collisional relaxation processes, and cannot induce non-equilibrium energy state populations. ”

“ Are not percussion and the friction of bodies actually means of raising their temperature, of making it reach spontaneously a higher degree than that of the surrounding bodies, and consequently of producing a destruction of equilibrium in the caloric, where equilibrium previously existed? It is a fact proved by experience, that the temperature of gaseous fluids is raised by compression and lowered by rarefaction. This is a sure method of changing the temperature of bodies, and destroying the equilibrium of the caloric as many times as may be desired with the same substance. ”

“ In statical equilibrium, any downward movement of an air mass would simply be accompanied by the natural rise in temperature corresponding to the transformation of its energy of position, but in this condition of stable equilibrium any motion downwards must involve, not only this natural temperature rise, but also a return, either in whole or in part, of the energy absorbed from the aqueous vapour. ”

“ It is determined, namely, by the value as positive, negative, or zero, i.e., by the effect of heat as increasing or diminishing the pressure when the volume is maintained constant, and by the nature of the internal thermodynamic equilibrium of the body as stable or neutral,—an unstable equilibrium, except as a matter of speculation, is of course out of the question. ”

“ The system must have and maintain the greatest entropy consistent with constant energy; or for adiabatic systems (at constant entropy) , the intrinsic energy or heat function should have minimum values for constant volume or pressure, respectively, but for isothermal systems (at constant temperature) the free energy potential or the thermodynamic potential should have minimum values for constant volume or pressure. Any deviation from these maxima or minima will again disturb equilibrium and produce changes of physical or chemical state. ”

“ Thus, a subversion of the equilibrium of temperature has been bonâ fide effected. Heat has been driven from the air into the metal, while every thing else remains unchanged.
We have here a means by which, it is evident, heat may be obtained, to any extent, from the air, without fuel. For if, in place of withdrawing the piston and letting the same air expand, within the reservoir, it be allowed to escape so suddenly as not to re-absorb the heat given off, and fresh air be then admitted and the process repeated, any quantity of air may thus be drained of its heat. ”

“ Coal being capable of producing, by its combustion, a temperature higher than 1000°, and the cold water, which is generally used in our climate, being at about 10°, we can easily procure a fall of caloric of 1000°, and of this only 120° are utilized by steam-engines. Even these 120° are not wholly utilized. There is always considerable loss due to useless re-establishments of equilibrium in the caloric. ”

“ The relation of heat energy to work as determined is a demonstration of the first law of thermo-dynamics, namely, that heat and mechanical energy are mutually convertible in the ratio of 778 foot pounds for one British thermal unit. ”

“ The latter would thus be still further expanded against gravity; the aqueous vapour itself would suffer a loss of energy equivalent to the work transmitted from it. It is therefore clear that in a composite atmosphere formed in the manner described, any gas possessed of energy properties superior to the other constituents is forced of necessity to transmit energy to these constituents. This phenomenon is merely a consequence of the natural disposition of the atmospheric gaseous substances towards a condition of equilibrium with more or less uniform temperature gradation. ”

“ The function J=E−θφ, has been called the “ free energy ” of the substance by Helmholtz, and 04> the “bound energy.” These functions do not, however, represent energy existing in the substance, like the intrinsic energy; but the increment of θφ represents heat su plied to, and the decrement of (E−θφ) represents work obtainable from, the substance when the temperature is kept constant. The condition of stable equilibrium of a system at constant temperature and volume is that the total J should be a minimum. ”

“ If we attempt to change either the temperature or the pressure ice will melt, water will evaporate or vapour condense until one or other of the phases has vanished. We then have in equilibrium two phases only, and the temperature and pressure may change. Thus, if we supply heat to the mixture of ice, water and steam ice will melt and eventually vanish. We then have water and vapour in equilibrium, and, as more heat enters, the temperature rises and the vapour-pressure rises with it. But, if we fix arbitrarily the temperature the pressure of equilibrium can have one value only. ”

“ In the case of the conduction or diffusion of heat the process is not only irreversible, but it involves the irreversible diminution of that part of the whole stock of thermal energy which is capable of being converted into mechanical work. ”

“ Irreversible Processes.—In order that a process may be strictly reversible, it is necessary that the state of the working substance should be one of equilibrium at uniform pressure and temperature throughout. If heat passes “of itself” from a higher to a lower temperature by conduction, convection or radiation, the transfer cannot be reversed without an expenditure of work. If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted. ”

“ This means that no physical condition, pressure or temperature can be varied without destroying a phase, so that such a system can only exist in equilibrium at one fixed temperature, with a fixed value for its vapor-pressure. ”

“ These two forces—the natural cohesion of the particles, and the repulsive energy introduced by heat—are directly opposed to one another, and the state of the body will be decided by the predominance of the one or the other, or their mutual equilibrium. If the natural cohesion of the constituent particles of the body considerably predominate over the repulsive energy introduced by the heat, then the cohesion will take effect ”

“ In the course of the mutual energy reactions, some will lose a portion of their energy. Others will gain at their expense. All are in equilibrium as constituents of the composite atmosphere, but none approach the condition of statical equilibrium peculiar to an atmosphere composed of one gas only (§ 35) . The precise energy operations which would thus take place in any composite atmosphere would of course depend in nature and extent on the physical properties of [Pg 141] the reacting constituents. ”

“ On the other hand, water in contact with hydrogen and oxygen at the ordinary temperature is a case only of apparent equilibrium; on changing the pressure and temperature continuously within certain limits there is no continuous change observed in the relative amounts of the two gases. On heating beyond these limits there is a sudden and not a continuous change, and the system no longer regains its former condition on being cooled to the ordinary temperature. ”

“ If we consider only the dotted line on the right, representing the equilibria under atmospheric pressure, we see that the points in which the dotted line cuts the other two curves must represent systems in which carbon monoxide and carbon dioxide are in equilibrium with FeO + Fe3O4 + C, on the one hand, and with Fe + FeO + C on the other. These systems can only exist at one definite temperature, if we make the restriction that the pressure is maintained constant (atmospheric pressure) . ”

“ If suitable quantities of these are present, diminution of volume will ultimately lead to the total condensation of the vapour phase, and there will remain the univariant system ice—hydrate—solution. The temperature of equilibrium of this system will alter with the pressure, but, as in the case of the melting point of a simple substance, great differences of pressure will cause only comparatively small changes in the temperature of equilibrium. ”

“ Heat a Degraded Form of Energy.—We have seen that thermal energy is not directly transformed into chemical energy. There is yet another restriction in the case of this thermal energy if we study the laws which govern the circulation and the transformations of thermal energy; and the most important comes from the impossibility of transporting it from a body at a lower temperature to a body at a higher temperature. On the whole, and because of these restrictions, thermal energy is an imperfect variety of universal energy, or, as the English physicists call it, a degraded form. ”

“ All that is necessary is to rapidly cool the fused mass, after equilibrium has been established, and find the freezing point at which solid is deposited; that is, find the point at which the line of constant temperature cuts the freezing point curve. The composition corresponding to this temperature gives the composition of the equilibrium mixture at the given temperature. ”

“ There are systems in which the equilibrium states are but very slightly dependent on temperature and pressure within wide limits, outside which reaction takes place. Thus while there are cases in which a state of mobile dissociation exists in the system which changes continuously as a function of these variables, there are others in which change does not sensibly occur at all until a certain temperature of reaction is attained, after which it proceeds very rapidly owing to the heat developed, and the system soon becomes sensibly permanent in a transformed phase by completion of the reaction. ”

“ It is not merely that heat produces mechanical effect, but that a given quantity of heat absolutely passes out of existence as heat in producing its equivalent of work. If, therefore, we could measure the mere heat produced in an engine by the burning of a ton of coals, we should find it to be less when the engine was doing work than when it was at rest.
In like manner, when a gas expands suddenly its temperature falls, because a certain amount of its heat passes out of existence in the act of producing mechanical effect. ”

“ Static caloric is what we call latent heat, and dynamic caloric is what we call electricity. Therefore what may we expect of it (electricity) is merely a matter of economy in the development and utilization of dynamic caloric; in other words, can we unlock static caloric by non-luminous combustion, and thus develop dynamic caloric as a first power more economically per foot pound than we now do or can hereafter do by luminous combustion? Second, can we utilize water and wind for the production of dynamic caloric as a first power? ”

“ The more complicated the systems considered are, the more apparent becomes the advantage of this method, and there is no doubt in my mind that in chemical circles it will be more and more employed, especially, since in general it is now the custom to deal directly with the energies, and not with cyclic processes, in the calculation of heat effects in chemical changes. ”