THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 
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7 
The equation of transfer becomes, consequently, after a little reduction, 
(246) 
3T d f f 3T\ 2 T f du 0 3Vn 3 w, 
p — = —) -sM l — + 0^- + 
dt 
dx \ dx 
dx 
dz 
+ 3 
2 _ ) 9 v / _ 2 / y \ _■y 
3 dll' 1 \ 032 / 3 \ dx ) 
3% 3 w, 
dz dy 
which is the equation of energy. 
The Thermal Conductivity of a Gas. 
§ 11 (C) In the equation of energy which we have just obtained, the second term 
on the right-hand side represents the change of heat per unit volume due to the 
variation in density at the point considered, while the third term may be proved 
equal to the heat produced by internal friction. The first term, by comparison with 
Fourier’s equation of conduction of heat (3- being the thermal conductivity and C„ the 
specific heat at constant volume), i.e., with 
dt 
3T 
dx V dx 
is seen to represent the change of heat by conduction, and to indicate that the 
coefficient of thermal conductivity of a gas is given by 
(247) 
c„. 
The value of f in this well-known formula is, for a general monatomic gas, given by 
(243), i.e., 
(248) 
/= lm/ 2 y r 
In general f is a function of the temperature only. 
Formula for p and 3- for Particular Molecular Models. 
§ 11 (D) By substitution of the values of C 0 and 2/3 r /2y r given in §§ 9, 10, for the 
particular molecular models there discussed, we obtain the following special cases of 
(237) and (248) 
(249) Ptigid elastic spheres, 
,l = 1*016 bm (h 
64tt V \m 
(250) Attracting spheres, 
T 
f= f. 1-010 = 2-525, 
/.= (l+O-^^-T '’' 1 
5 m 
647r ^a- 2 
m 
1 + S/T 
2 z 2 
J — i (1 + <k)> 
