Modern Thermodynamics
- Chapter 1
7
s(T,n) u(T,n)
n(x) T(x)
diS/dt0
deS/dt
(a)
T1
T2
T(x)
(b)
Fig. 1.2. (a) In a nonequilibrium system, the temperature number density nk(x) may vary with position.
The entropy and energy of such a system may be described by an entropy density s(T, nk) and an energy
density u(T, nk). The total entropy,
S = s[T(x),nk
(x)]dV,
∫V
the total energy
U = u[T(x),nk (x)]dV
∫v
and the total mole number Nk = nk (x)dV.
∫V
For such a nonequilibrium system, the total entropy S is
not a function of U, N and the total volume V. The term diS /dt is the rate of change of entropy due to
chemical reactions, diffusion, heat conduction and other such irreversible processes; according to the
second law diS/dt can only be positive. In open system, entropy can also change due to exchange of
energy and matter; this is indicated by the term deS/dt, which can be either positive or negative. (b) A
system in contact with thermal reservoirs of unequal temperatures is a simple example of a
nonequilibrium system. The temperature is not uniform and there is a flow of heat due to the temperature
gradient. The term deS/dt is related to the exchange of heat at the boundaries in contact with the heat
reservoirs while diS/dt is due to the irreversible flow of heat within the system.
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