Second law of thermodynamics

“ The state thus defined we will call the "micro-state." The macroscopic-observer on the other hand gets along with much fewer data; he will say that the state of the contemplated homogeneous gas is already determined by the density, the visible velocity and the temperature at each place of the gas and he will expect, when these magnitudes are given, that the course of the physical events will be completely determined, namely, will occur in obedience to the two laws of thermodynamics and therefore be bound to show an increase in entropy. The state thus defined we will call the "macro-state." ”

“ 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. ”

“ 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 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.) ”

“ If we hold to the supposition that the molecules in the gaseous and the liquid state are the same—which we may call the supposition of the identity of the two conditions of aggregation—then the heat which is given out by the condensation at constant T is due to the potential energy lost in consequence of the coming closer of the molecules which attract each other, and then it is equal to a (1/vl - 1/vv) . If a should be a function of the temperature, it follows from thermodynamics that it would be equal to (a - T·da/dT) (1/vl - 1/vv) . ”

“ For thermal equilibrium can only be defined as the final state toward which all irreversible processes strive. In this way the question as to temperature leads necessarily to the nature of irreversibility and this in turn is solely founded on the existence of the entropy function. This magnitude is therefore the primary, general conception which is significant for all kinds of states and changes of state, while temperature emerges from this with the help of the special condition of thermal equilibrium, in which condition the entropy attains its maximum. ”

“ A = Q, A = RT log K;
and since the change of A with temperature, as required by the principles of thermodynamics, follows from the specific heats of the reacting substances, it seems further possible to calculate chemical equilibria from heats of reaction and specific heats. The circumstance that chemical affinity and heat-evolution so nearly coincide at low temperatures may be derived from the hypothesis that chemical processes are the result of forces of attraction between the atoms of the different elements. ”

“ Thus, e. g., the law of Avogadro in pure thermodynamics is only a definition, while in the kinetic theory it is a necessary consequence; furthermore, the value of , the mol-heat of a gas, is completely undetermined by pure thermodynamics, but from the kinetic theory it is of equal magnitude for all monatomic gases and, in fact, equal to , corresponding to our experimental knowledge. ”

“ When our theory of Thermotics is tolerably complete and certain, we may with propriety undertake to connect it with our theory of Chemistry. But at present we are not far enough advanced in our knowledge of heat to make this attempt with any hope of success. We can hardly expect to understand the part which heat plays in the union of two bodies, when we cannot as yet comprehend in what manner it produces the liquefaction or vaporization of one body. We cannot look to account for Gay Lussac and Dalton’s Law, that all gases expand equally by heat, till we learn how heat causes a gas to expand. ”

“ The second law teaches us that the real value of heat, as a source of mechanical power, depends upon the temperature of the body in which it resides; the hotter the body in relation to its surroundings, the more available the heat.
In order to see the relations which obtain between the first and the second law of thermo-dynamics, it is only necessary for us to glance at the theory of the steam-engine. ”

“ Having defined compressed air, we must next define heat; for in dealing with compressed air, we are brought face to face with the complex laws of Thermodynamics. We cannot produce compressed air without also producing heat, and we cannot use compressed air as a power without producing cold. Based on the material theory of heat, we would say that when we take a certain volume of free air and compress it into a smaller space, we get an increase in temperature because we have the heat of one volume occupying less space, but no one at this date accepts the material theory of heat. ”

“ 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. ”

“ Thermodynamics teaches that external work may be gained by the mere mixing of two such gases (see Diffusion) , and these amounts of work, which assume very considerable proportions at high temperatures, naturally affect the value of the maximum work and so also of the affinity, in that they always come into play when gases or solutions react. ”

“ 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. ”

“ Travers at University College, London, who are to be credited also with first publishing a detailed account of the various stages of the process. It appears that the use of the self-intensification principle alone is not sufficient with hydrogen as it is with the less volatile gases, including air, for the reason that at all ordinary temperatures hydrogen does not cool in expanding, but actually becomes warmer. It is only after the compressed hydrogen has been cooled by immersion in refrigerating media of very low temperature that this gas becomes amenable to the law of cooling on expansion. ”

“ Such calculations took into account only the first law of thermo-dynamics, which deals with the equivalents of heat and work, and have very little bearing upon the practical question of efficiency, which requires us to have regard also to the second law. According to that law, the fraction of the total energy which can be converted into work depends upon the relative temperatures of the boiler and condenser ”

“ The answer is partly to be found in a statement made by Joule in 1843, which practically embodies what is known as the first law of Thermo-dynamics, and is as follows: “When equal quantities of mechanical effects are produced by any means whatever, from purely thermal sources, or lost in purely thermal effects, then equal quantities of heat are put out of existence or are generated, and for every unit of heat measured by raising a pound of water one degree F. in temperature, you have to expend 772 foot-pounds of work.” ”

“ 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. ”

“ 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. ”

“ Even when mixed with a large excess of other gases, its heat conductivity is about a hundred times that of hydrogen, and this will probably be increased many times when it is obtained pure. Taking the heat conductivity at this figure—a very moderate estimate—the mean molecular velocity of the new gas is calculated to be more than a hundred miles a second, and its density only a thousandth part that of hydrogen, while the specific heat is found to be six thousand times greater than that of hydrogen. ”

“ Now, very little reflection would show that all change of temperature which is not due to a change of volume of the bodies can be only a useless re-establishment of equilibrium in the caloric. [11] The necessary condition of the maximum is, then, that in the bodies employed to realize the motive power of heat there should not occur any change of temperature which may not be due to a change of volume. Reciprocally, every time that this condition is fulfilled the maximum will be attained. This principle should never be lost sight of in the construction of heat-engines ”

“ The part played by heat in effecting chemical combination would seem to consist simply in producing a molecular disturbance, whereby unavoidably some molecules are urged towards each other so as to pass the outer neutral point, which is the necessary preliminary to combination. No doubt, when heated elements combine, the original heat adds itself to the work thus to be derived, as the heat cannot be destroyed, though it cannot increase the work of combination. ”

“ If we differentiate this equation with relation to t alone, and if we represent it by T' and U', the differential coefficients of T and U, we shall get
is simply the specific heat of the gas under constant volume, and our equation (1) is the analytical expression of the law stated on page 86.
If we suppose the specific heat constant at all temperatures (hypothesis discussed above, page 92) , the quantity will be independent of t; and in order to satisfy equation (5) for two particular values of v, it will be necessary that T' and U' be independent of t ”

“ That the process of diffusion obeys the laws of irreversible thermodynamics (if these laws are properly stated) is proved by the fact that the compensating transformations required to separate mixed gases do not essentially involve anything but transformation of energy. The process of allowing gases to mix by diffusion, and then separating them by a compensating transformation, thus constitutes an irreversible cycle, the outside effects of which are that energy somewhere or other must be less capable of transformation than it was before the change. ”

“ Thermochemistry.—This branch of chemistry has to do with heat evolved or absorbed in chemical reactions. It is important chiefly because in many cases it furnishes the only measure we have of the energy changes involved in reactions. To a great extent, it dates from the discovery by Hess in 1840 of a fundamental law which states that the heat evolved in a reaction is the same whether it takes place in one or in several stages. This law has made it possible to calculate the heat values of a large number of reactions which cannot be determined by direct experiment. ”

“ It is only thermometrical or sensible heat, that destroys the attraction of cohesion existing between the particles of bodies, the repulsive power of latent heat being barely able to counteract this property, when the elements under its dominion are removed beyond a certain distance from each other ”

“ 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. ”

“ Thermodynamics is the profit and loss branch of physics as it were; and like the profit and loss branch of fire insurance, thermodynamics is completely abstracted from any consideration of the details of any physical phenomenon. Thermodynamics is concerned with the measurement and counting of that type of physical degeneration which accompanies turbulence just as fire insurance is concerned with the estimate and counting of what we might call, using a fine phrase, structural degeneration by fire. ”