THE KINETIC THEORY OF MATTER. 1S7 



For nitrogen we must divide by Vl4, and 

 V = 49000 nearly, 

 U = 45400 nearly. 



If we assume that V 2 is the same for a given temperature, whatever 

 the pressure and this is the natural assumption, seeing that the 

 temperature of a gas only alters very slightly if its volume is changed 



) 



without doing external work then at once we have = constant for a 



given temperature, or Boyle's Law follows. 



It must, however, be observed that our investigation is based on the 

 assumption that the collisions of each molecule take up only a negligible 

 fraction of the time. If through a crowding up of the molecules this 

 ceases to be true, we can no longer- assume that a molecule of type 

 having velocity u perpendicular to a face of the cube will travel u cm. 

 per sec., for some of the time will be wasted in collisions. The more 

 time thus wasted the fewer returns will the molecules make to the wall, 

 and it will contribute to the pressure a less amount than that calculated. 

 But we shall return to this point later and consider how we may obtain 

 a more correct relation between pressure and volume than that given by 

 Boyle's Law. 



Mixture Of Gases. Maxwell showed that in a mixture of gases 

 the different kinds of molecules will exchange energy with each other till 

 the average kinetic energy of a single molecule of each kind is the same, 

 and that this is the condition for steadiness of distribution. 



Now, assuming this, suppose that we have equal volumes of two 

 different gases at equal pressures and of densities p 1 and /a 2 , the equality 

 of pressure gives 



If the two gases be allowed to mix there is no work done externally, 

 and no change of temperature, and the pressure remains the same. 

 This is accounted for if we suppose that the velocity of mean square of 

 each gas is the same after mixture as before. 



But if m^ is the mass of a molecule of the first gas, and m 2 that of a 

 molecule of the second gas, Maxwell's investigation shows that 



or _ 



ra x ra 2 



But if Nj N" 2 be the numbers of the two kinds of molecules in unit 

 volume before mixture, 



whence Nj = N 2 



or two different gases at the same temperature and pressure contain the 

 same number of molecules per c.c. This is known as Avogadro's Law. 



Relation between V and Temperature. If we take a volume of 



