ENERGETICS . The most fundamental result attained by the progress of See also:

• PHYSICAL

See also:

• MAYER, JOHANN TOBIAS (1723-1762)
• MAYER, JULIUS ROBERT (1814-1878)

In its application to kinetics a purely physical principle, also indicated by Newton, but See also:

• DEVELOPED

To establish a doctrine of energetics that shall form a sufficient foundation for a theory of the trend of chemical and physical change, we have, there-fore, to impart precision to this motion of available energy. See also:

• CARNOT, LAZARE EIPPOLYTE (18ot-1888)
• CARNOT, MARIE FRANCOIS SADI (1837-1894)
• CARNOT, SADI NICOLAS LEONHARD (1796-1832)

Every reversible change in an isolated system thus maintains the entropy of that system unaltered; no possible spontaneous change can involve decrease of the entropy; while any defect of reversibility, arising from See also:

• DIFFUSION (from the Lat. diffundere; dis-, asunder, and fundere, to pour out)

. . ; in all cases where this is possible the single equation ENERGETICS SE =TSB—pbv+µ,Sm,+µ2&m2+• • . •+e &ni (i) thus expresses the complete variation of the energy-function E arising from change of state; and when the part involving the n constitutive differentials has been expressed in terms of the number of them that are really independent, this equation by itself becomes the unique expression of all the thermodynamic relations of the system. These are in fact the various relations ensuring that the right-hand See also:

• SIDE
• SIDE (mod. Eski Adalia)

The former passage, moreover, is often effected by introducing a new substance into the system; sometimes that substance is recovered unaltered at the end of the process, and then its action is said to be purely catalytic; its presence modifies the form of the function E— Tq5 so as to obliterate the See also:

• RIDGE (a word. common to many Teutonic languages, meaning " back," whether of a man or an animal, cf. German Rucke)
• RIDGE, WILLIAM PETT (1864- )

291, seq.). Thus the striking new advance contained in the more modern work of J. See also:

• WILLARD, FRANCES ELIZABETH (1839–1898)

Another aspect of the matter will be developed below. A somewhat different See also:

• PROCEDURE (Fr. procedure, from Lat. procedere, to go for-ward)

34). Available Energy.—The same quantity 4), which Clausius named the entropy, arose in various ways in the early development of the subject, in the See also:

• TRAIN (M. Eng. trayn or trayne, derived through Fr. from Late Lat. trahinare, to drag, draw, Lat. trahere, cf. trail, trace, ultimately from the same source)

But we can obtain an intrinsically different and self-contained comparison of the available energies in a system in two different states at different temperatures, by ascertaining how much energy would be dissipated in each in a reduction to the same standard state of the system itself, at a standard temperature To. We have only to See also:

• REVERSE

The quantity µr is called by Willard Gibbs the potential of the corresponding substance of mass m,.; it may be defined as its marginal available energy per unit mass at the given temperature. If then a system involves in this way coexistent phases which remain permanently separate, the potentials of any constituent must be the same in all of them in which that constituent exists, for otherwise it would tend to pass from the phases in which its potential is higher to those in which it is lower. If the constituent is non-existent in any phase, its potential when in that phase would have to be higher than in the others in which it is actually present; but as the potential increases logarithmically when the See also:

• DENSITY (Lat. densus, thick)

The example above mentioned, of two coexistent phases liquid and vapour, indicates that there may thus be relations between the constitutions of the phases present in a chemical system which do not involve their total masses. These are developed in a very direct manner in Willard Gibbs's original procedure. In so far as attractions at a distance (a uniform force such as gravity being excepted) and capillary actions at the interfaces between the phases are inoperative, the fundamental equation (r) can be integrated. Increasing the volume k times, and all the masses to the same extent—in fact, placing alongside each other k identical systems at the same temperature and pressure—will increase el) and E in the same ratio k; thus E must be a homogeneous function of the first degree of the independent variables di, v, ml, . .., zn,,, and therefore by Euler's theorem relating to such functions E=Tpv+µimi+ .... +g,,mn• This integral equation merely expresses the additive character of the energies and entropies of adjacent portions of the system at uniform temperature, and thus depends only on the absence of sensible physical action directly across finite distances. If we form from it the expression for the complete differential BE, and subtract (I), there remains the relation o=SST—vap+m,Sµi+ .... } mnSµn. (2) This implies that in each phase the change of pressure depends on and is determined by the changes in T, µl, . . . µ„ alone; as we know beforehand that a physical property like pressure is an analytical function of the state of the system, it is therefore a function of these n+ i quantities. When they are all independently variable, the densities of the various constituents and of the entropy in the phase are expressed by the partial fluxions of p with respect to them: thus _—dp, mr_dp.

v dT v —dµ, But when, as in the case above referred to of chloride of ammonium gas existing partially dissociated along with its constituents, the masses are not independent, necessary linear relations, furnished by the laws of definite combining proportions, subsist between the partial fluxions, and the form of the function which expresses p is thus restricted, in a manner which is easily expressible in each special case. This proposition that the pressure in any phase is a function of the temperature and of the potentials of the independent constituents, thus appears as a consequence of Carnot's axiom combined with the energy principle and the absence of effective actions at a distance. It shows that at a given temperature and pressure the potentials are not all independent, that there is a necessary relation connecting them. This is the equation of stale or constitution of the phase, whose existence forms one mode of expression of Carnot's principle, and in which all the properties of the phase are involved and can thence be derived by simple differentiation. The Phase See also:

• RULE

Finally, when but one phase, say water, is present, both pressure and temperature can vary independently. The first example illustrates the case of systems, physical or chemical, in which there is only one possible state of equilibrium, forming a point of transition between different constitutions; in the second type each temperature has its own completely determined state of equilibrium; in other cases the constitution in the equilibrium state is indeterminate as regards the corresponding number of degrees of freedom. By aid of this phase rule of Gibbs the number of different chemical substances actually interacting in a given complex system can be determined from observation of the degree of spontaneous variation which it exhibits; the rule thus lies at the foundation of the modern subject of chemical equilibrium and continuous chemical change in mixtures or See also:

• ALLOYS (through the Fr. aloyer, from Lat. alligare, to combine)

They are the cases of mixtures of perfect gases, and of very dilute solutions. If, following Gibbs, we apply his equation (2) expressing the pressure in terms of the temperature and the potentials, to a very dilute solution of substances m2, m,, . . . M,, in a solvent substance m,, and vary the co-See also:

• ORDINATE

If there are v molecules in the unit mass, and N per unit volume, we have my = Nmv, each being 2 where v' is the number of molecules per unit mass in hydrogen; thus the free energy per See also:

• MOLECULE (from mod. Lat. molecula, the diminutive of moles, a mass)

This conception is akin to that of potential, except that it is given to us directly by our sense of heat. But if that were not so, we could still demonstrate, on the basis of Carnot's principle, that there is a definite function of the state of a body which must be the same for all of a See also:

• SERIES (a Latin word from serere, to join)

266-28o), which forms perhaps the most vivid and most direct procedure. The available energy per molecule of any kind, in a mixture of perfect gases in which there are N molecules of that kind per unit volume, has been found to be d+R'T logbN where R' is the universal physical constant connected with R above. This expression represents the marginal increase of available energy due to the introduction of one more molecule of that kind into the system as actually constituted. The same formula also applies, by what has already been stated, to sub-stances in dilute solution in any given solvent. In any isolated system in a mobile state of reaction or of internal dissociation, the condition of chemical equilibrium is that the available energy at constant temperature is a minimum, therefore that it is stationary, and slight change arising from fresh reaction would not sensibly alter it. Suppose that this reaction, per molecule affected by it, is equivalent to introducing n1 molecules of type NI, n2 of type N2, &c., into the system, nl, n2, ... being the See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

Thus as the constitution of the system changes with the temperature, we have dA dE d~ oT=dT-TdT—(0—0o) where sE =SH +-SW, OH =TS4, SH being heat and SW mechanical and chemical energy imparted to the system at constant temperature; hence d(dT`~' _ -4-00, so that A=E+Td( d_W) which is equivalent to d /A —W' E—W=—T'dT1 T ) This general formula, applied differentially, expresses the heat SE—SW absorbed by a reaction in terms of SA, the change produced by it in the available energy of the system, and of SW, the mechanical and See also:

• ELECTRICAL
• ELECTRICAL (or ELECTROSTATIC) MACHINE

The conditions that a specified new phase may become developed when two other given ones are brought into contact, i.e. that a chemical reaction may start at the interface, are thence formally expressed in terms of the surface tensions of the three transition layers and the pressures in the three phases. In the case of a thin See also:

• SOAP

In other topics the same restrictions on the scope of the simple statical theory of energy appear. From the ascertained behaviour in certain respects of gaseous media we are able to construct their characteristic equation, and correlate their remaining relations by means of its consequences. Part of the experimental knowledge required for this purpose is the values of the gas-constants, which prove to be the same for all nearly perfect gases. The doctrine of energetics by itself can give no See also:

• CLUE

This then looks like a real failure, or rather See also:

• LIMITATION, STATUTES OF

See also:

• CONNECTICUT

The theory of energetics, which puts a diminishing limit on the amount of energy available for mechanical purposes, is closely implicated in the discovery of natural radioactive substances by H. See also:

• BECQUEREL

See also:

• STRUTT, JEDEDIAH (1726-1797)