Water in Dairy Products - Advanced Dairy Chemistry - page 453

a b

Figure 11.1a. (a) Schematic representation of the difference in water vapour pressure above
pure water (P w0 ) and above concentrated milk (P w ), measured at the same temperature (T).
(b) Since the chemical potential of water in the concentrated milk is less than in pure water, there
is a tendency for water to move into the milk through the semi-permeable plate. A downward
pressure, , on the piston is required to maintain it in place.

measured over pure water and over a food product (Figure 11.1a), or in the
energy necessary to compensate for the osmotic pressure of a solution
(Figure 11.1b). Water activity (a w ) is defined by the following relation:

m w m w0 ¼ RT ln a w (1)

where m w and m w0 are, respectively, the chemical potential of water in the
material and of pure water at the same temperature, T, and pressure. From
the definition of chemical potential (Emschwiller, 1951), the difference
(m w -m w0 ) is equal to the variation of free energy (DG) of the system when the
water chemical potential changes from m w to m w0 .CalculationofDG, e.g. the
work corresponding to the upward motion of the piston if water is allowed to
enter the concentrated solution (Figure 11.1b), allows derivation of relations
between a w and physical properties, which lead to measurement methods and
technological applications (calculations can be found in, e.g., Griffin, 1981):
Vapour pressure, equilibrium relative humidity (ERH):

a w ¼ p w
p w0

a w ¼ ERH
100

(2)

p w and p w0 are the water vapour pressures at equilibrium, respectively, of the
sample and pure water at the same temperature.
Osmotic pressure:

ln a w ¼ V w
RT

(3)