Environmental Engineering Reference
In-Depth Information
Energy balance is the basic method for solving problems of thermodynamics. If
sometimes one wants to start analysis of any problem but does not know how, the
general advice is to try to make an energy balance of a system which would represent
the problem subject. The energy balance can be applied to diversified problems which,
however, require an appropriately well defined system for consideration. The system
boundary should be the same for energy and substance balances because the substance
balance is the basis for balance of energy. Sometimes only the specific definition of
the system and particular tracing of the system boundary allows for the solution of
the thermodynamic problem. In other cases the solution can be obtained by defining
more different sub-systems.
Generally, the energy
E
in
delivered to system remains partly within the system as
the increase
E
S
of the system energy, and the rest is the energy
E
out
leaving the system.
Thus, the general equation of energy balance is:
E
in
=
E
S
+
E
out
(2.3.2)
Usually, for better illustration of the balance equation, the particular terms of the
equation are shown in the bands diagram. The principle of such a diagram is shown
by a simple example (Fig. 2.3.1), illustrating equation (2.3.2).
In principle, for energy considerations, the reference state for calculation of energy
of the matters included in consideration can be defined arbitrarily; however, it is
recommended to select this reference as for the exergy consideration, to make fair
comparison of both, energy and exergy viewpoints.
Generally, application of an energy balance does not require analyzing of pro-
cesses occurring within the system boundary. It is sufficient only to know (e.g. from
measurements) the parameters determining components of the energy delivered and
leaving the system as well as to know the parameters determining the initial and final
state of the system. Obviously, if only the one unknown magnitude appears in the
balance equation then the equation can be used to calculate this magnitude.
The energy balance can be differently tailored depending on the considered view-
point and actual conditions. For example, there are some possibilities to categorize
the case under consideration as: a) energy delivered is spent entirely for an increase of
system energy at no energy leaving the system, b) energy leaving system comes entirely
from the decrease of energy of system at no energy delivered to system, c) there is
neither delivered nor leaving energy but only energy exchange (e.g. by work or heat)
within the system, d) energy delivered is equal to energy leaving the system at no
change of the system energy. Other possibilities are that some components of energy
can be neglected either due to relatively small changes, or because they are unchanged
at all. The balance equation can be written for the steady or transient systems, for the
system considered on macro scale or micro scale for which differential equations are
applied, etc.
For example, for the elemental process lasting an infinitely short time, the balance
equation (2.3.2) can take the form:
dE
in
=
dE
S
+
dE
out
(2.3.3)
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