If a gas mixture is at a relatively high pressure or low temperature, the
deviation from the ideal-gas behavior should be accounted for by incorpo-
rating more accurate equations of state or the generalized entropy charts.
15–7 SECOND-LAW ANALYSIS
OF REACTING SYSTEMS
Once the total entropy change or the entropy generation is evaluated, the
exergy destroyedXdestroyedassociated with a chemical reaction can be deter-
mined from
(15–23)where T 0 is the thermodynamic temperature of the surroundings.
When analyzing reacting systems, we are more concerned with the
changes in the exergy of reacting systems than with the values of exergy at
various states (Fig. 15–30). Recall from Chap. 8 that the reversible work
Wrevrepresents the maximum work that can be done during a process. In the
absence of any changes in kinetic and potential energies, the reversible work
relation for a steady-flow combustion process that involves heat transfer
with only the surroundings at T 0 can be obtained by replacing the enthalpy
terms by h
- °fh
- h
- °, yielding
- h
(15–24)An interesting situation arises when both the reactants and the products are
at the temperature of the surroundings T 0. In that case,h
- T 0 s–(h
- T 0 s–)T 0
g– 0 , which is, by definition, the Gibbs function of a unit mole of a sub-
stance at temperature T 0. The Wrevrelation in this case can be written as
- T 0 s–)T 0
(15–25)or
(15–26)where g–°fis the Gibbs function of formation (g–°f0 for stable elements like
N 2 and O 2 at the standard reference state of 25°C and 1 atm, just like the
enthalpy of formation) and g–T 0 g–° represents the value of the sensible
Gibbs function of a substance at temperature T 0 relative to the standard
reference state.
For the very special case of TreactTprodT 0 25°C (i.e., the reactants,
the products, and the surroundings are at 25°C) and the partial pressure
Pi1 atm for each component of the reactants and the products, Eq. 15–26
reduces to
(15–27)We can conclude from the above equation that the g–°fvalue (the negative
of the Gibbs function of formation at 25°C and 1 atm) of a compound
represents the reversible workassociated with the formation of that com-
pound from its stable elements at 25°C and 1 atm in an environment at
25°C and 1 atm (Fig. 15–31). The g–°fvalues of several substances are listed
in Table A–26.
WrevaNrg°f,ranpg°f,p¬¬ 1 kJ 2
WrevaNr 1 g°fgT 0 g° (^2) raNp 1 g°fgT 0 g° (^2) p
WrevaNrg0,raNpg0,p
WrevaNr 1 h°fhh°T 0 s (^2) raNp 1 h°fhh°T 0 s (^2) p
XdestroyedT 0 Sgen¬¬ 1 kJ 2
Chapter 15 | 775
T, P State
Reactants
Reversible
work
Products
Exergy
FIGURE 15–30
The difference between the exergy
of the reactants and of the products
during a chemical reaction is the
reversible work associated with that
reaction.
2525 °C,C,
1 atm 1 atm
C + OC + O 2 → CO CO 2
Wrevrev = = – g–f, , (^) COCO 2 2 = 394,360 k= 394 , 360 kJJ//kmolkmol
StableStable
T 0 = 25 = 25 °C
elementselements CompoundCompound
2525 °C,C,
1 atm 1 atm
2525 °C,C,
1 atm 1 atm
°
FIGURE 15–31
The negative of the Gibbs function of
formation of a compound at 25C, 1
atm represents the reversible work
associated with the formation of that
compound from its stable elements at
25 C, 1 atm in an environment that is
at 25C, 1 atm.