140 



Physical Properties 



[CH. vi 



Unfortunately the value of b appears in the calculations as the difference 

 of two larger quantities. The accuracy of the results, therefore, is not great. 

 For instance in the case of hydrogen, Regnault's experiments lead to different 

 values of b of which the extreme values are '0005 and '0008, The number 

 '00069 is, however, the mean of a very great number of experiments, so that 

 the probable error is nothing like so great as the difference between the 

 mean and either of the extremes. The agreement amongst themselves of the 

 experiments in the case of the other two gases is much better. For instance, 

 taking the value b = '0030 for carbon dioxide, Van der Waals calculates for 

 a x 10 4 from Regnault's experiments the values 127, 114, 115, 107, 120, 113, 

 116, 111, 116. The first number according to Van der Waals is, from the 

 experimental conditions, likely to be the least trustworthy: the remainder, 

 as will be seen, agree to within a few per cent. 



There are other ways of determining b, besides observations on the 

 pressure and volume coefficients. Of these the most important is probably 

 by measurement of the Joule-Thomson effect. From calculations by Rose- 

 Innes*, Callendarf deduces the following values for b: 



Air 1-62, 



Nitrogen 2'03, 



Hydrogen 10'73. 



These values are in cubic centimetres referred to unit mass of gas. 

 Reduced to a cubic cm. of gas at normal pressure, the two sets of values 

 stand as follows : 



VALUES FOR b. 



As we have already seen, the value of 6 is - r- v<r 3 , and to give values 



o 



of b corresponding to those in the above table, v rmTStrbe supposed to be the 

 number of molecules per cu. cm. of the gas at normal temperature and 

 pressure. Thus v is the same for all the gases, and if we take the value 



v = 4 x 10 19 , from 8 we obtain the following series of values for - , the radius 



~L 



of the molecules : 



* Phil. Mag. n. p. 130. 



t Phil. Mag. v. p. 48, or Pros. Phys. Soc. xvni. p. 282. 



