Page 237 - Advanced thermodynamics for engineers

224 CHAPTER 10 THERMODYNAMICS OF COMBUSTION

Combustion equation is:

U P T P ¼ ðQ v Þ þ U R T R U R T s þ U P T s (10.30)
s
Reactants energy [U R (T R ) U R (T s )] is

Constituent CH 4 O 2 N 2
21,883.9 15,105.9 14,587.7
u 689.2
5719.6 6032.0 6025.8
u 298
Difference 16,164.3 9073.9 8561.9
n 1 2 7.52
nu 16,164.3 18,146.4 64,385.5

4
Thus U R T R U R T s ¼ 9:8696 10 kJ
Products energy at standard temperature, U P (T s ), is

Constituent CO 2 H 2 O N 2
7041.6 7223.3 6025.8
u 298
n 1 2 7.52
7041.6 14,446.6 45,314.0
nu 298
Hence U P ðT s Þ¼ 66802:2kJ:

Substituting these values into Eqn (10.30), and converting the calorific value to molar terms gives
4
U P ðT P Þ¼ 50144 16 þ 9:8696 10 þ 66802:2
5
¼ 9:678 10 kJ:
The value of specific internal energy for the mixture of products is

U P ðT P Þ 9:678 10 5

u P T P ¼ ¼ ¼ 92000 kJ kmol:
n P 10:52
An approximate value of the temperature can be obtained by assuming the exhaust products to be
70% N 2 and 30% CO 2 . Using this approximation gives

U P (T P )
T
2500 76,848.7
3000 94,623.3