The KINETIC-MOLECULAR THEORY and ITS RELATION to HEAT PHENOMENA* JOHN A. TIMM Yale University, New Haven, Connecticut
A qualitative understanding of the kineticmolecular theory and its relation to heat phenomena is essential to genuine mastery of the pincifiles of elementary chemistry. Such an understanding can be readily im@rted to students of general chemistry. The effort exfiaded to this end i s repaid immediately i n greater achieuement i n the elementary course, and later by reason of the solid foundation thus laid for advanced study.
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HE molecules of a gas are perfectly elastic." I wonder how many of our students lose faith in the theoretical side of science when they are asked to accept this statement so contrary to their experience and repulsive to their common sense. Drop a tennis ball. Is its collision with the earth a perfectly elastic one? Does it, therefore, rise to the same height from which it fell? Never has there been a single instance of such behavior in the experience of any one of our students. Yet soon after they have been persuaded to accept the existence of molecules, which no human eye can ever see, we endow these nonentities with perfect elasticity. Here the splendid opportunity to remove the student's skepticism by explaining the nature of heat energy is neglected in the average general chemistry course. No chemistry teacher can ignore the importance of thermodynamics and of statistics to his science. If the general chemistry course is to serve as a faitl'introduction to the study of the science of chemistry so that its students may intelligently decide whether or not they desire to make this science their life-long study, it must lay the foundations for the courses which follow. Paradoxical though it may seem, there are many firstrate chemists today who have seldom balanced an oxidation-reduction equation or carried out a qualitative analysis since their undergraduate days hut who are constantly applying the equations of thermodynamics to solve extremely practical problems in our science. The application of both thermodynamics and statistics to chemistry was well begun long before the end of the nineteenth century, so that in this respect the general chemistry course, far from being up to date, is definitely mid-Victorian. The author is not urging any mathematical and, therefore, quantitative treatment of either
* Delivered before the Division of Chemical Education of the
A. C. S. at Cleveland, Ohio, -September 12, 1934, in the Symposium on Modernizing the Course in General Chemistry.
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statistics or thermodynamics in an elementary course. Perish the thought! Such treatment must come later. However, the implications which can he drawn from a qualitative understanding of the nature of heat energy and of its relation to other forms are many and of lively interest to the average elementary student. Such topics as the ultimate fate of all forms of energy, the efficiencyof heat engines, and the improbability of perpetual motion machines are of great economic significance. From a practical standpoint how is this material to be introduced? We may not have time to teach all of what follows, nor, indeed, may it he expedient to do so. However, it will do no harm to consider some of the possibilities. At least three postulates of the kinetic theory are important stepping-stones to a discussion of the nature of heat in particular and of energy in general. The uniform pressure of a gas is explained by the postulate that molecular motion is so random that on the average the number of molecules moving in one direction is the same as the number mo,ving in any other. Second, the constancy of the pressure of a gas maintained at a constant temperature in a certain volume suggests that the molecules are perfectly elastic, since no loss of kinetic energy is apparent in spite of their countless collisions. Finally, the fact that in a constant volume the pressure of a gas varies directly as the absolute temperature leads to the dehition of the latter as a measure of the translational kinetic energy of molecules. With these postulates in mind the discussion may be led easily to the nature of heat and its relation to other forms of energy. A history of the development of the concept of energy and of establishment of the law of its ronservation is interesting to. elementary students. The classic contributions of Count Rumford, Sir Humphry Davy, Joule, Lord Kelvin, and von Helmholtz have definite inspirational value. However, it is doubtful if time can be spared for this purpose. The fundamental nature of the various forms of energy must, nevertheless, he explained. The various forms of kinetic energy may be defined in terms of the motion of different degrees of subdivision of matter. Thus, mechanical energy is that of a moving state of matter, solid, liquid, or gaseous; heat energy, that of molecular motion; and electrical energy, that of moving electrons. Whenever energy is freed entirely of matter, it moves with a characteristic velocity through space and becomes radiant
energy. The various forms of potential energy are best related t o the three types of action-at-a-distance upon which they depend. These three types are gravitational, electrical, and magnetic. The fact that every two bodies in space tend to move toward each other is the well-known phenomenon, gravity. The cause of this tendency is unknown. Man likes to explain this action-at-a-distance by assuming that some force is pushing, or, perhaps, pulling the two bodies together. The agent which exerts the force of gravity has yet to give any independent evidence of its existence, so that in employing the concept of force to explain the gravitational tendency man is guilty of inventing a concept to satisfy some mental inclination to visualize the mechanism of the process. The tendency of electrically charged bodies to move toward or away from each other, depending upon whether their charges are unlike or like, is another familiar example of action-at-a-distance, as is the tendency of unlike poles of two magnets t o move together and of like poles to move apart. These three forces, gravitational, electrical, and magnetic, vary inversely as the square of the distance between the two bodies involved. Due t o the gravitational tendency, work must be done, or in other words energymust be expended, on two bodies when they are moved apart. This energy is absorbed by the two bodies as they are being separated. When they finally come to rest, .they possess energy due to their respective positions relative to each other. Such energy is called potential energy. The gain in potential energy by the bodies is exactly equal to the energy required to pull them apart. In a similar manner, potential energy is acquired when work is done against electrical and magnetic forces. The forces of attraction hetween molecules are partly gravitational, partly electrical, and partly magnetic. They make possible the possession of potential energy by the molecules in amounts which become greater when the molecules are moved apart andless when they come nearer together. An expanding gas absorbs heat energy, converting it into potential energy. FoP the same reason energy is absorbed when a liquid evaporates, since this process involves a separation of the evaporating molecules from their fellows. The heat absorbed in this way is the heat of vaporization. The reverse changes must, of course, liberate potential energy as one of the forms of kinetic energy. The student is now in a position t o consider the unique nature of heat. Of all fonns of kinetic energy, heat alone consists of unordered motion. The mechanical energy of the wind blowing against the sails of a ship or driving a windmill, the expansion of steam against the piston head of a steam engine, the energy of flowing water, that of a rotating engine fly-wheel or of electrons flowing through a wire is due in each case to directed motion. Heat, the energy of molecular motion, alone is unordered. At any instant within a gas a chaos of motion exists. Under standard conditions every cubic centimeter contains 27 million, million, million molecules moving a t average velocities of nearly a mile a
second. At a given temperature all freely moving molecules, regardless of kind, have the same average translational kinetic energy-the law of equipartition of energy. Since the kinetic energy of a moving particle varies as the product of its mass by its velocity squared, a t a given temperature the average* velocities of different kinds of molecules will vary as the square rwts of their masses-really another way of stating Graham's law of effusion. The average velocity of the oxygen molecule a t O°C. is 425 m. per second, whereas that of hydrogen, one-sixteenth as heavy, is four times as great. Each oxygen molecule on the average collides with its fellows several hundred thousand million times a second under standard conditions and moves an average distance of a hundred thousandth of a centimeter between collisions. This random motion results in a uniform distribution in space of molecular velocities and in the uniform pressure which the gas exerts on every surface exposed to it. That the pressure of a gas in a given volume and a t a constant temperature remains the same indefinitely is the best evidence that molecular kinetic energy is not converted into other forms by collisions between molecules. Such collisions are, therefore, between perfectly elastic bodies. They permit the only type of perpetual motion possible: the unordered motion of freely moving- particles. The kinetic theory has been extended to liquids, and here conditions below the surface are much the same as in gases. The molecules are more closely packed, their mean free path is much shorter, but within the liquid each molecule is free to move in the same unhampered way. Intermolecular forces of attraction between individual mol~culesare greater because of closer proximity, but these cancel out when the single molecule is uniformly surrounded by its fellows. At the surface conditions are unique since here the molecules are not uniformly surrounded and tend to move together; that is, toward the inside of the liquid, producing a surface tension. In this respect alone liquids differ essentially from gases. Now the law of equipartition of energy applies to all systems of freely moving particles. Hence a t the same temperature a water molecule in the liquid state has the same average translational kinetic energy as a molecule of gaseous hydrogen. In the solid state molecular motion for any distance in a straight line is out of the question, since the atoms or molecules occupy fixed points in a crystal lattice. However, even under such conditions the constituent particles vibrate a t these fixed points in the crystal structure in the unordered manner characteristic of molecular motion in gases and liquids. At this point it is desirable to illustrate with lecture experiments the type of motion characteristic of molecules, and the Brownian movement affords excellent
* More strictly the root-mean-square velocity; that is, the square root of the average of the velocity squares, since the average kinetic energy is proportional to the average of the squares of the velocities.
material for such experiments. The classical experiments of Jean Perrin should also be called to the student's attention. By a process of fractional centrifugalization he was able t o obtain colloidal suspensions of gamboge and gum mastic in water in which the suspended particles were of the same mass. By direct observation under an ultramicroscope he could determine their velocity, and hence calculate their kinetic energy. The results of his calculations were astounding. Particles, varying in mass from 60,000 to 1, he found not only had the same average kinetic energy but also that the latter was identical with the kinetic energy of gas molecules a t the same temperature. One of his largest particles was some one hundred thousand million times as heavy as the hydrogen moletruly cule. Yet. each had the same kinetic energyremarkable extension of the law of equipartitiou of energy. We now come to a consideration of temperature. The various thermometric scales were devised long before the true nature of heat energy was fully understood. All were defined in terms of the properties of one substance, water. The modem theory conceives of temperature as a measure of the translational kinetic energy of molecules. On this basis although there can he no upper limit to the temperature to which a substance may be heated, there must necessarily be a lower limit. There can be no temperature when molecular motion ceases. A body whose molecules have stopped moving is absolutely cold. This is the absolute zero on the true, or thermodynamic, scale. The most direct evidence we have of molecular motion is the pressure of gases. This pressure, therefore, is one of the most accurate means of measuring temperature. The absolute temperature scale has been defined in such a way that i t is directly proportional to the pressure which the perfect gas exerts in a constant volume. This, in turn, is proportional to the total translational kinetic energy of its molecules. For a given amount of gas the latter'depends on the average translational kinetic energy of thqindividual molecules. Hence the absolute temperature is a direct measure of the energy of translatory motion of molecules. In this defmition of temperature nothing is inferred as to the intensity of heat; that is, the quantity of heat energy per unit quantity of material. The hypothetical, ideal gas consists of molecules which are points in space between which there are forces neither of attraction nor repulsion. Such a gas would never liquefy and would obey the gas laws however low the temperature or high the pressure. Of the known gases helium approaches nearest t o this ideal. I n a constant volume gas-thermometer, the pressure of helium is the most accurate measure of the true temperature. The change in temperature of a substance is related t o the amount of heat it absorbs. For the ideal gas all of this heat goes to increasing the translational kinetic energy of its molecules, of which the temperature is a measure. We can easily calculate from the kinetic theory that
three calories of heat are necessary to raise the temperature of a mol of the ideal gas one degree a t constant volume. Monatomic gases like helium have molecular heats exactly equal to this theoretical value. All the heat supplied goes t o raising the translational kmetic energy; that is, the temperature. The molecular heat a t constant volume of gases like hydrogen, oxygen, and nitrogen, which are composed of diatomic molecules, is nearly five calories. Here only 3/s of the heat absorbed raises the temperature. The remainder is distributed within the molecules themselves. Here i t exists as the kinetic energy of the two atoms vibrating and rotating with respect to each other. As the complexity of the constituent molecules increases, that portion of the heat absorbed which raises the temperature decreases. Less than ' / 8 of the heat absorbed by the molecules of benzene vapor is used to raise the temperature. Furthermore, if these changes are allowed t o take place a t constant pressure, they will be accompanied by a volume increase, and a considerable portion of the heat supplied performs the work of expansion against the external atmospheric pressure and the internal forces of intermolecular attraction. Wken changes of state occur, relatively large amounts of heat are either absorbed or emitted a t constant temperature. In general, changes like evaporation and melting, which involve an increase in the average distance between the molecules, and absorb heat to-dothe work of separation against intermolecular forces, and, therefore, store it as potential energy. Conversely any change involving the closer approach of molecules liberates positional energy as the kmetic energy of heat. Such a discussion may serve as an introduction to a later,study of specific .. and latent heats. We are now in a position to consider the reason why all other forms of kinetic energy degrade eventually into heat. The mechanism of the conversion of mechanical energy into heat consists in a conversion of directed motion of the object as a whole into the uncoordinated motion of its constituent *molecules. A body of water a t rest in its container consists of millions upon millions of molecules, each of which is moving with an average kinetic energy which determines the temperature of the water. If, now, this water is allowed to flow through a siphon into another vessel, a certain amount of directed mechanical energy of the flowing water is superimposed on the uncoordinated thermal energy of the molecules. As the water flows through the siphon, friction develops between the water molecules and the walls of the tube and a portion of the directed mechanical energy of the body of water molecules as a whole is scrambled, loses its direction, and becomes heat. The rest of the mechanical energy is converted into heat when the water comes to rest in the lower vessel. The temperature of the water, the siphon tube, and the lower vessel will be raised, due t o the heat energy into which the mechanical energy of the falling water is changed. Whenever collisions occur between objects of visible size, the resulting impacts scramble a portion of the regimented molecular motion
of the colliding bodies and friction occurs. The kinetic law of thermodynamics, our old friend, the law of conenergy of a single molecule, however, is entirely heat servation of energy, does not deny the possibility of energy. When two molecules collide, no scrambling such machines. We may imagine a supply of water in of translational energy can occur and the collision must an elevated reservoir possessing a certain amount of be frictionless. Hence molecules are perfectly elastic. potential energy. I t could be allowed to flow through When the temperature of a body is greater than that a water-motor to a lower reservoir and in so doing its of its surroundings, part of its thermal energy may be energy would be transferred to the rotating paddleconverted into other forms. Heat usually passes spon- wheels of the motor. These in turn could pass the taneously from the hotter body into its surroundings energy on to a water-pump which would complete the until the temperature of the two is the same, but in cycle of pumping the water hack to the higher reserthis process no other form of energy is produced. How- voir. Nothing in the first law prohibits the perpetual ever, it may also be allowed to pass through a suitable operation of such a system, but the second law predicts machine in which the directed flow of thermal energy is its extreme improbability. For frictionless conversion converted into some other useful form of kinetic energy. of one form of energy into another is a practical imposTo utilize all the thermal energy of a body, its tempera- sibility and friction involves a destruction of useful ture would have to be reduced to absolute zero. No ordered motion. Thermal conduction soon adds engine has ever been devised which can do this. The heat developed by friction to the tremendous store of best an engine can do is the quantitative conversion useless thermal energy. This is the ultimate fate of into mechanical energy of the heat which is liberated all energy on this earth. when the temperature of a body is reduced to that of The future of all civilization on the earth lies in the its surroundings. If we consider a body cooling with- fate of its energy resources. For countless ages radiant out change of state from 100°to O°C., that is, from 373' energy from the sun has been stored by plants as poto 273'A., only 'Oo/an of the original thermal energy tential energy in the chemical compounds of their tisof the hot body may be converted into useful work. sues. Part of this energy is available to us in the form Furthermore, this could only be accomplished by a of coal, petroleum, and natural gas. Continually hypothetic engine working under perfect conditions. water is being pumped from sea-level to the mountainPractically no heat engine has ever approached this tops and the highlands by energy from the same vitalefficiency. The higher the initial temperature of the izing sun. These are the sources of energy which sciheated body and the cooler its surrou&mgs, the ence has developed as food for the machinery of civiligreater the efficiency with which its thermal energy can zation. In so far as water power is harnessed to do the be converted into mechanical energy by a heat engine. work of the world, the result is pure gain on the ecoFor this reason mercury boilers are much more e5cient nomic balance sheet of energy. But this power is not than those which depend on the thermal energy of steam. enough. We must draw on our capital supplies of coal, Once the temperature of an object is the same as that that priceless heritage of thk ages. Science has proved of its surroundings, the thermal energy which it still of inestimable value in conserving natural resources possesses cannot be made available for useful work. by pointing out more efficient methods of utilization. Such a process wonld involve bringing order out of But she has as yet developed no means of restoring the chaos. If some process could be devised whereby all energy which civilization must use. the molecules of a body could be made to move in one In conclusion may I quote from a little book bySoddy, direction only, then a quantitative conversion of ther- called "Matter and Energy".' I have found it of great mal into mechanical energy wonld result and the body value as collateral reading for elementary students as a whole wonld acquire mechanical energy equal in when the subject we have been discussing is studied. amount to the total kinetic energy of its molecules. Sooner or later, hut certainly not indefinitely later, nothing Smce all of its molecules wonld then be movina in one h o r n will remain to supplement the natural rate of supply of direction only, the body would be at absolute zero. enerw. save the prim& stom of atomic energy on the one and the waste heat of uniform temperature on the otherN~ one has ever been able to devise such a process, ahand state of things that might be aptly represented by the proverb Of course* there is the chance that, if left to . of the devil and the deep blue sea, so far as any existing knowledge themselves long enough, all the molecules might be goes. ~t is probable that the first of these alternatives is the found at some instant to be moving in the same direc- less hopeless, and that the problem of artificial transmutation tion, since their motion is entirely random. l-his will in the future come to be regarded, no longer in the light it was a few years ago, as an impossible chimera sunriving from the dischance is so remote, because of the billions of molecules creditable epoch in which the science of chemistry originated, in an object of any size, as to be, to say the least, ex- but as the final phase of the agelong conflict of interests between Nature and Man. Success would remove forever the ohvsical tremdv imorobable. . . mo. limit to the continuous advance of progress, and would endow it The'pos&,ility of the invention of a with a permanent significance which at present it does not postion machine has always intrigued M~~ sess. Failure, on the other hand, would mean a gradual future continue to inpeople have invested and relapse of the race into a more primitive condition, and the lass vest their good money in ~chemesto promote the manu- of much, if not most, of what distinguishes life today from that facture of such machines. No one who understands of our unscientific ancestors. the peculiar nature of heat and its relationship to other 'SoDDY, F,, and energy," Henry Halt and Company, forms of energy could ever be so gullible. The first New York City. 1912, p. 249.
