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Then, the entropy generation per mole of constituents becomes:
= S g;A + S g;B
n A + n B
R [x A lnx A + (1 x A )ln(1 x A )]
(9.4)
and in general,
2 X
= R
x i lnx i
(9.5)
i=1
As x i is always less than unity, is always positive. This equation can also
be extended to ideal liquid and solid mixtures, whereby is the minimum entropy
generation of mixing.
Furthermore, the Gouy-Stodola theorem relates the destruction of exergy (irre-
versibility) in a process, denoted I, with entropy generation, , through I = T 0 ,
leading to:
2 X
I = T 0 = R
x i lnx i
(9.6)
i=1
with T 0 representing environment temperature.
If I is plotted against x, one observes a symmetric curve with a maximum of
x = 1=2, which in turn corresponds to maximum irreversibility of I max = RT 0 ln2,
whereby the value drops to zero upon reaching absolute purity, x A = 1 (Fig. 9.1).
Fig. 9.1 Irreversibility as a function of concentration in a mixture of two substances Eq. (9.6).
The curve gradient for Eq. (9.6) represents the increase in irreversibility upon
decreasing the concentration of one component and increasing in the same level of
magnitude the other. This corresponds to the minimum amount of thermodynamic
 
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