RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 82

HUpV =+ (2.12)

and the Helmholtz free energy ,

FUTS =- (2.13)

These functions are more generally used in thermodynamic description of
gaseous systems.
Particular functions are most valuable in dealing with particular thermal
processes. For example, presuming that no fields, stresses, or strains are
involved, when heat

Q is added to a system at constant pressure to raise tem-
perature by an amount

D

T , one does not directly obtain a measure of the
change of energy U . Equation (22.12) shows that one has

D

dH =+ dQ V dp (2.14)

Hence, at constant pressure ( dp = 0 ),

∂
∂

H
T

D
D

H
T

Ê
Ë

ˆ
¯

Ê
Ë

ˆ
¯ =

= c (2.15)

p

p

which is termed the specific heat at constant temperature . Likewise, the specific
heat at constant volume c v is defined as

∂
∂

U
T

Ê
Ë

ˆ
¯

c = (2.16)

v

p

While c v is useful in dealing with gaseous systems, the specific-heat values for
solids are generally taken at constant pressure.
An inhomogeneous system, as are most of the biological systems, is com-
posed of several parts. The separable parts are termed phases . Then, the exten-
sive parameters of the entire system are the sums of the extensive parameters
of the separate phases. For example, the volume of the liquid plus the volume
of the solid phases equals the total volume in the iced drink. Likewise, the
energy U is the sum of the energies of the two parts. The same applies for S ,
F , G ,....In one phase, however, one cannot measure extensive parameters
for each of the chemical constituents present. (Dissolution of sugar in coffee
does not increase the volume of the sweetened coffee by an amount equal to
the volume of the dissolved sugar.)
At equilibrium, in the absence of field- and stress-dependent terms, tem-
perature is the same in all phases, as generally is pressure. In addition to
changes of the entropy and volume of a phase, there may also be changes in
composition. The addition of an atom or molecule, or even an electron, will
generally raise its internal energy by a small amount.
In a one-constituent, one-phase system at equilibrium, temperature and
pressure are the only variables (dispensing with fields and stresses). In a more
complex system, however, molecules or atoms move from one phase to