278 THE REALITIES OF MODERN SCIENCE 



or 3.33X10" 24 gram per molecule. For oxygen it is 

 32/2.016 times as large or 52.8 X 10~ 24 gram per molecule. 

 The root mean square velocity of a gaseous molecule 

 may be obtained without a knowledge of N by con- 

 sidering equation (2) of page 164. Thus 



p=Nmv 2 /3V = dv*/3 (4) 



where d is the density. Then v is the square root of 

 3p/d or 



v a = 0.921*; = 0.921 VZp/d (5) 



where v a is the average velocity. The factor, 0.921, is 

 to be obtained only by a mathematical analysis be- 

 yond the scope of this book. For hydrogen under 

 standard condition p = 1.013Xl0 6 dynes/sq.cm., and 

 d = 2.016/22410 g./c. c., hence v a = 169,200 cm./sec., that 

 is, of the order of one mile a second. 



The velocity of any other gas will be less than this, 

 being inversely as the square root of its molecular 

 weight. Oxygen will have an average molecular veloc- 

 ity, under the same conditions of temperature and 

 pressure, of one fourth this amount or 42,500 cm./sec. 

 If the temperature is not C. the velocity will be to 

 the velocity under standard conditions in the ratio of 

 the square roots of the absolute temperatures. Since 

 pressure is directly as density, the velocity will not 

 vary with the pressure. 



The mean free path of a gaseous molecule may be 

 obtained by measurements of its viscosity. We have 

 seen that a force is required to maintain a difference 

 in mass motion of two parallel layers of a gas because 

 of the collisions which occur between molecules of 

 originally different layers and hence of different mass 



