
676 Chapter 13 Reacting Mixtures and Combustion
13.74 Carbon monoxide at 25C, 1 atm enters an insulated re-
actor operating at steady state and reacts completely with the
theoretical amount of air entering in a separate stream at 25C,
1 atm. The products exit as a mixture at 1 atm. Determine in
kJ per kmol of CO
(a) the exergy entering with the carbon monoxide.
(b) the exergy exiting with the products.
(c) the rate of exergy destruction.
Also, evaluate an exergetic efficiency for the reactor. Perform
calculations relative to the environment of Problem 13.63. Ig-
nore kinetic and potential energy effects.
13.75 Liquid octane (C
8
H
18
) at 25C, 1 atm and a mass flow
rate of 0.57 kg/h enters a small internal combustion engine op-
erating at steady state. The fuel burns with air entering the en-
gine in a separate stream at 25C, 1 atm. Combustion products
exit at 670 K, 1 atm with a dry molar analysis of 11.4% CO
2
,
2.9% CO, 1.6% O
2
, and 84.1% N
2
. If the engine develops
power at the rate of 1 kW, determine
(a) the rate of heat transfer from the engine, in kW.
(b) an exergetic efficiency for the engine.
Use the environment of Problem 13.63 and neglect kinetic and
potential energy effects.
13.76 Evaluate an exergetic efficiency for the gas turbine power
plant of Problem 13.36. Base exergy values on the environ-
ment of Problem 13.63.
13.77 Consider a furnace operating at steady state idealized as
shown in Fig. P13.77. The fuel is methane, which enters at
25C, 1 atm and burns completely with 200% theoretical air
entering at the same temperature and pressure. The furnace de-
livers energy by heat transfer at an average temperature of
60C. Combustion products at 600 K, 1 atm are discharged to
the surroundings. There are no stray heat transfers, and kinetic
and potential energy effects can be ignored. Determine in kJ
per kmol of fuel
(a) the exergy entering the furnace with the fuel.
(b) the exergy exiting with the products.
(c) the rate of exergy destruction.
Also, evaluate an exergetic efficiency for the furnace and com-
ment. Perform calculations relative to the environment of
Problem 13.63.
13.78 Coal enters the combustor of a power plant with a mass
analysis of 49.8% C, 3.5% H, 6.8% O, 6.4% S, 14.1% H
2
O,
and 19.4% noncombustible ash. The higher heating value of
the coal is measured as 21,220 kJ/kg, and the lower heating
value on a dry basis, (LHV)
d
, is 20,450 kJ/kg. The following
expression can be used to estimate the chemical exergy of the
coal, in kJ/kg:
where hc, oc, and nc denote, respectively, the mass ratio
of hydrogen to carbon, oxygen to carbon, and nitrogen to
carbon, and s is the mass fraction of sulfur in kg per kg of
fuel.
4
The environment is closely the same as in Problem 13.64,
but extended appropriately to account for the presence of sul-
fur in the coal.
(a) Using the above expression, calculate the chemical exergy
of the coal, in kJ/kg.
(b) Compare the answer of part (a) with the values that would
result by approximating the chemical exergy with each of
the measured heating values.
(c) What data would be required to determine the chemical
exergy in this case using the methodology of Sec. 13.6?
Discuss.
13.79 For psychrometric applications such as those considered
in Chap. 12, the environment often can be modeled simply as
an ideal gas mixture of water vapor and dry air at temperature
T
0
and pressure p
0
. The composition of the environment is de-
fined by the dry air and water vapor mole fractions re-
spectively. Show that relative to such an environment the flow
exergy of a moist air stream at temperature T and pressure p
with dry air and water vapor mole fractions y
a
and y
v
, re-
spectively, can be expressed on a molar basis as
where and denote the molar specific heats of dry air and
water vapor, respectively. Neglect the effects of motion and
gravity.
13.80 For each of the following, use the result of Problem 13.79
to determine the specific flow exergy, in kJ/kg, relative to an
environment consisting of moist air at 20C, 1 atm, 100%
(a) moist air at 20C, 1 atm, 100%.
(b) moist air at 20C, 1 atm, 50%.
(c) dry air at 20C, 1 atm.
c
pv
c
pa
RT
0
cy
a
ln a
y
a
y
e
a
b y
v
ln a
y
v
y
e
v
bd
1 ln a
T
T
0
bd R ln a
p
p
0
bf
e
f
T
0
e1y
a
c
pa
y
v
c
pv
2 ca
T
T
0
b
y
e
a
, y
e
v
,
0.0549
n
c
b 6740s
e
ch
1LHV2
d
a1.0438 0.0013
h
c
0.1083
o
c
Combustion products
at 600 K, 1 atm
Furnace
Heat transfer
Temperature = 60°C
Methane
(T
0
, p
0
)
Air
(T
0
, p
0
)
Figure P13.77
4
Moran, Availability Analysis, pp. 192–193.