Page 154 - Physical Chemistry

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The first thing to note is that the statement S 0 applies only to systems that are Section 4.10
both closed and thermally isolated from their surroundings; see Eq. (3.37). Living or- Summary
ganisms are open systems, since they take in and expel matter; further, they exchange
heat with their surroundings. According to the second law, we must have S syst
S surr 0 for an organism, but S syst ( S of the organism) can be positive, negative, or
zero. Any decrease in S syst must, according to the second law, be compensated for by
an increase in S surr that is at least as great as the magnitude of the decrease in S syst . For
example, during the freezing of water to the more ordered state of ice, S syst decreases,
but the heat flow from system to surroundings increases S surr .
Entropy changes in open systems can be analyzed as follows. Let dS syst be the en-
tropy change of any system (open or closed) during an infinitesimal time interval dt.
Let dS be the system’s entropy change due to processes that occur entirely within the
i
system during dt. Let dS be the system’s entropy change due to exchanges of energy
e
and matter between system and surroundings during dt. Any heat flow dq into or out of
the system that occurs as a result of chemical reactions in the system is considered to
contribute to dS . We have dS syst dS dS . As far as internal changes in the system
e
i
e
are concerned, we can consider the system to be isolated from its surroundings; hence
Eqs. (3.38) and (3.35) give dS 0, where the inequality sign holds for irreversible in-
i
ternal processes. However, dS can be positive, negative, or zero, and dS syst can be pos-
e
itive, negative, or zero.
The state of a fully grown living organism remains about the same from day to day.
The organism is not in an equilibrium state, but it is approximately in a steady state.
Thus over a 24-hr period, S syst of a fully grown organism is about zero: S syst 0.
The internal processes of chemical reaction, diffusion, blood flow, etc., are irre-
versible; hence S 0 for the organism. Thus S must be negative to compensate for
e
i
the positive S . We can break S into a term due to heat exchange with the sur-
e
i
roundings and a term due to matter exchange with the surroundings. The sign of q, and
hence the sign of that part of S due to heat exchange, can be positive or negative, de-
e
pending on whether the surroundings are hotter or colder than the organism. We shall
concentrate on that part of S that is due to matter exchange. The organism takes in
e
highly ordered large molecules such as proteins, starch, and sugars, whose entropy per
unit mass is low. The organism excretes waste products that contain smaller, less or-
dered molecules, whose entropy per unit mass is high. Thus the entropy of the food in-
take is less than the entropy of the excretion products returned to the surroundings; this
keeps S negative. The organism discards matter with a greater entropy content than
e
the matter it takes in, thereby losing entropy to the environment to compensate for the
entropy produced in internal irreversible processes.
The preceding analysis shows there is no reason to believe that living organisms
violate the second law.

4.10 SUMMARY
The Helmholtz energy A and the Gibbs energy G are state functions defined by A
U TS and G H TS. The condition that the total entropy of system plus sur-
roundings be maximized at equilibrium leads to the condition that A or G of a closed
system with only P-V work be minimized if equilibrium is reached in a system held at
fixed T and V or fixed T and P, respectively.
The first law dU dq dw combined with the second-law expression dq rev TdS
gives dU TdS PdV (the Gibbs equation for dU) for a reversible change in a closed
system with P-V work only. This equation, the definitions H U PV, A U TS,
G H TS, and the heat-capacity equations C (
H/
T) T (
S/
T) and C
P
V
P
P
(
U/
T ) T (
S/
T ) are the basic equations for a closed system in equilibrium.
V
V