Page 105 - Advanced thermodynamics for engineers

90 CHAPTER 4 AVAILABILITY AND EXERGY

the sink is one of increasing entropy. Hence, in Fig. 4.12, the areas 1-2-8-9-1 and 5-6-10-8-5 are equal.
This means that areas
ða þ b þ cÞ¼ðb þ c þ d þ eÞ:
By definition the exergy change of the source is given by:

DB source ¼ B 2 B 1 ¼ðU 2 U 1 Þ T 0 ðS 2 S 1 Þ (4.59)
This equation assumes that the heat transfer takes place at constant volume. In a similar way the
exergy change of the sink is given by:

DB sink ¼ B 6 B 5 ¼ðU 6 U 5 Þ T 0 ðS 6 S 5 Þ (4.60)
Since the source and sink are isolated from the surroundings (the remainder of the universe), then
the entropy change of the universe is

DB univ ¼ DB source þ DB sink
¼ðU 2 U 1 Þ T 0 ðS 2 S 1 Þþ½ðU 6 U 5 Þ T 0 ðS 6 S 5 ފ (4.61)
¼ T 0 ðS 1 S 6 Þ
The term T 0 (S 1 S 6 ) is depicted by the area marked e on Fig. 4.12. Since S 6 is greater than S 1 , then
the exergy of the universe (that is its ability to do work) has decreased by this amount. Thus whilst the
energy of the universe has remained constant the quality of that energy has declined. This is true of all
processes which take place irreversibly; that is all real processes.

4.9.2 EXERGY APPLIED TO COMBUSTION PROCESSES
Combustion processes are good examples of irreversible change: these are discussed in more detail in
Chapter 10 et seq. In a combustion process the fuel, usually a hydrocarbon, is oxidised using an
oxidant, usually air. The structure of the hydrocarbon is broken down as the bonds between the carbon
and hydrogen atoms are broken and new bonds are formed to create carbon dioxide, carbon monoxide
and water vapour (see Chapter 11). These processes are basically irreversible because they cannot be
made to go in the opposite direction by the addition of a very small amount of energy. This seems to
suggest that exergy of the universe is decreased by the combustion of hydrocarbon fuels. The following
section describes how combustion can be considered using an exergy approach.
Consider a constant pressure combustion process. When the system is in equilibrium with its
surroundings the exergy of component, i,is

b i ¼ðh i h 0 Þ T 0 ðs i s 0 Þ (4.62)

4.9.2.1 Exergy of reaction of water
Applying this to the simple reaction

2H 2 ðgÞþ O 2 ðgÞ/2H 2 OðgÞ (4.63)
DB ¼ B 2 B 1 ¼ B P B R ¼ Sðb i Þ Sðb i Þ R (4.64)
P
where suffix R indicates reactants and suffix P indicates products.