Page 29 - Chemical equilibria Volume 4

Physico-Chemical Transformations and Equilibria 5
This exchanged heat is expressed as a function of the variables by way of
the specific heat coefficients χ , which enables us to write the following for
k
the entropy flux exchanged:
p
d S = ∑ χ k dY k + χ T dξ [1.8]
e
dt k= 1 T dt T dt
By comparing expressions [1.6] and [1.8], we obtain the contribution of
the internal production to the variation in entropy as a function of the system
variables:
d S = ∑ ⎛ S ∂ − χ ⎞ k dY k + ⎛ S ∂ − χ ⎞ T dξ [1.9]
p
i
⎜
dt k= ⎝ 1 ∂ Y k T ⎟ dt ⎜ ⎝ ⎠ ξ ∂ T ⎟ ⎠ dt
According to the second law, this entropy production must be positive or
null in any spontaneous transformation. If we envisage a transformation
whereby the external intensive variables Y k are kept constant, if the
transformation is spontaneous, it means that we satisfy the inequality:

d S = ⎛ S ∂ − χ ⎞ T dξ ≥ 0 [1.10]
i
dt ⎜ ⎝ ξ ∂ T ⎟ ⎠ dt

Thus, expression [1.10] is a condition needing to be fulfilled during any
real transformation keeping the intensive variables Y constant.
k

1.3. Affinity of a transformation

We shall introduce a new value – the affinity – pertaining to any
transformation. The variables for this affinity are the (intensive or extensive)
Thermodynamic variables, the quantities of material and the extent of the
transformation.

1.3.1. Definition

De Donder proposed to use the term affinity of the transformation,
denoted as A, for the entity:

⎛ S ∂ χ ⎞
A = T ⎜ − T ⎟ [1.11]
⎝ ∂ξ T ⎠