52
HENRY EYRING, RlCHAfiD i>. BOYCE AND JOHN D. SPIKES
The quantity — Y νιμι is called the affinity and is given the symbol A.
i
Letting Θ = dS irr /dt we have
θ = ±Α-ν
(82)
For / simultaneous reactions the equation modifies to
(83)
= TLJ
AjVj
3
The Second Law then states that
Θ=
IX
AjVj >
°
(84)
3
Thus we see that we have a bilinear form of the affinities and rates of
chemical reactions. Suppose / = 1, 2. Then it may happen that Ait>i < 0
and A 2 v 2 > 0 provided that
A 1 v 1 + A 2 v 2 >0
(85)
Both reactions are then said to be coupled. This permits one of the reactions to progress in the direction contrary to that prescribed by its
own affinity, or change in AF. Thus, as Prigogine (11) suggests, in
thermodiffusion the diffusion of matter against a concentration gradient
is characterized by a negative entropy production, but this effect is
compensated by positive entropy production due to flow of heat. We
see that coupled reactions are extremely interesting in the case of biological systems, because they are concerned with the apparent decrease
in entropy and an evolution always towards the more complex. The
following question then arises: is the decrease of entropy compensated
by coupled processes within the organism itself, or are other processes
involved? We would like a general scheme to provide us with an analysis revealing which processes may be coupled in the organism. Here
the theory of Onsager appears to offer a promising approach. But before proceeding to a consideration of his theory, we will first investigate
entropy production in natural processes.
C. ENTROPY PRODUCTION
1. Entropy Production in Flow of Electric Current
For electrical conduction the rate of performance of work is
dW
HENRY EYRING, RlCHAfiD i>. BOYCE AND JOHN D. SPIKES
The quantity — Y νιμι is called the affinity and is given the symbol A.
i
Letting Θ = dS irr /dt we have
θ = ±Α-ν
(82)
For / simultaneous reactions the equation modifies to
(83)
= TLJ
AjVj
3
The Second Law then states that
Θ=
IX
AjVj >
°
(84)
3
Thus we see that we have a bilinear form of the affinities and rates of
chemical reactions. Suppose / = 1, 2. Then it may happen that Ait>i < 0
and A 2 v 2 > 0 provided that
A 1 v 1 + A 2 v 2 >0
(85)
Both reactions are then said to be coupled. This permits one of the reactions to progress in the direction contrary to that prescribed by its
own affinity, or change in AF. Thus, as Prigogine (11) suggests, in
thermodiffusion the diffusion of matter against a concentration gradient
is characterized by a negative entropy production, but this effect is
compensated by positive entropy production due to flow of heat. We
see that coupled reactions are extremely interesting in the case of biological systems, because they are concerned with the apparent decrease
in entropy and an evolution always towards the more complex. The
following question then arises: is the decrease of entropy compensated
by coupled processes within the organism itself, or are other processes
involved? We would like a general scheme to provide us with an analysis revealing which processes may be coupled in the organism. Here
the theory of Onsager appears to offer a promising approach. But before proceeding to a consideration of his theory, we will first investigate
entropy production in natural processes.
C. ENTROPY PRODUCTION
1. Entropy Production in Flow of Electric Current
For electrical conduction the rate of performance of work is
dW