THE DYNAMICAL THEORY OF GASES. 



67 



Thermal Effects of Diffusion. 



If two gases are diffusing into one another, then, omitting the terms rela- 

 ting to heat generated by friction and to conduction of heat, the equation (94) 

 gives 



-...(118). 



By comparison with equations (78), and (79), the right-hand side of this equa- 

 tion becomes 



X (p,u, + pM) + Y (p^ + Pi v,) + Z ( Pl w, + p,w t ) 



/dp l dp t dp, \ /dp, dp., dp,, 



- \-&+- **+-: Vi] ~ \^r u *+ j ! v, + -4-' 

 \dx ay dz J \dx dy dz 



- M % (u' + v? + <) - ip, - + v; + wfi. 



The equation (118) may now be written 



d.pW\ 



-- 



...(119). 



The whole increase of energy is therefore that due to the action of the 

 external forces minus the cooling due to the expansion of the mixed gases. 

 If the diffusion takes place without alteration of the volume of the mixture, 

 the heat due to the mutual action of the gases in diffusion will be exactly 

 neutralized by the cooling of each gas as it expands in passing from places 

 where it is dense to places where it is rare. 



92 



