Complete Text (Part 7)

by ice makers, much better results may be obtained; this is, to use the steam direct from the boiler and the exhaust steam from the engine, to make from filtered water other steam, from which the water for ice making is obtained. This steam is not contaminated by the constantly accumulating filth in the boiler, nor has it been in contact with the oil used in the engine,and con- sequently, with suitable provision to prevent exposure to the air, water for ice making can be obtained as nearly pure as it is possible to make it. The cost of this last named method of distillation would, it is believed, compare favorably with the method in general use. There are makers of suitable apparatus for this improved method who will guarantee to give fourteen tons of distilled water with one ton of coal. The first cost of the apparatus may be something mote, but the manipulation is much less, and the quality of the water is superior in every respect to that ob- tained by the usual methods. To those who believe that the time is coming, and is not far distant, when artificial ice will supplant natural ice in every household, any information relating to its purity will be of interest, and it is for these persons that this paper is written. —W. 0. Campbell, receiver of the Stone Lake Ice Co., Hamilton, Ohio, has been directed by the court to sell all property of the company at auction. JULY, 193. {Reprint from Tueory ov Heat.! THE THERMODYNAMIC MODEL. THE RESEARCHES OF PROF. J. WILLARD GIBBS PN THERMODYNAMICS RESULTS OF STUDIES LITTLE KNOWN BY AMERICANS — ERMODYNAMIC PROPERTIES OF A SUISTANCE. Na late issue of Ick anp Rerriceration we had oc- ] casion to refer to the German translation of the ther- modynamic researches by Prof. J. Willard Gibbs, of Yale College, which mark so important a step in the progress of this science, and which are so little known among his countrymen. One of the most interesting chapters of Mr. Gibbs’ studies relates to an original and exceedingly valuable method of studying the properties, and more especially the thermodynamic properties of a substance by means of a surface and model; and we here- with reprint from J. Clerk Maxwell’s work, ‘‘ Theory of Heat,” some further details of this interesting topic, as follows: According to this method, the volume, entropy and energy of the body in a given state are represented by the three rectangular co-ordinates of a point in the sur- face, and this point on the surface is said to correspond to the given state of the body. We shall suppose the volume measured toward the east from the meridian plane corresponding to no volume, the entropy measured toward the north froma vertical plane perpendicular to the meridian, whose position is entirely arbitrary, and the energy, measured downward from the horizontal plane of no energy the position of which may be considered as arbitrary, because we cannot measure the whole energy existing in the body. The section of this surface by a vertical plane per- pendicular to the meridian represents the relation be- tween volume and energy when the entropy is constant, that is, when no hcat enters or leaves the body. If the pressure is positive, then the body, by ex- panding, would do work against external resistance, and its intrinsic energy would diminish. The rate at which the energy diminishes as the volume increases is repre- sented by the tangent of the angle which the curve of section makes with the horizon. The pressure is therefore represented by the tangent of the angle of slope of the curve of section. The press- ure is positive when the curve slopes downward toward the west. When the slope of the curve is toward the east the corresponding pressure is negative. A tension or negative pressure cannot exist in a gas. It may, however, exist in a liquid, such as mercury. Thus, if a barometer tube is well filled with clean mer- cury, and then placed in a vertical position, with its closed end uppermost the mercury sometimes does not fallin the tube to the point corresponding to the atmos- pheric pressure, but remains suspended in the tube, so as to fill it completely. The pressure in this case is negative in that part of the mercury which is above the level of the ordinary barometic column. In solid bodies, as we know, tensions of consider- able magnitude may exist. Hence in our thermodynamic model the pressure of the substance is indicated by the tangent of the slope of the curve of constant entropy, and is reckoned pos- itive when the energy diminishes as the volume in- creases. «. ICE .. AND .. REFRIGERATION .:. at The section of the surface by a vertical plane par- allel to the meridian is a curve of constant volume. Ia this curve the temperature is represented by the rate at which the energy increases as the entropy increases, that is to say, by the tangent of the slope of the curve. Since the temperature, reckoned from absolute zero, is an essentially positive quantity, the curve of constant volume must be such that the entropy and energy al- ways increase together. To ascertain the pressure and temperature of the substance in a given state, we may draw a tangent plane to a corresponding point of the surface. The normal to this plane through the origin will cut a horizontal plane at unit of distance above the origin at a point whose co-ordinates represent the pressure and temperature, the pressure being represented by the co- ordinate drawn toward the west, and the temperature by the co-ordinate drawn toward the north. The pressure and temperature are thus represented by the direction of this normal, and if, at any two points of the surface, the directions of the normal are parallel, then in the two states of the substance cor- responding to these two points the pressure and tem- perature must be the same. If we wish to trace out on a model of the surface a series of lines of equal pressure, we have only to place it in the sunshine and to turn it so that the sun's rays are parallel to the plane of volume and energy, and make an angle with the line of volume whose tangent is proportional to the pressure. Then, if we trace on the surface the boundary of light and shadow, the pressure at all points of this line will be the same. In like manner, if we place the model so that the sun’s rays are parallel to the plane of entropy and energy, the boundary of light and shadow will be a line such that the temperature is the same at every point, and proportional to the tangent of the angle which the sun's rays make with the line of entropy. In this way we may trace out on the model two series of lines; lines of equal pressure, which Professor Gibbs calls Isopiestics; and lines of equal temperature, or Isothermals. Besides these we may trace the three systems of plane sections parallel to the co-ordinate planes, the iso- metrics, or lines of equal volume, the isentropics or lines of equal entropy,which we formerly called,after Rankine, adiabatics, and the isenergics or lines of equal energy The network formed by these five systems of lines will form a complete representation of the relations be- tween the five quantities, volume, entropy, energy, press- ure and temperature, for all states of the body. The body itself need not be homogeneous either in chemical nature or in physical state. All that is nec- essary is that the whole should be at the same pressure and the same temperature. By means of this model Professor Gibbs has solved several important problems relating to the thermody- namic relations between two portions of a substance, in different physical states, but at the same pressure and temperature. Let a substance be capable of existing in two differ- ent states, say liquid and gaseous, at the same tem- perature and pressure. We wish to determine whether the substance will tend of itself to pass from one of these states to the other. 22 «. ICE .. AND .. REFRIGERATION .°. JULY, 1893. Let the substance be placed in a cylinder, under a piston, and surrounded by a medium at the given tem- perature and pressure, the extent of this medium being so great that its pressure and temperature are not sensibly altered by the changes ot volume of the working sub- stance, or by the heat which that body gives out or takes in. The two physical states which are to be compared are represented by two points on the surface of the model; and since the pressure and temperature are the same, the tangent planes at these points are either coin- cident or parallel. The surface representing the thermodynamic prop- erties of the surrounding medium must be supposed to be constructed on a scale proportional to the amount of this medium; and as we assume that there is a very great mass of this medium, the scale of the surface will be so great that we may regard the portion of the surface with which we have to do as sensibly plane; and since its pressure and temperature are those of the working substance in the given state, this plane surface is par- allel to the tangent plane at the given point ze of the surface of the Le model. 3a Q Let ABC be three points of the model at which the _ tangent planes are parallel, the energy being reckoned down- ward. Let Aa’ abe the tangent plane at A,and let usconsider it as part of the model representing the external me- dium, this model being so placed that volume, entropy and energy are reckoned in the opposite directions from those in the model of the working substance. Now let us suppose the substance to pass from the state A to the state B, passing through the series of states represented by the points on the isothermal line joining the points of equal temperature A and B. Then since the working substance and the external medium are always at the same temperature, the en- tropy lost by the one is equal to that gained by the other. Also the one gains in volume what is lost by the other. Hence, during the passage of the working substance from the state A to the state B, thestate of the external medium is always represented by a point in the tangent plane in the same vertical line as the point representing the state of the working substance. For the same horizontal motion which represents a gain of volume or entropy of the one substance repre- sents an equal loss of volume or entropy in the other. Hence, when the state of the working substance is represented by the point B, that of the external medium will be represented by the point a, where the vertical line through B meets the tangent plane through A. Now the energy is reckoned downward for the work- ing substance and upward for the external medium. Hence, drawing A K horizontal, K B represents the gain in energy of the working substance, and K a@ the loss of the external medium. The line B a, or the vertical height of the tangent plane above the point B, represents the gain of energy in the whole system, consisting of the working sub- stance and the external medium, daring the passage from the state A to the state B. But the energy of the system can be increased only by doing work on it. But if the system can of itself pass from one state to another, the work required to produce the correspond- ing changes of configuration must be drawn from the energy of the system, and the energy must therefore diminish. The fact, therefore, that in the case before us the energy increases, shows that the passage from the state A to the state B in presence of a medium of constant temperature and pressure, cannot be effected without the expenditure of work by some external agent. The working substance, therefore, cannot of itself pass from the state A to the state B, if B lies éc/ow the plane which touches the surface at A. We have supposed the substance to pass from A to B bya process during which it is always at the same temperature as the external medium. In this case the entropy of the system remains constant. If, however, the communication of heat between the substances occurs when they are not at the same tem- perature, the entropy of the system will increase; and if in the figure the gain of entropy of the working sub- stance is represented by the horizontal component of AB, the loss of entropy of the external medium will be represented by a smaller quantity, such as the horizontal component A a’. Hence a’ will be to the left of a, and therefore higher. The gain of entropy of the system will therefore be represented by the horizontal part of aa Now since temperature is essentially positive, a gain of entropy at a given volume always implies a gain of energy. Hence the gain of energy is greater when there is a gain of entropy than when the entropy remains con- stant. There is, therefore, no method by which the change from A to B can be effected without a gain of energy, and this implies the expenditure of work by an external agent. If, therefore, the tangent plane at A is everywhere above the thermodynamic surface, the condition of the working substance represented by the point A is essentially stable, and the substance cannot of itself pass into any other state while exposed to the same external influences of pressure and temperature. This will be the case if the surface is convexo-convex upward. If, on the other hand, the surface, at the point B, is either concave upward in all directions, or concave in one direction and convex in another, it will be possible to draw on the surface a line from the point of contact lying entirely above the tangent plane, and therefore representing a series of states through which the sub- stance can pass of itself. In this case the point of contact represents a state of the substance which, if physically possible for an instant, is essentially unstable, and cannot be per- manent. There is a third case, however, in which the surface, as at the point C, is convexo-convex, so that a line drawn on the surface from the point of contact must lie below the tangent plane; but the tangent plane, if pro- duced far enough, cuts the surface at C, so that the point A lies above the tangent plane. In this case the sub- JULY, 1. stance cannot pass through any continuous series of states from C to A, because any line drawn on the sur- face from C to A begins by dipping below the tangent plane. But if a quantity, however small, of the sub- stance in the state Ais in physical contact with the rest of the substance in the state C, minute portions will pass at once from the state C to the state A without passing through the intermediate states. The energy set at liberty by this transformation will accelerate the subsequent rate of transformation, so that the process will be of the nature of an explosion. Instances of such a process occur when a liquid not in presence of its vapor is heated above its boiling point, and also when a liquid is cooled below its freezing point, or when a solu supersaturated. In the first of these cases the contact of the small- est quantity of vapor will produce an explosive evapora- tion; in the second, the contact of ice will produce ex- plosive freezing; in the third, a crystal of the salt will produce explosive crystallization; and in the fourth, a bubble of any gas will produce explosive effervescence. Finally, when the tangent plane touches the surface at twoor more points, and is above the surface every- ion of a salt, or of a gas, becomes where else, portions of the substance in states cor- responding to the points of contact can exist in presence ofeach other, and the substance can pass freely from one state to another in either direction. The state of the whole body when part is in one physical state and part in another is represented by a point in the straight line joining the center of gravity of two masses equal respectively to the masses of the sub- stance in the two states, and placed at the points of the model corresponding to these states. Hence, in addition to the surface already considered, which we may call the primitive surface, and which represents the properties of the substance when homo- gencous, all the points of the line joining the two points of contact of the same tangent plane belong to a secondary surface, which represents the properties of the substance when part is in one state and part in another. To trace out this secondary surface we may suppose the doubly tangent plane to be made to roll upon the surface, always touching it in two points called the node- couple. The two points of contact will thus trace out two curves such that a point in the one corresponds to a point in the other. These two curves are called in geometry the node-couple curves. The secondary surface is generated by a line which moves so as always to join corresponding points of con- tact. Itis adevelopable surface, being the envelope of the rolling tangent plane. To construct it, spread a film of grease on a sheet