Page 30 - Chemical equilibria Volume 4

6 Chemical Equilibria
According to expression [1.10], the entropy production can be expressed
on the basis of that activity by:
d S = A dξ [1.12]
i
dt T dt
On the basis of this definition, we shall be able to express the affinity
another way.

1.3.2. Affinity and characteristic functions

The variation of internal energy is, according to the first law of
thermodynamics:

dU = dQ + dW = T d S + dW = T dS − T d S + dW [1.13]
i
e
dt dt dt dt dt dt dt dt
If all the exchanges are reversible, apart from the transformation under
study (we then say that the system is at physical equilibrium), then the work
term is written:

dW = ∑ YdX [1.14]
p
dt k= 2 k k

The sum that appears in the above expression is extended to all couples of
conjugate variables, with the exception of the temperature–entropy couple
(which is why the index k begins at the value of 2). By substituting this back
into expression [1.13] and taking account of relation [1.12], we obtain:

dU = ∑ Y d X k + T d S − A dξ [1.15]
p
dt k= 2 k dt dt dt

This gives us a new expression of the affinity, which is therefore the
opposite of the differential of the function U in relation to the fractional
extent with constant entropy and extensive variables:

⎛ U ⎞ ∂
A =− ⎜ ⎟ [1.16]
⎝ ∂ξ ⎠ , SX k