absorbed carbon dioxide gas at a high pressure, and when the bottle is opened the excess gas is evolved, and gives rise to the so-called sparkle of the liquid.

Metals such as silver and gold are capable, when in the molten condition, of absorbing gas from the air, just as other liquids; this gas being evolved when the metal solidifies.

Some metals, notably palladium, are able to absorb very large volumes of hydrogen, even when in the solid state. Thus if a slip of palladium is used as the negative pole in the electrolysis (§ 539) of a dilute solution of sulphuric acid, it will absorb about 900 times its own volume of hydrogen gas. Gases absorbed by solids are said to be occluded.

Almost all solid bodies possess the power of condensing gases on their surface, so that after being surrounded for some time by a gas, a solid becomes coated on the outside with a layer of this condensed gas, which cannot be immediately removed by merely placing the solid under the receiver of an air-pump and producing a vacuum. In order to completely remove this gaseous coating, it is necessary to heat the solid while it is in a vacuum, or to rub the surface with alcohol, or some fine powder, such as tripoli. The amount of gas which can in this way be occluded depending on the surface of the solid exposed, very porous bodies, such as wood-charcoal and platinum-black (¿.e. finely divided platinum obtained by heating platinic chloride), in which the surface bears a very large ratio to the mass of the body, are able to occlude comparatively large quantities of some gases. Thus freshly heated (in order to free it of occluded air) box-charcoal will occlude about ninety times its volume of ammonia gas.

141*. Kinetic Theory of Gases.-The phenomena of diffusion, in which a heavy gas will move upwards and mix with a lighter gas placed above, and this lighter gas will move down, show that, although such amounts of the gas as we are able to see, and particles of dust suspended in the gas appear at rest, yet there must be some kind of movement going on continuously within a mass of gas. We have seen that the most probable theory of the constitution of matter is to suppose it built up of fine particles or molecules. The kinetic theory of gases supposes that in a gas these molecules are endowed with a motion of translation, and that the spaces between adjacent molecules are fairly great compared with the size of the molecules. We may, as a first approximation, consider that the molecules are hard, elastic spheres, each molecule having a definite mass, and that a gas consists of an enormous number of these small spheres moving about in all directions with different velocities. During its movement each molecule will occasionally collide with another molecule, the two rebounding after collision like two billiard-balls; also some of the molecules will be continually striking the walls of the vessel containing the gas, and rebounding from them. In the intervals between its impacts with other molecules, or with the

walls, each molecule will travel in a straight line, so that the path of a molecule consists of a zigzag line. On account of their frequent collisions, the velocities of the different molecules must vary considerably, as also the velocity of any given molecule at different times. Hence, in investigating the properties of gases according to this theory, we have to adopt what is called the statistical method. In this method we do not consider the behaviour of one particular molecule, but we take such a large number of molecules into consideration that, although the velocities of individual molecules may vary considerably, the mean velocity of all the molecules considered at any moment will be the same as the mean velocity of the same molecules, say one second later, or will be the same as the mean velocity of an equal number of other molecules of the same gas taken under the same conditions of temperature, pressure, &c. As an illustration of such a method, suppose cloth had to be bought to clothe an army of a million men, then, although the clothes made would be of many sizes, it is certain that the quantity of cloth used from year to year for this purpose would be the same, and we could calculate what is the quantity of cloth required to clothe the average-sized soldier. Instead, therefore, of attempting to allow for the various velocities of the different molecules, we shall suppose that they all move with the mean of their actual velocities. In the same way the length of the path traversed by each molecule between successive collisions varies greatly from time to time, but under given conditions the mean length of the path between successive collisions, or the mean free path, as it is called, will for any large number of molecules be the same, under similar conditions.

142*. Pressure Exerted by a Gas.-Suppose that a molecule of mass moving with a speed limpinges at right angles on a solid surface, then it will, if it is perfectly elastic, rebound with a speed V, but in the opposite direction. The change in momentum of the molecule due to the impact will therefore be 2m V. Hence, by § 60, the impulse of the blow on the surface is 2m V. Suppose now we have a certain mass of a gas enclosed in an envelope, which for simplicity we may take to be a cube having each edge one centimetre long. The molecules in this vessel will be moving in all directions, but we may resolve the velocity of each molecule along three directions parallel to the mutually perpendicular edges of the cube; or, what comes to the same thing, if the number of molecules is very great, we may suppose that one-third of the total number of molecules are moving parallel to each of these three edges with the mean velocity V. Under these circumstances, the molecules of each group are moving parallel to four faces of the cube, and therefore will not impinge on them: they will only impinge on the two faces which are at right angles to their direction of motion. If we consider one molecule of one of these groups moving with the velocity 1', then the interval between two consecutive impacts of this molecule on one of the

faces will be the time taken by this molecule to travel to the opposite face of the cube and back again, that is, through a distance of two centimetres. Hence the interval between two consecutive impacts on the face will be 2/V, and there will be 2 impacts on the face by this molecule in each second. The impulse acting on the face due to each impact being 2m V, the total impulse during a second will be mV2, which is what would be produced by the action of a continuous force m V2, since the impulse of this force, if it acted for one second, would be m√2 × 1. If the total number of molecules per cubic centimetre at the given pressure, &c., is N, then since N/3 molecules may be considered as moving parallel to the one considered above, the total force acting on the face will be }NmV2. Since this force acts on unit area, if p is the pressure which the gas exerts on the containing wall, then

p=1NmV2

Now, since there are by supposition / molecules in the cubic centimetre, and the mass of each molecule is m, the total mass of the gas is mN, but the mass of unit volume of a body is the density; hence, if p is the density of the gas,

or

p = } p V2, p/p = V2/3.

Now according to Boyle's law pv constant, if v is the volume of a given mass of gas. But the density of the gas is equal to M/v, or v=M/p, so that for a given mass of gas the volume is inversely proportional to the density, and Boyle's law may be written

pp=constant.

Hence we see that, if Boyle's law holds, the mean velocity of the molecules Vis constant.

From the equation =

the value of can be calculated if we

know the density of a gas at any given pressure. Since the value of V is inversely proportional to the square root of the density, this result enables us to see why it is that the rate of diffusion of a gas is inversely as the square root of the density.

In the following table the values of I, at a temperature of o° C., are given for some gases :-

143*. Avogadro's Law. If we have two gases under the same pressure, and at the same temperature, N1 being the number of mole

cules per unit volume of one gas, m1 the mass of each molecule, and V1 the mean velocity of translation of the molecule; N2, m, and V, being the corresponding quantities for the other gas. Then, since the pressure is the same in each gas, we have, from the result obtained in the previous section,

Now mV is the kinetic energy of one of the molecules of the first gas when it is moving with the mean velocity. The mean kinetic energy of the molecules depends on the temperature, as we shall see later on. Also, if two gases are at the same temperature, the mean value of the molecular kinetic energy must be the same, for otherwise, when they are mixed, since now by collisions between the molecules the kinetic energy would become equalised, the temperature would alter. Thus the mean kinetic energy being the same for the gases, if the temperature is the same, we have

Combining this equation with equation (1) above, we get

N1 = N

or, under the same condition of pressure and temperature, equal volumes of all gases contain an equal number of molecules. This law was enunciated by Avogadro, who was led to it by purely chemical considerations.

The effect of temperature on the movements of the molecules of a gas will be considered in the section on Heat. Space and the scope of this book will not allow of our pursuing the subject of the kinetic theory of gases any further, and we must refer readers for further information on the subject to Clerk Maxwell's "Theory of Heat," or Risteen's "Molecules and Molecular Theory."

CHAPTER XVII

PROPERTIES OF LIQUIDS

144. Equilibrium of a Liquid at Rest.-In the case of a liquid at rest under the influence of gravity the free surface must be horizontal. If it were inclined to the horizon, then the weight of a particle P (Fig. 112) of the liquid at the surface would have a component parallel to the surface of the liquid. Since the surface is everywhere

at the same pressure, there would be nothing in the nature of a hydrostatic pressure to resist this force, and as the liquid itself would offer no resistance, the particle P would move along the surface, and hence the liquid would not be at rest.

FIG. 112

Although a comparatively small surface of a liquid is for all practical purposes plane, it is not absolutely so, and when dealing with large surfaces, this departure from planeness becomes appreciable. The condition that the particle P (Fig. 112) should be at rest is that the line of action of the attraction of gravity on P should be normal to the surface at P. Hence the surface of a

B

A

FIG. 113.

E

liquid is always normal to the radius of the earth at the point considered, and therefore forms part of a sphere having the earth's radius as radius. The fact that the surface of a liquid is always horizontal is made use of in the spirit-level. This consists essentially of a glass tube ABC (Fig. 113), which is slightly bent, and fitted, with the convex surface upwards, D in a frame DE. This tube is closed at either end, and is filled with alcohol1 except for a bubble of air B, which is left in. This bubble constitutes the only free surface of the liquid, and it always sets itself at the highest point of the curved tube. Hence, if the tube is fixed in the frame in such a way that when the lower surface of the frame is horizontal the highest point of the bent tube is opposite a fixed mark on the top of the tube, then, whenever the bubble is opposite this mark, the lower surface of the stand will be horizontal. If one end, say E, is tilted up, then the marked point of the tube is no longer the highest, and the bubble moves towards E. 1 Alcohol is used on account of its extreme mobility.