Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 15 | 769

1 lbmol CH 4

CO 2

1 atm^77 °F 1800 R

P 2

BEFORE

REACTION

H 2 O

3 lbmol O (^2) O 2
AFTER
REACTION
FIGURE 15–24
Schematic for Example 15–7.
The h

• f° of liquid propane is obtained by subtracting the h
  
  
  • fgof propane at
    25°C from the h
  
  
  
  


• 
  

  f° of gas propane. Substituting gives

  
  

Thus 363,880 kJ of heat is transferred from the combustion chamber for
each kmol (44 kg) of propane. This corresponds to 363,880/44 8270 kJ
of heat loss per kilogram of propane. Then the rate of heat transfer for a
mass flow rate of 0.05 kg/min for the propane becomes

EXAMPLE 15–7 First-Law Analysis of Combustion in a Bomb

The constant-volume tank shown in Fig. 15–24 contains 1 lbmol of methane
(CH 4 ) gas and 3 lbmol of O 2 at 77°F and 1 atm. The contents of the tank
are ignited, and the methane gas burns completely. If the final temperature
is 1800 R, determine (a) the final pressure in the tank and (b) the heat
transfer during this process.

Solution Methane is burned in a rigid tank. The final pressure in the tank
and the heat transfer are to be determined.
Assumptions 1 The fuel is burned completely and thus all the carbon in the
fuel burns to CO 2 and all the hydrogen to H 2 O. 2 The fuel, the air, and the
combustion gases are ideal gases. 3 Kinetic and potential energies are negli-
gible. 4 There are no work interactions involved.
Analysis The balanced combustion equation is

(a) At 1800 R, water exists in the gas phase. Using the ideal-gas relation for
both the reactants and the products, the final pressure in the tank is deter-
mined to be

Substituting, we get

Pprod 1 1 atm2a

4 lbmol

4 lbmol

ba

1800 R

537 R

b3.35 atm

PreactVNreactRuTreact

PprodVNprodRuTprod

f¬PprodPreacta

Nprod

Nreact

ba

Tprod

Treact

b

CH 41 g 2 3O 2 SCO 2 2H 2 OO 2

Q

#

outm

#q

out^1 0.05 kg>min^21 8270 kJ>kg^2 413.5 kJ>min6.89 kW

363,880 kJ>kmol of C 3 H 8

¬
1 28.2 kmol N 22310 47,073
86692 kJ>kmol N 24

¬
1 2.65 kmol O 22310 49,292
86822 kJ>kmol O 24

¬
1 4 kmol H 2 O 231
241,82057,999
99042 kJ>kmol H 2 O 4

¬
1 0.3 kmol CO 231
110,53047,517
86692 kJ>kmol CO 4

¬
1 2.7 kmol CO 2231
393,52071,078
93642 kJ>kmol CO 24

¬ 1 28.2 kmol N 22310  8141
86692 kJ>kmol N 24

¬ 1 7.5 kmol O 22310  8150
86822 kJ>kmol O 24

Qout 1 1 kmol C 3 H 8231 
118,910h 298 
h 2982 kJ>kmol C 3 H 84