233 



§ 4. The pressure, a. We will assume that the relation 



2 U 



P=3F («) 



as depending on the isotropy of molecuhir motion and on the 

 elementary fundamental law of dynamics regarding the connection 

 between force and momentum, remains generally valid. As Tetrode 

 1. c. shows, we have then also in general 



10 U 



'' = ^M' (') 



J/ being the molecular weight. By (4), (5), (6) and (7) the equation 

 of state of the ideal monatomic gas is given. 



It is easily demonstrated, that the expression for the entroi)y 

 deduced from (1) is consistent wdtli tliis equation ^). 

 If we introduce 



hv hv,n 



Ü' = ^'W = -' ■ • («> 



we obtain 



9 (1 I r§' di) 







By introducing the "characteristic temperature" ^, determined by 



'=^=r{r.v) -{ym) ('*" 



we can write 



•v = - ......... (11) 



b. High temperatures. Developing for high temperatures ^), we obtain 

 3 I 3 5. 3R 3 2?, ) 



2 1^52! 7 4! ^ 9 6! j ^ ' 



1 1 1 



where B. =z - , 7? — — - , i? — -— . . are the Bernouillian coefficients, or 

 6 30 42 



3 111 1 1 



U ^- Nk 7' 1 -I x' x' H x' ....... (13) 



2 I ^ 20 1680 ^ 90720 ! ^ ' 



Limiting ourselves to the two tiist terms the })ressure becomes 



NkT i 1 <9M 

 ü = \l\ (14) 



F I 20 2'M 



and according to (10), substituting for ^^ oidy the first term of (13): 



1) Cf. H. Tktrode, 1. c. 



2) According to Debije 1. c. this development is suitable from x = to a; = 2. 



