Laws of Irreversible Phenomena. 403 



teristic period t for the coercion of the disturbance will be 



1 (pi + p 2 )^ 



Mpi + Pi) V 



(3) 



In a system composed of nitrogen and oxygen, at 0° 0. and 

 normal pressure, the value of t (from v. Obermayer's experi- 

 mental results) is about 4*5 X 10" 10 of a second. Returning 

 to (2) we obtain 



D(m 2 — Mi) u 2 — u x . . 



Dt " t ' W . 



and two other equations which may be written down from 

 symmetry ; hence (1) reduces to 



D(w 2 — Ui) 



F^—iffidxdydzApjpjrf (tt a — t*i) 

 and this gives 



Dt 



+ fe-^)^^+K-^^^}, • • (5) 



DF_ _2F 



D* ~ t * 



(6) 



Let us verify that, as stated above, 2F is the rate at which, 

 owing to diffusion, heat is being irreversibly generated. First, 

 from conservation of energy, we have 



D<JJJ 9 'l+PiitZ+tZ + vi + G + rii + W) 



Then, from (2) we obtain 



jy t SI dx d y dz lPi( M ! + v \ + w ?) =JH"^ ^ dz K P*P* 



x{u l (u 2 ^u 1 ) + v l (v 2 -v 1 )-\-iv 1 (w 2 — iv 1 )} i . (8) 



jyffidxdy<kip i {ul + vl + w$)=ffida:dt/dzA Pi p l 



x {w 2 (% — w 2 ) +^2(^1—^2) +Wa(«^-" ^2)}* • (9) 

 whence by (7) it follows : — 



= JJj ^ ^ d,S A/9^-1 (tt 2 "" Wi) 2 + (V 2 — Vi) 2 + ^2"~^l) 2 } 



= 2F . (10) 



and this proves the proposition. 



2 F 2 



