Modern Engineering Thermodynamics

15.10 Entropy Production in Chemical Reactions 621
WHAT IS C-4?
C-4 (or Compound 4) is an off-white plastic explosive that feels like modeling clay. About 91% of C-4 is an explosive
called RDX (C 3 H 6 N 6 O 6 ) with the remainder being plasticizer and binder. C-4 is 1.34 times as explosive as trinitrotoluene
(TNT) and detonates with a pressure wave of about 8040 m/s (26,400 ft/s or about 18,000 mph).
C-4 is actually very stable. It can be detonated only by a combination of extreme heat and a shockwave brought about by
inserting and firing a detonating device. It cannot be detonated by a gunshot, by dropping it onto a hard surface, or even
by blowing it up. When ignited with a flame, C-4 burns slowly rather than explodes. Even though soldiers knew that burning
C-4 produces poisonous fumes, during the Vietnam War, they used small amounts of it as fuel for cooking.
More accurate calculations that include the energy-absorbing effects of chemical dissociation of the products at
high temperatures show that the maximum adiabatic flame temperature of octane with pure oxygen is only
about 3100 K (5580 R). Therefore, the maximum explosion temperature calculated in Example 15.11 is high by
a factor of about 2, and the actual maximum pressure inside the bomb calorimeter is closer to 5400 psi. Gas
pressures at this level can be very dangerous (especially at high temperatures) and the calorimeter must be
designed to withstand them.
15.10 ENTROPY PRODUCTION IN CHEMICAL REACTIONS
When the entropy rate balance is applied to a steady state, steady flow, open system combustion or reaction
chamber with isothermal boundaries at temperature T b , the total entropy production rate for the reaction is
_S p
r = ∑ out
= ∑
out
_ms −∑ _ms − _Q r /T b
in
_ns −∑_ns − _Q r /T b
in
where _Q r is the heat transport rate of the reaction. In most instances, the products exit the system mixed
together in a single flow stream, but the reactants can enter the system either (a) premixed in a single flow
stream or (b) in individual flow streams. If the reactants enter through separate flow streams, each carrying a
pure substance, then the entropy production rate of the mixing process that must occur inside the system before
the reaction can occur is included in the previous equation, which then has the form
_S P
r = _n Ps P −∑_n i s i − _Q r /T b
R
On the other hand, if the reactants enter the system already mixed together in a single flow stream, then this
equation becomes
_S P
r = _n Ps P − _n R s R − _Q r /T b
where the mixture molar specific entropies are given in Table 12.3 as
s P = ∑
P
χ i^s i and sR = ∑ χ i^s i
R
where χ i is the mole fraction of substance i, and^s is the partial molar specific entropy, defined in Chapter 12. If
both the reactants and the products can be considered mixtures of ideal gases that obey the Gibbs-Dalton ideal
gas mixture law discussed in Chapter 12, then s i = ^s i , the molar specific entropy of gas i. If one or more of the reactants
or products is a liquid or a solid or if the mixture does not obey the Gibbs-Dalton ideal gas mixture law,
then a much more complex analysis must be carried out.
Assuming both the reactants and the products to be premixed ideal gases, the total entropy production rate of
the reaction is
_S P
r = _n P∑
P
= ∑
P
χ i s i − _n R ∑ χ i s i − _Q r /T b
R
_n i s i −∑ _n i s i − _Q r /T b
R