Page 302 - Advanced Thermodynamics for Engineers, Second Edition

12.13 PROBLEMS 291

p CO 2
The equilibrium constant for the CO 2 reaction at 2900 K is K p r ¼ 1=2 ¼ 4:50, and it
p CO p
O 2
can be assumed that the degree of dissociation for the water reaction is one quarter of that
for the carbon dioxide one. Indicate the processes, including a heat transfer process, on the
U–T diagram. The internal energy of propane at 25 C is 12,380 kJ/kmol, and the internal

energies of formation for the various compounds are
CO 2 391032; H 2 O 239342; CO 108052 kJ=kmol

[0.0916; 0.0229; 0.1450; 0.0076; 0.01527; 0.7176]
P12.5. Methane (CH 4 ) is burned with 50% excess air. The equilibrium products at a pressure of
10 bar and a temperature of 1600 K contain CO 2 , CO, H 2 O, H 2 ,O 2 and N 2 . Calculate the
partial pressures of these gases, assuming that the partial pressures of CO and H 2 are small.
5
5
[0.6545; 1.6383 10 ; 1.3089; 1.0524 10 ; 0.6545; 7.3822]
P12.6. The exhaust gas of a furnace burning a hydrocarbon fuel in air is sampled and found to be
13.45% CO 2 ; 1.04% CO; 2.58% O 2 ; 7.25% H 2 O; 75.68% N 2 and a negligible amount of
H 2 . If the temperature of the exhaust gas is 2500 K, calculate
(a) the carbon/hydrogen ratio of the fuel;
(b) the equivalence ratio;
(c) the equilibrium constant for the dissociation of CO 2 (show this as a function of
pressure) and
(d) the pressure of the exhaust gas.
1/2
[1.0; 0.898; 80.52/p ; 8.874]
P12.7. A weak mixture of propane (C 3 H 8 ) and 50% excess air is ignited in a constant volume
combustion chamber. The initial conditions were 1 bar and 300 K and the final composition
was 7.87% CO 2 , 0.081% CO, 10.58% H 2 O, 0.02% H 2 , 6.67% O 2 and 74.76% N 2 by
volume. Evaluate the final temperature and pressure of the products. Prove that the
temperature obeys the conservation of energy, if the calorific value of propane is 46440 kJ/
kg at 300 K.
The equilibrium constant for the carbon dioxide reaction is given by
2

28600
p CO p O 2
10
2 T
K p ¼ where log K p ¼ 8:46 ; and T ¼ temperature in K:
p CO 2
The specific heats at constant volume (c v,m ) of the constituents, in kJ/kmol K, may be taken as
3 3
CO 2 12:7 þ 22 10 T H 2 O 22:7 þ 8:3 10 T
3 3
CO 19:7 þ 2:5 10 T N 2 17:7 þ 6:4 10 T
3 3
O 2 20:7 þ 4:4 10 T H 2 17:0 þ 4:0 10 T
neglect the internal energy in the reactants
C 3 H 8
The internal energies of formation of the constituents at 300 K are
3
3
3

CO 2 393 10 ; H 2 O 241 10 ; CO 112 10 kJ kmol
[2250 K; 7.695 bar]