Modern Engineering Thermodynamics

15.16 Chemical Availability 641
and, since the enthalpies and Gibbs functions of formation of the elements H 2 and O 2 are always zero, the maximum reaction
efficiency becomes (using Tables 15.1 and 15.7)
ðη r
Þ max
= ðg°Þ f H2OðÞ
l
h° 237:178 MJ/kgmole
=
f
285:838 MJ/kgmole = 0:830
H2OðÞ
l
or 83%. The theoretical open circuit voltage can now be determined from Eq. (15.48) as
" #
ϕ o = ∑ ðn i /n fuel Þh i −∑ ðn i /n fuel Þh i ð ηr Þ max /jF
R
P
h
= −ðn H2O/n H2 Þ h° i
f ð ηr Þ
H2OðÞ
l max /jF
=
− ð 1 kgmole H2 O/kgmole H 2 Þ − 285,838 KJ/kgmole H 2 O
ð2:00 kgmole electrons/kgmole H 2
= 1:23 V
ð Þ ð0:8298Þ
Þ 96,487 kJ/ ðV . kgmole electronsÞ
where j = 2.00 kgmole of electrons per kgmole of H 2 (i.e., the valence of 2H + ). Finally, Eq. (15.47) can be used to find
_W max /_n fuel = W max /n fuel = ϕ o jF
= ð1:23 VÞð2:00 kgmole electrons/kgmole H 2 Þ
× 96,487 KJ/ ðV . kgmole electronsÞ
= 237,000 kJ/kgmole H 2 = g°
f ðto significant figuresÞ
H2OðÞ l
Exercises
52. Determine the power produced by the fuel cell discussed in Example 15.18 per kilogram of H 2 rather than per kgmole
of H 2 . Answer: _W/ _m = 118,600 kJ/(kg H 2 ).
53. Determine the maximum thermal efficiency of the fuel cell discussed in Example 15.18 when the product H 2 Oisat
116°C = 700. R and 0.100 MPa and the reactants are at the standard reference state. Answer: (η T ) max = 90.1%.
54. What would the theoretical open circuit voltage be for the fuel cell discussed in Example 15.18 if product H 2 O was at
116°C = 700. R and 0.100 MPa and the reactants were at the standard reference state. Answer: ϕ 0 = 1.32 V.
Table 15.10 lists the maximum theoretical reaction efficiencies and open circuit voltages for a variety of fuel cell materials at
the standard reference state. Those reactions showing efficiencies greater than 100% must absorb heat from the surroundings
to maintain steady state operation.
Table 15.10 Fuel Cell Maximum Reaction Efficiency and Open Circuit Voltage for Various
Fuels at 25.0°C and 0.100 MPa
Fuel Reaction
ϕ o ðVÞ ðη r Þ max
ð%
Þ
H 2 + 0:5ðO 2 Þ!H 2 OðlÞ 1.23 83.0
CO + 0:5ðO 2 Þ!CO 2 1.33 90.9
CðsÞ + O 2 ! CO 2 1.02 100.2
C 3 H 8 + 5ðO 2 Þ!3ðCO 2 Þ + 4ðH 2 OðgÞÞ 1.08 101.5
C 8 H 18 ðgÞ + 12:5ðO 2 Þ!8ðCO 2 Þ + 9ðH 2 OðlÞÞ 1.10 96.3
Note: Unlabeled elements and compounds are in a gaseous (g) physical state.
15.16 CHEMICAL AVAILABILITY
In Chapter 10, we define the thermodynamic property availability as the maximum reversible useful work that can be
produced by a system. Equation (15.43) describes the rate of work produced or absorbed by a steady state, open
system with negligible flow stream kinetic and potential energies. This equation becomes the maximum reversible
work rate when there are no losses within the system, or _S P = 0. Since this equation focuses on the energy