Modern Engineering Thermodynamics

Problems 649
77. Determine the molar specific entropy of formation s f ° for (a)
methane (CH 4 ), (b) acetylene (C 2 H 2 ), and (c) propane (C 3 H 6 ).
78. Determine the molar specific entropy of formation s f ° of liquid
octane C 8 H 18 (l), and explain why it is negative.
79.* Determine the specific molar Gibbs function of formation g f ° at
25.0°C and 0.100 MPa for the reaction C + O 2 ! CO 2 , and
compare your result with the value given in Table 15.7.
80.* Use Eq. (15.35) and Table C.17 to find the molar specific Gibbs
function of formation at 25.0°C and 0.100 MPa of atomic
hydrogen gas from the equilibrium reaction H 2 ⇄ 2H:
81. The equilibrium constant for the reaction
0:5ðN 2 Þ + 0:5ðO 2 Þ ⇄ NO is 0.0455 at 4500. R and atmospheric
pressure. Assume that air at room temperature and atmospheric
pressure contains 21.0% oxygen and 79.0% nitrogen on a molar
basis.
a. As the dissociation occurs, does the total number of moles in
the reaction (i) increase, (ii) decrease, or (iii) remain constant?
b. The equilibrium constant formula (K e ) for the dissociation
equation is which of the following? (a)
pNO
(c) p ffiffiffiffiffiffiffiffiffiffiffi
pN 2
pO 2
(d) ðpNOÞ2
pN 2
pO 2
pNO
(b) pN 2 pO 2
pN 2
pO 2
pNO
c. Air at 4500 R and atmospheric pressure contains what
percentage of NO on a molar basis? (a) 0.617, (b) 1.803,
(c) 4.55, (d) more than 4.55, (e) less than 0.617.
82.* Determine the equilibrium constant (K e ) for the reaction
CH 4 + H 2 O ⇄ CO + 3ðH 2 Þ at 25.0°C and 0.100 MPa.
83.* Algebraically solve the cubic equation given in Example 15.15
for the degree of dissociation (y) and use Table C.17 to verify
the three example computer results given there for
a. p m = 0:100 MPa, T = 2000: K:
b. p m = 0:100 MPa, T = 3000: K:
c. p m = 1:00 MPa, T = 3000: K:
84.* Carbon is burned with 100.% excess oxygen to form an equilibrium
mixture of CO 2 ,CO,andO 2 at 3000. K and 1.00 MPa pressure.
Determine the equilibrium composition when only the CO 2
dissociates as CO 2 ⇄ CO + 0:5ðO 2 Þ: Assume ideal gas behavior.
85.* The equilibrium constant for the water‒carbon monoxide
reaction CO + H 2 O ⇄ CO 2 + H 2 at 0.100 MPa and 1000. K is
K e = 1.442. Determine the equilibrium mole fraction of each gas
present under these conditions. Assume ideal gas behavior.
86. Determine the maximum reversible electrical work output of the
fuel cell shown in Figure 15.16, where g is the specific Gibbs
free energy.
Fuel
m = 0.0100 lbm/h
g = 20,000. Btu/lbm
FIGURE 15.16
Problem 86.
W E = ?
Fuel
cell
Products
m = 0.0100 lbm/h
g = 1000. Btu/lbm
87.* Determine the maximum theoretical efficiency, open circuit
voltage, and maximum theoretical work output per mole of
carbon consumed in a carbon‒oxygen fuel cell operating with
the reaction CðsÞ + O 2 ! CO 2 , when each component in the
reaction is at 25.0°C and 0.100 MPa.
88.* Repeat Example 15.18 for a fuel cell that operates on hydrogen
and 100.% theoretical air (instead of pure oxygen), each at
25.0°C and 0.100 MPa.
89.* Determine the maximum efficiency and open circuit voltage for
the methane‒oxygen fuel cell, CH 4 + 2ðO 2 Þ!CO 2 + 2½H 2 OðlÞŠ,
when each component in the reaction is at 25.0°C and
0.100 MPa.
90.* Repeat Problem 89 for the case where the reactants are premixed
to a total pressure of 0.100 MPa at 25.0°C.
91.* Determine the maximum efficiency and open circuit voltage for
the propane‒oxygen fuel cell,
C 3 H 8 + 5ðO 2 Þ!3ðCO 2 Þ + 4½H 2 OðlÞŠ, when each component in
the reaction is at 25.0°C and 0.100 MPa.
92.* Repeat Problem 91 for a propane‒air fuel cell in which the
propane is premixed with 200.% theoretical air at a total
pressure of 0.100 MPa and 25.0°C. Assume the combustion
products are also mixed and are at a total pressure of 0.100 MPa
at 25.0°C.
93.* An inventor claims to have perfected a hydrogen‒oxygen fuel
cell, H 2 + 0:5ðO 2 Þ!H 2 OðlÞ, that produces 300 MJ per kgmole
of hydrogen consumed at 25.0°C and 0.100 MPa. Is this
possible? If not, what is the maximum possible power output?
Assume each component in the reaction is at 25.0°C and
0.100 MPa.
94.* Determine the open circuit, internal entropy production rate per
unit molar flow rate of CO in the carbon monoxide‒oxygen fuel
cell, CO + 0:5ðO 2 Þ!CO 2 , when each component in the
reaction is at 25.0°C and 0.100 MPa.
95. An inventor claims to have invented a fuel cell that contains a
catalyst for the ammonia reaction N 2 + 3H 2 ! 2NH 3 at the
standard reference state. The molar enthalpy of formation of
ammonia = −19,750 Btu/lbmole and the Gibbs function of
formation of ammonia = −7140 Btu/lbmole. Determine
a. The maximum theoretical reaction efficiency.
b. The maximum theoretical electrical work output of this fuel
cell per lbmole of N 2 consumed.
Design Problems
The following are open-ended design problems. The objective is to
carry out a preliminary thermal design as indicated. A detailed design
with working drawings is not expected unless otherwise specified.
These problems have no specific answers, so each student’s designis
unique.
96. Design a burner for a furnace that will produce 2:00 × 10 6 Btu/h
at 1500. °F. Choose the fuel, flow rates, air/fuel ratio, burner
material, burner geometry, flow controls, and the like.
97. Design a bomb calorimeter to be used to measure the heat of
combustion of municipal solid waste. Because of the
heterogeneous nature of the waste, the test sample size must be
at least 1 lbm. Make the calorimeter either adiabatic or
isothermal. Assume all noncombustibles (e.g., metal, glass) have
been removed from the waste before it is tested.
98.* Design a system to produce 0.1 kg/h of hydrogen gas from the
catalytic reaction of methane and steam,
CH 4 + H 2 OðgÞ !3ðH 2 Þ + CO, at 1500. R and 14.7 psia. Assume
the system has an equilibrium composition of
CH 4 + H 2 OðgÞ !aðCH 4 Þ + b½H 2 OðgÞŠ + cðH 2 Þ + dðCOÞ