Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 39

The chemical exergy , discussed in paragraph 2.2.3.3, is assumed to be the same
for the substance considered as the component of the system and for the substance
component separately exchanged with the system.
An exergy balance is usually carried out on the assumption of constant parameters
of environment during the consideration time. The effects of varying environmen-
tal parameters are usually small and the assumption of the mean environmental
parameters is sufficient for the exergy analysis. The inclusion of the variations of
the environment parameters would make the analysis more difficult because the con-
sidered exergy values should be taken for instantaneous environment parameters, i.e.,
the values used in the balance equation would need calculations by integration over
assumed time period.
Moreover, usually the balance equation would need the introduction of an addi-
tional member without which the equation is not fulfilled. For example, such a need
appears when a perfectly insulated container has been closed while being filled with
a substance in equilibrium with the environment and if, meanwhile, the environment
parameters after closing are changed. Then it can be deduced that the enclosed sub-
stance gains the positive exergy and the exergy balance equation is not fulfilled (Petela
(2010)). In another example, ice stored during a frosty winter has exergy close to zero,
whereas the exergy of the same ice existing in hot summer time is relatively large and
again the exergy balance equation for the ice taking part in such a season change ris
not fulfilled.
Therefore generally, the exergy balance equation for the process occurring at the
varying environmental parameters should contain the compensation term B e which
modifies equation (2.3.9) as follows:

fin fin fin

B in dt B out dt ˙ T 0 dt

= B S + + + B e (2.3.14)

inl inl inl

where B e is the exergy gain due to variation of the environment from the initial state
( inl ) to the final ( fin ) state, B is the respective rates of exergy and ˙ is the overall
entropy growth. As mentioned, the B e can be positive or negative or zero. The bands
diagram for exergy balance at varying environment parameters is shown in Figure
2.3.3. Direct calculation of B e is not easy, thus the best method is to calculate this
value as a completion of the balance equation.
The Gouy-Stodola law, expressed by equation (2.2.10), was derived for a constant
environment temperature T 0 .If T 0 is varying, then the law can be applied only for
the infinitely short process as is expressed by the presence of the appropriate integral
term in equation (2.3.14). The Gouy-Stodola law cannot be applied to the processes
which occur at the varying environment temperature if such variation is caused by
the considered process. An example calculation illustrating the effect of the varying
environment temperature is given by Petela (2010).
The variation of environment parameters can instantaneously generate or destroy
exergy at no role of internal processes of the examined system. Therefore, if the environ-
ment variations are significant, then wherever possible, the process should be organized
to utilize the instantaneous positive value of B e . The predicting data on the change in