Here is an alternative to the method used in the text for showing that k 12 = k 21 if a = 0 [eqs XXXXXXXXXXand (12.130)]. Rely on the a 12 expression derived above [or simply start with eq...

Here is an alternative to the method used in the text for showing that k₁₂
= k₂₁
if a = 0 [eqs. (12.129) and (12.130)]. Rely on the a₁₂
expression derived above [or simply start with eq. (12.118)] to show that

in other words, that k₁₂
= k₂₁
if a₁₂
(or a) is zero.

While examining the two flux relations of nonisothermal diffusion in a binary mixture [eqs. (12.177) and (12.178)], note that the energy flux J_U
is not necessarily equal to the heat flux q′′. If the thermal conductivity k is defined under zero-mass-flux conditions,