Environmental Engineering Reference
In-Depth Information
In equation (2.3.3) only d E S is the total differential and in order to demonstrate
it clearly it is better to write equation (2.3.3) as follows:
E in ( t ) dt
dE S + E out ( t ) dt
=
(2.3.4)
where E in and E out are the respective fluxes (e.g. in W) of energy delivered and extracted
from the system and t is the time.
Determination of dE S requires not only accounting for the change of intensive
parameters of the system state but also on the eventual change in the amount of matter
in the system. If, e.g. the considered system contains only a homogeneous substance
then:
dE S =
d ( m S e S )
=
m S de S +
e S dm S
(2.3.5)
where m S and e S are, respectively, the amount of substance and its specific energy
contained within the system.
Sometimes the subject of consideration can be recognized as moving in space (e.g.
solar vehicle, radiometer vane). Then the simplest energy balance equation is obtained
by assuming that the coordinates system determining velocity and location is moving
together with the system boundary. However there are some consequences of such
an assumption. Kinetic energy should be determined for the velocity relative to the
moving system. The useful work done by the system does not appear in the energy
balance because the forces acting on the system do not make replacements relative
to the coordinates system. The useful work can be determined only for velocity and
location relative to earth.
The components of an energy balance equation are the energy of the system and
energy exchanged with the system.
Energy of system ( E S ) depends on its state. An increase E S of an energy system,
changing from its initial to final state, does not depend on the means of change between
these states and is a difference of final E S , fin and initial E S , inl energy of the system:
E S
=
E S , fin
E S , inl
(2.3.6)
Generally, the system energy can consist of macroscopic components like E macr , i
due to velocity (kinetic energy), surface tension (surface energy), gravity (potential
energy), or any other energy of field nature (e.g. radiation). The remaining part of the
system energy, containing microscopic components U j , constitutes the internal energy:
=
E macr i +
E S
U j
(2.3.7)
i
j
where i and j are the successive numbers of the macro and micro components,
respectively, of the system energy.
If the kind of substance, before and after process (e.g. physical process), is the
same, then the reference state for calculation of the energy of the substance can be
established with a certain degree of freedom. For example, the reference state can be
assumed as the state of the substance entering the system. Thus, the substance energy
entering the system is zero whereas the energy of this substance exiting the system is
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