Intercalation

“ The procedure will then consist in assuming a definite excess of energy, of entropy, and of the masses of the various components, each per unit surface, at the interface, the potential of each component being of necessity, in equilibrium, the same as it is in the adjacent masses. The interfacial transition layer thus provides in a sense a new surface-phase coexistent with those on each side of it, and having its own characteristic equation. ”

“ In that part of the diagram which represents a mixture of liquid and vapor, the isothermals, which of course are identical with the isopiestics, are straight lines. For when a body is vaporized under constant pressure and temperature, the quantities of heat received are proportional to the increments of volume; therefore, the increments of entropy are proportional to the increments of volume. As and , any isothermal is cut at the same angle by all the isodynamics, and is divided into equal segments by equidifferent isodynamics. ”

“ Thus although we may regard the equilibrium in such an enclosure as being due to equal exchanges of heat in all directions, the equal and opposite streams of radiation annul and neutralize each other in such a way that no actual transfer of energy in any direction takes place. The state of the medium is everywhere the same in such an enclosure, but its energy of agitation per unit volume is a function of the temperature, and is such that it would not be in equilibrium with any body at a different temperature. ”

“ Similarly if A is hotter than B, or if there is a gradient of temperature between adjacent layers, the diffusion of molecules from A to B tends to equalize the temperatures, or to conduct heat through the gas at a rate proportional to the temperature gradient, and depending also on the rate of interchange of molecules in the same way as the viscosity effect. Conductivity and viscosity in a gas should vary in a similar manner since each depends on diffusion in a similar way. The mechanism is the same, but in one case we have diffusion of momentum, in the other case diffusion of heat. ”

“ An incandescent solid or liquid gives a continuous spectrum, i.e. all the different wave-lengths are represented, but the part of the spectrum which has the greatest energy is different for different substances and for different temperatures: cf. arc and gas flame in Fig. 16. This is quite in keeping with the idea already suggested that in solids and liquids there are electrons of almost every period of vibration. When they are agitated by being heated, a mixture of simple waves of all periods will be sent out giving a very irregular wave. ”

“ As we may make and for any state of the body which we may choose, we may place the origin of co-ordinates at any point in the plane . Again, it is evident from the form of equation (1) that whatever changes we may make in the units in which volume, entropy, and energy are measured, it will always be possible to make such changes in the units of temperature and pressure, that the equation will hold true in its present form, without the introduction of constants. It is easy to see how a change of the units of volume, entropy, and energy would affect the surface. ”

“ The expression for the change of entropy between any two states is found by dividing either of the expressions for dH in (8) by θ and integrating between the given limits, since dH/θ is a perfect differential. In the case of a solid or a liquid, the latent heat of isothermal expansion may often be neglected, and if the specific heat, s, be also taken as constant, we have simply φ−φ0=s logeθ/θ0. If the substance at the temperature θ undergoes a change of state, absorbing latent heat, L, we have mercl to add the term L/θ to the above expression. ”

“ Diagrams in which the Isometrics, Isopiestics, Isothermals, Isodynamics and Isentropics of a Perfect Gas are all Straight Lines.
There are many cases in which it is of more importance that it should be easy to draw the lines of equal volume, pressure, temperature, energy and entropy, than that work and heat should be represented in the simplest manner. In such cases it may be expedient to give up the condition that the scale () of work and heat shall be constant, when by that means it is possible to gain greater simplicity in the form of the lines just mentioned. ”

“ If C is the intensity of the current through a simple thermocouple, the junctions of which are at temperatures t and t′, a quantity of heat, P×C, is absorbed by the passage of the current per second at the hot junction, t, and a quantity, P′×C, is evolved at the cold junction, t′ The coefficients, P and P′, are called coefficients of the Peltier effect, and may be stated in calories or joules per ampere-second. ”

“ On the electronic hypothesis, the source of all inertia is the inertia of the ether, and until we are able to dissect this last quality into anything simpler than the time-element involved in the production of an ether strain or displacement, we must accept it as an ultimate fact, not more elucidated because we speak of it as the inductance of the electron. ”

“ If the temperature of the experiment is at the melting point of a metal which forms the ion and the electrode, a slight variation of temperature will cause the ion to be deposited in the solid or in the liquid state, or, if the current is in the opposite direction, to be taken up from a solid or from a liquid body. Since this will make a considerable difference in the variation of energy, we obtain different values for the electromotive force above and below the melting point of the metal, unless we also take account of the variations of entropy. ”

“ In fact, [9] suppose that one charged particle of mass μ is free to move, and that the other charges are spread uniformly over the surface of a hollow spherical insulator in which the particle is enclosed. The equation of conservation of energy is
constant,
where e denotes the charge of the particle, v its velocity, V its potential energy with respect to the mechanical forces which act on it, and p denotes the quantity
,
where the integration is taken over the sphere, and where σ denotes the surface-density; p is independent of the position of the particle μ within the sphere. ”

“ A heated mass can impart vibratory motion to the ether which fills space, and the wave-motions of ether are able to reproduce in other bodies motions similar to those by which they are caused. At this end of the line I merely measure the electromotive force developed by the difference in temperature of two similar thermo-electric junctions, opposed. We call those junctions in a thermopile 'couples,' and by getting the recording instruments sensitive enough, we can measure one one-thousandth of a degree. ”

“ An example of a more general form of fundamental equation for a solid, is afforded by an equation between the energy and entropy of a given quantity of the solid, and the quantities which express its state of strain, or by an equation between {see (3) } as determined for a given quantity of the solid, the temperature, and the quantities which express the state of strain.
Capillarity.—The solution of the problems which precede may be regarded as a first approximation, in which the peculiar state of thermodynamic equilibrium about the surfaces of discontinuity is neglected. ”

“ A perfectly steady beam of heat and light is made to fall on a small metallic disc, and the amount of heat which is absorbed per second is calculated from the mass of the metal and the rate at which its temperature rises. The disc is first coated with lamp-black, and the rate at which it then receives heat is taken as the rate at which a full absorber absorbs heat under these conditions. The disc is then coated with the surface whose absorbing power is to be measured, and the experiment is repeated. ”

“ I have made a new radiator, where the oscillatory discharge takes place between two small circular plates 12 mm. in diameter and an interposed ball of platinum 9·7 mm. in diameter. The sparking takes place at right angles to the circular plates. The intensity of radiation is by this expedient very greatly increased.
In my previous experiments to determine the index of refraction, I used tubes to surround the radiator. This I was obliged to do to protect the receiver as much as possible from external disturbances. ”

“ A given refraction always corresponds to a given density, though the pressure and temperature may be different. The principle is applied by the method of interference. A luminous beam is split up into two parts, which traverse two tubes filled with the same gas, and the initial appearance of the interference fringes is noted. ”

“ Imagine next that the to and fro movement of the electrons or charges is sufficiently rapid to bring into play the inertia quality of the medium. We then have a different state of affairs. The lines of strain in the external medium cannot contract or collapse quickly enough to keep up with the course of events, or movements of the electrons in the rods, and hence their regular contraction and absorption is changed into a process of a different kind. ”

“ In the theory of heat the first mode is represented by the application of the atomic theory to the study of heat phenomena, and the second mode is represented by what is called thermodynamics." In solving the special problem before us, as to the physical meaning of entropy and of the Second Law, our main dependence must be on the first mode of attack. ”

“ Following the preparatory considerations of the last lecture we shall treat today the problem which we have come to recognize as one of the most important in the theory of heat radiation: the establishment of that universal function which governs the energy distribution in the normal spectrum. The means for the solution of this problem will be furnished us through the calculation of the entropy of a resonator placed in a vacuum filled with black radiation and thereby excited into stationary vibrations. ”

“ When the rigidity of the luminiferous medium is supposed to have the same value in all bodies, the conditions to be satisfied at an interface reduce to the continuity of the displacement e, of the tangential components of curl e, and of the scalar quantity (k + 4/3n) div e across the interface. ”

“ But as the conductivity persisted afterwards, even for the weakest thermo-electric currents, there is some ground for supposing that the insulating medium [Pg 107] is transformed by the passage of the current, and that certain actions, such as shock and rise of temperature, bring about a modification of this new state of the insulating body. Actual movement of the metallic particles cannot be imagined in experiments where the particles, in a layer a few millimetres thick, were fixed in an invariable relative position by extreme pressures, reaching at times to more than 100 kilogrammes per sq. ”

“ The method in which the co-ordinates represent volume and pressure has a certain advantage in the simple and elementary character of the notions upon which it is based, and its analogy with Watt's indicator has doubtless contributed to render it popular. On the other hand, a method involving the notion of entropy, the very existence of which depends upon the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. ”

“ The ordinary thermal motions within any solid, liquid, or gas must cause occasional shootings out of electrons from the substance, and the motion of these electrons, under the influence of electrostatic force, must contribute to the electric conductivity of the gas; must, in fact, constitute all of it which was not due to transport of atoms of the gas carrying less than the neutralizing quantum of electrons. ”

“ The system consists of one component, because all three phases have the same chemical composition, represented by the formula H2O. As the criterion of equilibrium we shall choose a definite pressure, and shall study the variation of the pressure with the temperature; and for the purpose of representing the relationships which we obtain we shall employ a temperature-pressure diagram, in which the temperatures are measured as abscissæ and the pressures as ordinates. In such a diagram invariant systems will be represented by points; univariant systems by lines, and bivariant systems by areas. ”

“ For if C1 and C2 are the capacities and Q1 and Q2 are the charges after contact, then Q1/C1 and Q2/C2 are the potential differences of the coatings and must be equal. Hence Q1/C1 = Q2/C2 or Q1/Q2 = C1/C2. It is worth noting that if we have a charged sphere we can perfectly discharge it by introducing it into the interior of another hollow insulated conductor and making contact. The small sphere then becomes part of the interior of the other and loses all charge. ”

“ Examples of such a triple point have already been given in sulphur and tin, and a list of other substances capable of yielding two solid phases is given below. The triple point S-S-V is not precisely the same as the transition point, but is very nearly so. The transition point is the temperature at which the relative stability of the two solid phases undergoes change, when the vapour phase is absent and the pressure is 1 atm.; whereas at the triple point the pressure is that of the system itself. ”