The above are completely general expressions of the general fundamental equation of thermodynamics.
Internal work or energy, positive or nega tive, is the work performed in changing the relative distances between molecules, atoms or corpuscles, or in causing variation of their rela tive velocities, and within the mass and out of reach of the human senses. In the fundamental equation, it is measured by dL.
External work is that performed by mass or molecule, by atom or corpuscle against outside resistances, as where steam expands, doing work upon a piston. As indicated by the above laws, it must do so by surrendering an equivalent quantity of heat-energy. This is dW.
Heat-energy, thermal or dynamic, is of the same nature and may be measured in either thermal or dynamic units, foot-pounds and kilo grammetres, or in British or metric thermal units or ((calories?' One B. T. U., expressed in thermal units, is 778 foot-pounds expressed in dynamic units; one metric unit, the calorie, is 3.96832 times as great as the British, or the B. T. U. is 0251996 of the metric unit. The en gineer often conducts his thermodynamic inves tigations in dynamic terms; the physicist and the chemist employ 'the thermal; the one often uses British, the other always adopts the metric. Where work is performed by an expanding fluid upon a moving piston, the total work, (pe pi)as; where a is the piston-area, and s is the space traversed by the piston; mean pressures cor responding to the external and the internal work being pe and pi while as = v, the volume traversed.
The Perfect Gas is a fluid within which no internal work is done with varying volumes and which may be defined by the equations, pv= aT ; a. In thermodynamic equations, the perfect gas has zero values of internal en ergy and work. T is absolute temperature, p and v the pressures and volumes at that tem perature of unit mass.
Vapors are fluids in which the internal energy and work may be large, both absolutely and relatively, with changing volumes. Inter nal cohesive forces are often not only sensible but very great, the internal latent heat, which simply measures the internal work when ex panding water into vapor of one atmosphere pressure, as an example, is the equipment of the work of elevation of the weight affected to a height of about 150 miles. These forces, however, as with the gases, do not prevent the free movement of molecules in any direction and to any extent; nor do they fix the volume and density of the substance.
Liquids are fluids in which the action of in ternal molecular forces gives stability of vol ume, but not of form, and the energies, internal and external, are thus limited to comparatively small ranges and to comparatively small values; while range and values are often enormously great when the liquid becomes vaporous, not withstanding rapid diminution of molecular at tractions.
Solids have stability, both of volume and of form; the ranges of internal forces and of ener gies are still more restricted than with liquids and their extent of action and their values are still less than in liquids. By accession of heat, all solids become at some definite point liquid, liquids become vapors and vapors, when °super heated,'" become gases. It is to be noted that, whenever a substance, of whatever class, alter nately expands and contracts through a fixed range of volume, whatever its temperature or the pressure, precisely the same amount of in ternal energy is lost andgained by variation of volume against or with the constant effort of the internal forces.
Cycle is, thermodynamically, an operation in which a working substance passes through a series of changes of pressure, volume and tem perature resulting in the final return of the sub stance to its initial physical state. In this operation, it is evident that the net change of in ternal energy is zero. This process is illustrated in heat-engines in which the working substance is confined within the working chamber and therein passes through repeated cycles with repetition of the kinematic cycle of the machine itself. Obviously, also, where a working fluid traverses a cycle, the presence or the absence of the quantity of internal energy becomes a mat ter of no importance when we seek only to de termine the quantity of permanent thermo dynamic transformation. The magnitude and effect of internal forces and energies have no influence upon the efficiency of transformation; but they have importance as affecting the rela tions of pressure, volume and temperature and the magnitude of the working cylinder and of the heat-engine itself. In the highest boiler pressures now usual, these forces are about 10 times the gauge pressure. At atmospheric ex ternal pressure, they amount to 13 atmospheres. These pressures cannot be measured by any gauge, but may be readily computed with pre cision from easily ascertainable data; they are perfectly well known, as are the specific volumes of the fluid, which are very difficult, but not impossible, of direct measurement.