112 Physical Properties [OH. vi 



Charles Law. 



129. Again, replacing v by in equation (267), we obtain the pressure 



JYt 



in the form 



p = - ' pT ................................. (268), 



m r 



or, since Nm = pfl, 



pfl = RNT .............................. (269). 



Equation (268) contains the combined laws of Boyle and Charles : 

 When the temperature of a gas is kept constant, the pressure varies as the 



density, and when the density is kept constant, the pressure varies as the 



temperature. 



Numerical estimate of velocities. 



130. From equation (263), 



p = pu*, 



we can calculate the value of i? for any gas with considerable accuracy. If 

 we write c 2 = tt 2 + 1> 2 + w 2 , and (7 2 = c 2 , then 



u* = tf=^v* = ^(u?-\- v 2 + w 2 ) = c 2 = ^(7 2 ............... (270). 



The quantity which is of the greatest physical interest, and which is 

 usually tabulated, is G. The significance of this quantity is that the pressure 

 is the same as if all the molecules were moving with a uniform velocity G. 

 We have 



.(271), 



m 



hence G is proportional to the square root of the absolute temperature, and 

 inversely proportional to the square root of the molecular weight of the gas 

 in question. 



The equation connecting G' 2 with the pressure and density (equation 

 (263)) is 



P = i sP& ................................. (272). 



At normal pressure and temperature C. the weight of a cubic cm. of 

 oxygen reduced to Paris standard, is, according to Morley, '00142945 gms. 

 The normal pressure is the weight of a column of mercury 76 cm. in height. 

 The specific gravity of mercury is 13'5953, and at Paris the value of gravity 

 is 980'939. Hence for oxygen at C. equation (262) becomes 



76 x 13-5953 x 980-939 = x -00142945 x G 2 , 

 whence we obtain (7 = 461-18 metres per sec. 

 and hence by equation (271), 



= = tf 2 -=- 273-04 = 259-65 x 10 4 . 



