Environmental Engineering Reference
In-Depth Information
system appropriately representing the aimed problem. Description and definition of
the system is then a very important stage in the investigating approach. However, any
analysis not based on the precisely defined system can lead to astonishing but incorrect
results. The system has to be precisely determined by separating precisely the elements
included from those excluded. This is usually effectively rendered by applying an imag-
inary system boundary which tangibly separates the system from its surroundings. The
best practical way is to draw a scheme of contents of the system indisputably sepa-
rated from surroundings by the drawn system boundary. Sometimes the investigated
problem can be easily solved by introducing sub-systems, also precisely defined. Each
balance equation allows for determination of an unknown variable or for establishing
a relation between variables.
The radiation processes accompanying processing on substances can be non-
negligible and often the systems in which radiation and substance play roles together,
have to be considered.
As discussed, the variables obtained from mass and energy analyses are very impor-
tant, thus they have to be carefully prepared. The variables can be measured, assumed
or calculated. If the system is over-determined ; i.e. the number of unknowns is smaller
than the number of available independent equations, then all the variables can be
corrected based on the probability reconciliation calculus e.g. like that discussed for
radiation by Petela (2010).
2.3.2 Energy balance equations
The energy conservation equation is based on the substance balance equation. The
principle of conservation of substance claims that the number of molecules in physical
processes is constant, or a number of elements in chemical processes or a number of
nucleons in the processes of split and synthesis of nuclei is constant. The substance
conservation equation does not need to account for radiation or any other form of
matter except for substance. Such an equation is developed for the system defined
precisely by the system boundary. For the elementary process lasting a very short
period:
dm in
=
dm S
+
dm out
(2.3.1)
where m in and m out , kg, is the elementary amount of substance respectively deliv-
ered and extracted from the system, and m S is the elementary increase of amount
of substance within the considered system. The equation (2.3.1) can be appropriately
modified for steady state ( dm S =
0), or for a certain instant with use of mass flow rates,
or for a certain period of time. The equation can be separately applied for particular
compounds (if there is no chemical reaction) or elements. The amount unit can be kg,
kmol or the standard m 3 of the considered component.
A particular form of the substance conservation equation can be e.g. the equation
summarizing fractions of components in a considered composite material: f i =
1,
where f i is the fraction of the i -th component of the material.
The energy conservation equation is the result of observations and cannot be
proved or derived. From a long view of the history of mankind there are no phenomena
recorded occurring in disagreement with the First Law of Thermodynamics.
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