162 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
by means of which we may transform (12'09) into 
DT 
/ Du 
(12-11) fR, 0 ^ Zu' 0 ^ ~bW (X x -X 2 ) 
D* 
3m'o , 3i/ 0 3w' 0 ' 
.r-, I C)Un 3r^Q 
Ike Pxy d^ +Pxz dx 
, 3a: 3 y dz 
dw ^+z ^.u^+WSO?) = o. 
In this equation we substitute the values of p xx , p xy , p xz from (ll'04), (ll'05), et 
cetera. Also we divide throughout by J, the mechanical equivalent of heat, and 
replace f ——by C„, the specific heat of the gas at constant volume.* After a little 
" J m 0 
reduction we obtain the equation of energy in the following form :— 
/1 o • i o \ n HT 2 pm/3 m 0 ov n 3 w 0 \ 1 ^ f / v „„„ D u 0 
(12 12) +3PoCJ^ + -^+-^j - 
3 <r dy dz J J 
D* 
+ |-“(m 1 -m 2 )c 0 
3m' 0 . 3v' n , 3 w\ 
+ 
+ 
J \dx ' dy ' dz 
+ f{ 22 (^°J +2 (w + l s J- | ( 2 t 0 
3*/ dz , 
1 v ^ 11 
- j- ^(i^iUjCd + l-^Uo^ 2 ). 
x — m 
- Dt 
(b) The Interpretation of the Equation of Energy. 
We will now consider the significance of the various terms in the equation of 
energy (12'12). The terms on the right depend on diffusion, viscosity, and thermal 
conduction (as will be made clearer later). If we neglect the small changes of energy 
produced by these means, as a first approximation (12‘12) may be written 
(12-13) 
1 DT 2 /3w 0 dv 0 dw ( 
T Dt 3 \dx dy dz 
0 \ _ 
= o, 
where we have omitted the right-hand side of (12'12), and divided the left hand by 
p () C v T. 
* The specific heat of a simple gas at constant volume is § j^-, if m is the molecular mass (cf. Jeans’ 
‘ Dynamical Theory of Gases,’ 2nd edit., § 261, (512)). Hence for a composite gas we have 
R 
J ’ 
p 3 R . 3 R 3 R ( Pi t \ 3 P 
P oC„ = fpi j — + #2 y— = f v — + — = 4"o - 
Jm x J m 2 J \mi m 2 / 
and consequently 
p _ 3 R 
" 2 Jm 0 ’ 
