Thermodynamic expansion

“ There is no escaping this conclusion except through the perpetual motion, or the derivation of mechanical effect from the heat of a body already cold. It has been sometimes claimed that the latter alternative was no impossibility, that the expansion of a compressed gas, the expansion of a gas into a vacuum, or the diffusion of one gas into another, may perform work at the expense of its own heat, while being cooled down to a lower temperature than surrounding bodies. ”

“ Let us next allow the gas to expand without going down in temperature, until its pressure becomes reduced to its primitive value. The expansion which will take place will be , if the temperature be denoted by t; and hence, by (8) , the quantity of heat that must be supplied, to prevent any lowering of temperature, will be
, or . Hence the total quantity added is equal to
But, since B denotes the specific heat under constant pressure, the quantity of heat requisite to bring the gas into this state, from its primitive condition, is equal to Bτ ”

“ Cooling by expansion. Its own expansion is sufficient, provided the initial condition be properly chosen, and provided we take care, even more than in the former method, that there is no influx of heat. Those conditions being fulfilled, we may, simply by adiabatic expansion, not only lower the temperature of some substances down to T3, but also convert them into the liquid state. This is especially the case with substances the molecules of which contain few atoms.
Let us imagine the whole net of isothermals for homogeneous phases drawn in a pv diagram, and in it the border-curve. ”

“ At the same time the gas expands by a fraction 1/T of v, which is the same as 1/273 of its volume at 0° C. If now the air is suddenly compressed by an amount v/T, it will be restored to its original volume, and its temperature will be raised by the liberation of a quantity of heat R′, the latent heat of expansion for an increase of volume v/T. If no heat has been allowed to escape, the air will now be in the same state as if a quantity of heat S had been communicated to it at its original volume v without expansion. ”

“ Vapors of water can be formed only through the intervention of a boiler, while atmospheric air could be heated directly by combustion carried on within its own mass. Considerable loss could thus be prevented, not only in the quantity of heat, but also in its temperature. This advantage belongs exclusively to atmospheric air. Other gases do not possess it. They would be even more difficult to heat than vapor of water.
(3) In order to give to air great increase of volume, and by that expansion to produce a great change of temperature, it must first be taken under a sufficiently high pressure ”

“ Gases, however, having much less cohesion amid the particles, will expand far more under a given heat than either solids or liquids, and liquids expand more than solids for the same reason, and more rapidly at a high temperature than at a low one.
We have spoken of expansion. We may give an instance in which the subsequent contraction of heated metal is useful. Walls sometimes get out of the perpendicular, and require pulling together. No force which can be conveniently applied would accomplish this so well as the cooling force due to the potential energy of iron. ”

“ It is a little-known fact that any gas upon expanding may either heat up or cool down, or even do both in the same operation, depending upon the nature of the gas, the temperature at which the operation started, and the extent of the expansion. Below a certain temperature called the Joule-Thomson inversion temperature—different for each gas: -83° C for hydrogen; much higher for most gases—gases do indeed cool down upon expanding, as you state, but above this temperature, astonishingly enough, they heat up. ”

“ This rapid expansion of the gas would produce great cold, just as the rapid compression of a gas evolves heat and causes a rise in temperature. This cold was produced at the expense of the gas itself, for in rapidly expanding its particles were not able to absorb heat from the walls of the tube, and in cooling a portion of the expanding gas was transformed into liquid. ”

“ It only remains for us to express this result in terms of dq and τ, on which the given thermal agency depends. For this purpose we remark that φ and ω are alterations of volume and pressure which take place along with a change of temperature τ, and hence, by the laws of compressibility and expansion, we may establish a relation [14] between them in the following manner:
Let p0 be the pressure of the mass of air when reduced to the temperature zero, and confined in a volume v0; then, whatever be v0, the product p0v0 will, by the law of compressibility, remain constant ”

“ The passage of the fluid from the upper to the lower limit of temperature must be produced by expansion;” i.e., “it is necessary that the cooling of the gas shall occur spontaneously by its rarefaction;” which is simply his method of stating the now universally understood principle that, for highest efficiency, the expansion must be adiabatic, from a maximum to a minimum temperature. He goes on to explain these principles, and then says that the advantage of high-pressure engines lies “essentiellement dans la faculté de rendre utile une plus grande chute de calorique.” ”

“ It is manifest that when liquid air is removed from the extremely low temperature necessary for its liquefaction, and introduced into ordinary atmospheric temperatures, it will exert a most tremendous expansive force which can be utilized for driving machinery and thereby producing heat or electricity, or for any other purpose for which force is required. But, by the law of Conservation of Energy, the liquefied air by expansion can yield no more energy than was required to extract the heat from the air and compress it into the liquid state. ”

“ For every degree of heat between the freezing-point and the boiling-point, 32° and 212°, the expansion of air is about 1/490th part, so that any invention which seeks to use rarefied air as a motive power must employ a very intense degree of heat, enough to fuse many kinds of metals. ”

“ We suppose two gases occupying volumes V1 and V2 at equal pressure p to mix by diffusion, so that the final volume is V1 + V2. Then if before mixing each gas had been allowed to expand till its volume was V1 + V2, work would have been done in the expansion, and the gases could still have been mixed by a reversal of the process above described. In the actual diffusion this work of expansion is lost, and represents energy rendered unavailable at the temperature at which diffusion takes place. When divided by that temperature the quotient gives the increase of entropy. ”

“ The amount of heat resulting from compression is surprisingly large; for example, if a mass of gas at 0° C. is suddenly compressed to one half its original volume, its temperature rises 87° C.
91. Cooling by Expansion. If a gas expands suddenly, its temperature falls; for example, if a mass of gas at 87° C. is allowed to expand rapidly to twice its original volume, its temperature falls to 0° C. If the compressed air of a bicycle tire is allowed to expand and a sensitive thermometer is held in the path of the escaping air, the thermometer will show a decided drop in temperature. ”

“ After its escape the whole of the gas cooled by expansion passes through the spaces surrounding the pipe in which the compressed gas is passing to the point of expansion, and so makes this gas, still under pressure, cooler than it was itself while under compression. The compressed gas consequently becomes, at the point of expansion, cooler than that which preceded it, and in its turn follows backward the course of the still compressed gas, and so makes the latter cooler than before expansion, and also cooler than ever after expansion. ”

“ By such expansion heat is absorbed and the temperature of the surroundings is lowered. From the coolers the gas returns to the absorber, from which it is pumped, in liquid form, into the retort, to be again heated, the gas expelled and the process repeated. As the gas passes through the different processes, being heated under pressure, cooled, expanded again, more or less decomposition takes place, presumably from a combination of a small portion of the nitrogen with vegetable, animal, or mineral matter that finds its way into the system. ”

“ Heat may be devoted to the expansion of a solid against its cohesive forces. It may be expended against [Pg 26] the elastic forces of a gas, or it may be worked down against chemical or electrical forces. In every case a transformation of energy will result, varying in nature according to the peculiar conditions under which it is carried out. In this or a similar fashion each primary incepting influence may give rise to a series of secondary actions more or less complex in nature. ”

“ The expansion due to heat has been accounted for by supposing a subtile fluid, or caloric, capable of combining with bodies and of separating their parts from each other, and the absorption and liberation of latent heat can be explained on this principle. But many other facts are incompatible with the theory. For instance, metal may be kept hot for any length of time by friction, so that if caloric be pressed out it must exist in an inexhaustible quantity. Delicate experiments have shown that bodies, when heated, do not increase in weight. ”

“ 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. ”

“ 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. ”

“ He takes as the basis of his demonstration the well-established experimental fact that a gas is heated by rapid compression and cooled by rapid expansion, and that if compressed or expanded slowly in contact with conducting bodies, the gas will give out heat in compression or absorb heat in expansion while its temperature remains constant. He then goes on to say:—
“This preliminary notion being settled, let us imagine an elastic fluid, atmospheric air for example, enclosed in a cylinder abcd, fig. ”

“ 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. ”

“ The vapor of water employed in an inverse manner to that in which it is used in steam-engines can also be regarded as a means of destroying the equilibrium of the caloric. To be convinced of this we need but to observe closely the manner in which motive power is developed by the action of heat on vapor of water. Imagine two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. ”

“ From the fountains of heat, still so copious, in the interior the supply is gradually dissipating. Now heat is only a form of energy, and energy, like matter, cannot itself be created out of nothing. There can be no creation of heat in our earth without a corresponding expenditure of energy. If, therefore, the earth is radiating heat, then, as there is no known or, indeed, conceivable source of energy by which an equivalent can be restored, it follows that the earth must have less internal heat now than it had at any earlier period. No doubt the process of cooling is excessively slow. ”

“ 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? ”

“ 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. ”