76 



KNOWLEDGE 



[ApBrL 1,1893. 



used by scientific men. Let there be 1 gramme of oxygen 

 at 0"' C. and at a pressure of 76 c. m. of mercury. Using 

 the above expression for the pressure j> = ^ D V -, or 



V= -y^ and considering that the density of oxygen is 1"1 

 with reference to air, and a cubic centimetre of air weighs 

 •001293 grammes, the mass of unit volume {i.f. 1 

 cubic centimetre) of oxygen is 1-1 x •001293 = -00142 

 grammes. The pressure of the atmosphere being equal to 

 that of a column of mercury 76 c. m. in length, and the 

 density of mercury being 18^59C, the pressure of the 

 atmosphere equals 76 x 18596 grammes per square cm. 

 Multiplying this number by 981 (the value of the intensity 

 of gravity in the centimetre — gramme — second system) in 

 order to express the value in absolute imits, we have finally 

 for the velocity of oxygen molecules : — 



V 



V 



3 X 1033 X 981 

 •00142 



= 46250 cm. per second 



nearly. As 1 cm. = 2^34 inches, this velocity is rather 

 over a quarter of a mile per second. The velocity of the 

 hydrogen molecules we saw to be about GOOO feet per 

 second, or more than a mile per second. Thus the par- 

 ticles of hydrogen are four times more rapid than those of 

 the denser gas oxygen. Now it is found experimentally 

 that the rates of diffusion of gases through porous mem- 

 branes vary inversely as the square roots of their densities. 

 Oxygen is sixteen times as dense as hydrogen, and its 

 particles diffuse four times more slowly. So the rates of 

 diffusion of gases are proportional to the velocities of the 

 particles of the gas. This is just what we would expect if 

 the kinetic hypothesis was a true explanation of what 

 actually takes place. 



If a heavy gas, such as carbonic acid, be placed in a 

 vessel, and above it a layer of some lighter gas, such as 

 air or hydrogen, it is well kuo-n-n that after a lapse of time 

 the two gases will be found thoroughly mixed — any cubic 

 inch of the space contains the same relative amounts of the 

 two gases ; part of the heavy gas below has risen against 

 gravity and the lighter one has descended. The explana- 

 tion of this is that the particles of both the gases are in 

 constant motion, and in course of time, after being retarded 

 by a succession of collisions, they spread themselves 

 throughout the whole enclosing space. When the mixture 

 is complete the motion, of course, does not cease, but 

 henceforth it can produce no change on the average con- 

 stitution of the gaseous mixture. We do not require to go 

 farther than to the case of our atmosphere for a perfect 

 example of a uniform mixture of gases. The almost 

 unvarying ratio of the oxygen to the nitrogen is due to 

 this rapid motion of the gaseous particles from place to 

 place, coupled with the fact of the enormous number of 

 these particles. 



The well-known law relating to the pressure and volume 

 of gases, named after its discoverer, ]!oyle, is readily 

 deduced from the kinetic theory. Suppose a mass of gas 

 to be shut into a cylinder, the top of this cylinder being 

 formed by an air-tight piston. Push in the piston till the 

 gas is compressed and occupies only half its original 

 volume. If we may suppose that the average velocity of 

 the gas particles has not been altered, then the number of 

 impacts per second on the ends of the cylinder has been 

 doubled, for the lengths of the paths of these particles, 

 parallel to the axis of the cylinder, are now only half what 

 they were before, while the speed of the particles has not 

 changed. Moreover, the number of impacts on the curved 

 surface of the cylinder are as frequent and strong as 

 formerly, only they are now spread over only half the 

 former surface. Thus over all the area of the walls 



of the cylinder the pressure has doubled, owing to the 

 halving of the volume occupied by the gas. Thus the 

 pressure varies inversely as the volume, which ia Boyle's 

 law. 



But this law may also be expressed by saying that the 

 pressure and the density of a gas vary in the same 

 proportion. For the density of a body being the quantity 

 of matter in a unit of volume, when the volume of the gas 

 is halved its density is doubled, and the density varies 

 inversely as the volume. Now we saw above that 

 p = ^Dv- when // = the pressure, D the density, and c- the 

 square of the average velocity of the molecules. This 

 equation shows that when the density D varies the pressure 

 p must vary proportiovially. V= varies with the tempera- 

 ture, because the temperature of a gas depends on the 

 speed possessed by its particles — whatever the density of 

 the gas the speed of the particles is the same at the same 

 temperature. But as long as we consider the same gas at 

 an unvarying temperature the equation y; = i D V - holds 

 good. 



Gases expand ^rd of their volume at 0° C. (freezing 

 point) for every rise of 1° C. in temperatiire. Thus if a 

 gas is cooled down below freezing point at - ^273° C, it 

 would have contracted so as to occupy no volume. We 

 cannot imagine this happening, but the volume then 

 occupied by the gas, if we suppose this temperature 

 attainable, must be exceedingly small, probably approaching 

 the space actually occupied by the molecules themselves. 

 We cannot conceive a lower temperature than this to be 

 possible. This point in the Centigrade scale is therefore 

 called the zero of absolute temperature, and the existence 

 of this absolute zero is proved by more strict reasoning from 

 the principles of thermo-dynamics. 



The equation above for the pressure may be written : — 

 P '■=* v^ 



The product /) x r is proportional to the absolute tem- 

 perature as measured by a thermometer containing the 

 special gas we may be considering. Thus V', or the mean 

 square of the velocity of translation of the gaseous molecules, 

 is proportional to the absolute temperature, i.e. to the 

 temperature measured from the point 273° C. below 

 freezing point. On this " absolute " scale the temperature 

 of melting ice will thus be 273°. 



If M ^ the mass of a single gas molecule and N = the 

 number of molecules in an enclosure whose volume = unity 

 the mass of the contained gas is M x N. Now /i = g- D V- 

 -i-M N V-. 



Neither M nor N need be known, but the product of these 

 two quantities we are acquainted with, for it is the mass in 

 unit volume, /.'■. the density of the gas. Above we saw 

 that Ml Y, - : Mo V/ when there is no passage of heat from 

 one gas to another, that is, when they are at the same 

 temperature, as in general /) ^ ; i M N V-. 



Therefore for each gas this holds true ; thus /j, = -J MjNj Vj- 

 and /'o=-3- Mo No Vo' where y/^ and pa represent the respective 

 pressures of the two gases. When the two gases have the 

 same pressure M, Nj V,- = Mo M„ V„^. When they have 

 the same temperature M, Vj- = Mo V,-. Dividing the first 

 of these last two equations by the second, we get Nj = N„ ; 

 that is, when there arc two gases, each possessing the same 

 pressure and temperature, then the number of molecules 

 in the unit volume of these gases is the same in each 

 case. 



This deduction from the kinetic theory has been shown 

 to be true from reasoning based on chemical grounds. It 

 is of great importance, and is known as Avogadro's law. 

 Its deduction independently in this simple way from the 

 mechanical theory of gases, points to this theory being 



