Solutions for Ballistics: The Theory and Design of Ammunition and Guns, 3rd Edition Carlucci ,All Chapters included, Latest edition 2025

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AF
KM
N
BA
ST
TE

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2.1 The Ideal Gas Law
Problem 1 - Assume we have a quantity of 10 grams of 11.1% nitrated nitrocellulose
(C6H8N2O9) and it is heated to a temperature of 1000K and changes to gas somehow
without changing chemical composition. If the process takes place in an expulsion cup
with a volume of 10 in3, assuming ideal gas behavior, what will the final pressure be in
psi?
ST
 lbf 
Answer p = 292
 in 2 

Solution:
BA
This problem is fairly straight-forward except for the units. We shall write our ideal gas
law and let the units fall out directly. The easiest form to start with is equation (IG-4)

pV = mg RT (IG-4)

Rearranging, we have
N
mg RT
p=
V

Here we go
KM
1  kg    1  kgmol 
(10)g   (8.314)
kJ
  (737.6)ft − lbf (12)in (1000)K
 1000  g   kgmol  K  252  kg C H N O   kJ   ft 
 
2 9 
p=  3 8
 
6

(10) in
 lbf 
p = 292
 in 2 
AF
You will notice that the units are all screwy – but that’s half the battle when working
these problems! Please note that this result is unlikely to happen. If the chemical
composition were reacted we would have to balance the reaction equation and would
have to use Dalton’s law for the partial pressures of the gases as follows. First, assuming
no air in the vessel we write the decomposition reaction.
I
C6 H8 N 2 O9 → 4H 2 O + 5CO + N 2 + C(s)
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Then for each constituent (we ignore solid carbon) we have

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Ni T
pi =
TE
V

So we can write
    1   kgmol C 6 H 8 N 2 O 9 
(4) kgmolH O (8.314 )
kJ
 (1000 )K    (10 ) g  C6 H8 N 2O9   1  kg C6 H8 N 2O9
 

 kgmol C H N O   kgmol - K   252  kg C H N O  1,000  g C H N O 
2


=  6 8 2 9     6 8 2 9 
 
p
( ) 3  1  kJ  1  ft 
6 8 2 9
ST
H 2O

10 in    

 737.6 ft − lbf  12 in 

 lbf 
p H 2O = 1,168
 in 2 
    1   kgmol C 6 H 8 N 2 O 9 
(1000)K  (10)g
BA
kJ
(5) kgmolCO (8.314)  1  kg C6 H8 N2O9 

   kgmol - K     C6 H8 N2O9   
kgmol 252 kg 1,000 g
         

C H N O C H N O C H N O

( ) 
CO
p =
    
 
 1  ft 
6 8 2 9 6 8 2 9 6 8 2 9
3
10 in
N
 kJ
1
pCO 
= 1,460
 lbf   737.6  ft − lbf  12 in 
 in 2    kgmol C 6 H 8 N 2 O 9 
   kg C6 H8 N2O9 
 kgmol (1000)K 1   
KM
kJ
(1) (8.314) (10) g 1
2
N
   kgmol - K     C6 H8 N2O9   
kgmol 252 kg 1,000 g


( ) 
N2

 C H N O     C H N O    C H N O 
p = 
AF
6 8 2 9   6 8 2 9   6 8 2 9 
 1 
10 in 3  737.6 
kJ 
  
1 ft
p N 2 = 292 lbf  ft − lbf  12 in 
 in 2 
I
2 2
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Then the total pressure is
p = pH O + lbf
pCO + pN  lbf   lbf   lbf 
p = 1,168 in 2  + 1,460 + 292 = 2,920
  in 2   in 2   in 2 
2.2 Other Gas Laws
Problem 2 - Perform the same calculation as in problem 1 but use the Noble-Abel
equation of state and assume the covolume to be 32.0 in3/lbm

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 lbf 
TE
Answer: p = 314.2
 in 2 

Solution:

This problem is again straight-forward except for those pesky units – but we’ve done this
before. We start with equation (VW-2)
ST
p(V − cb) = mg RT (VW-2)

Rearranging, we have

mg RT
p=
BA
V − cb

Here we go
1  kg    1  kgmol 
(10)g   (8.314)
kJ
   (737.6) ft − lbf (12)in (1000)K
 1000  g   kgmol  K  252  kg C H N O   kJ   ft 
 
 6 8 2 9 
p=
 
( ) 3 − ( )  1  kg ( )lbm (  in 3 
N
10 in  10 g    2.2 
)
 32.0 lbm 
  1000  g   kg   
KM
 lbf 
p = 314.2
 in 2 

So you can see that the real gas behavior is somewhat different than ideal gas behavior at
this low pressure – it makes more of a difference at the greater pressures.

Again please note that this result is unlikely to happen. If the chemical composition were
AF
reacted we would have to balance the reaction equation and would again have to use
Dalton’s law for the partial pressures of the gases. Again, assuming no air in the vessel
we write the decomposition reaction.

C6 H8 N 2 O9 → 4H 2 O + 5CO + N 2 + C(s)

Then for each constituent (again ignoring solid carbon) we have
I
N i T
A@
pi =
(V - cb)
So we can write