Physical Chemistry of Foods

EntropyðSÞis a measure of disorder; it is given by

S¼kBlnO ð 2 : 1 Þ

where kB is the Boltzmann constant ð 1 : 38? 10
^23 J?K
^1 Þ and O is the
number of ways in which the system can be arranged, also called thenumber
of degrees of freedom. If the system consists of perfect spheres of equal size,
this only relates to the positions that the spheres can attain in the volume
available (translational entropy). This is illustrated in a simplified way in
Figure 2.1 for a two-dimensional case, where spherical particles or molecules
can be arranged in various ways over the area available. If the interparticle
energy¼0, which means in this case that there is no mutual attraction or
repulsion between the particles, the entropy is at maximum: the particles can
attain any position available and are thus randomly distributed (and they
will do so because of their thermal or Brownian motion). If there is net
attraction (Uis negative), they tend to be arranged in clusters, andSis much
lower. If there is repulsion (Uis positive), the particles tend to become
evenly distributed and also in this case entropy is relatively small. If we have
more realistic particles or molecules, there are more contributions to
entropy. Anisometric particles may attain various orientations (orienta-
tional entropy) and most, especially large, molecules can attain various
conformations (conformational entropy). If two or more kinds of molecules
are present, each kind must be distributed at random over the volume to
attain maximum entropy (mixing entropy).
The paramount thermodynamic property is thefree energy. Two kinds
are distinguished. TheHelmholtz (free) energyis given by

A:U
TS ð 2 : 2 Þ

Note that entropy is thus expressed in J?K
^1 ; T is the absolute
temperature (in K). At constant volume, every system will always change
until it has obtained the lowest Helmholtz energy possible. This may thus
be due to lowering ofUor increase ofS. Since we mostly have to do with
constant pressure rather than constant volume, it is more convenient to
use theGibbs (free) energy. To that end we must introduce theenthalpy
ðHÞ, defined as

H:U
pV ð 2 : 3 Þ

wherepis pressure (in Pa) andVvolume (in m^3 ). For condensed (i.e.,
solid or liquid) phases at ambient conditions, any change inpVmostly is
very small compared to the change in U. At constant pressure, every