Here is an Appendix that was added to the CRPS paper when it was published in "Critical Reviews in Plant Sciences". Sorry about the fonts, they got scrambled during a copy and paste. In the original h sub 1 etc. was eta sub 1 designating efficiency. The bottom line is that the author estimates that a fuel cell vehicle running on ethanol and converting it to hydrogen and then to shaft power would have an energy efficiency of only 38% not 60% as assumed in some studies (guess which ones>). Footnote 68 is a bit of a mess but I left it in. I gave up trying to fix "Delta H superscript 0 subscript f".
Dave: If the following violates any site rules please delete it.
APPENDIX: EFFICIENCY OF A FUEL CELL SYSTEM
In their Science paper, Deluga et al. (2004) claim the
following:
. ..Further, combustion used for transportation has .20% efficiency
as compared with up to 60% efficiency for a fuel cell . . . The
efficiency of these processes for a fuel cell suggests that it may be
possible to capture >50% of the energy from photosynthesis as electricity
in an economical chemical process that can be operated at
large or small scales. (p. 996)
Following Deluga et al.,Patzek (2004) used 60 percent as
an estimate of the overall efficiency of a hydrogen fuel cell car.
Even this optimistic estimate could not make the industrial corn-ethanol
cycle sustainable to within a factor of two. Not so with
sugarcane ethanol. It might be called somewhat sustainable if
the path from the ethanol to electric shaft work were 60 percent
efficient.
First, we assume that the cane ethanol-water mixture used to
generate hydrogen is analytically pure C2H5OH and H2O. Thus,
there are no other contaminants to poison 65 the delicate catalyst
that will convert this EtOH-H2O mixture to hydrogen, carbon
dioxide and carbon monoxide (Deluga et al., 2004). The catalyst
is made of a rare-earth metal, rhodium,66 and a Lanthanoid,
cerium. 67 The catalytic reaction is claimed to have 100 percent
selectivity and >95 percent conversion efficiency. We assume
the conversion efficiency h1=0.96.
After Bossel (2003) we summarize efficiency of a Proton
Exchange Membrane (PEM) fuel cell as follows. In fuel cells,
gaseous hydrogen is combined with oxygen to water. This process
is the reversal of the electrolysis of liquid water and should
provide an open circuit voltage of 1.23 V (volts) per cell. Because
of polarization losses at the electrode interfaces the maximum
voltage observed for PEM fuel cells is between 0.95 and
1.0 V. Under operating conditions the voltage is further reduced
by ohmic resistance within the cell. A common fuel cell design
voltage is 0.7 V. The mean cell voltage of 0.75 V may be representative
for standard driving cycles. Consequently, the average
energy released by reaction of a single hydrogen molecule is
equivalent to the product of the charge current of two electrons
and the actual voltage of only 0.75 V instead of the 1.48 V corresponding
to the hydrogen high heating value.68 Therefore, in
automotive applications, PEM fuel cells may reach mean voltage
efficiencies of
h2=0.75 V/1.48 V =0.50 [10]
However, there are more losses to be considered. The fuel cell
systems consume part of the generated electricity. Typically, automotive
PEM fuel cells consume 10 percent or more of the
rated stack power output to provide power to pumps, blowers,
heaters, controllers, etc. At low power demand the fuel cell efficiency
is improved, while the relative parasitic losses increase.
The small-load advantages are lost by increasing parasitic losses.
Let us assume optimistically that for all driving conditions the
net power output of an automotive PEM fuel cell system is about
h3=0 9 of the power output of the fuel cell stack.
Depending on the chosen drive train technology, the DC
power is converted to frequency-modulated AC or to voltage-adjusted
DC, before motors can provide motion for the wheels.
Energy is always lost in the electric system between fuel cell
and wheels. The overall electrical efficiency of the electric drive
train can hardly be better than h4=0 9.
By multiplying the efficiency estimates, one obtains for the
maximum possible tank-to-wheel efficiency of a hydrogen fuel
cell vehicle
h=h1*h2*h3*h4=0.96 ×0.50 ×0.90 ×0.90 =0.38 [11]
or 38 percent. This optimistic estimate agrees exactly with an-other
analysis (31 to 39 percent) (Fleischer and Ørtel, 2003), and
is significantly less than the 60 percent used by the promoters
of a hydrogen economy and hydrogen fuel cell vehicles.
65 The commercial ethanol fuel is very dirty by chemical catalysis
standards, but we will ignore this unpleasantness.
66 Rhodium is a precious metal whose price is about
US$30 000/kg, 3 ×more expensive than gold,
charts/rhodium.html.
67 The nanoparticles of cerium dioxide are called ceria, and cost
$250/kg,
68 According to Faraday’s Law, the standard enthalpy of combustion
of hydrogen, H 0
f =.285 9 kJ/mol, can also be expressed as an elec-trochemical
potential (“standard potential”) U 0
=.H 0
f /ne F =1.48
V with ne =2 being the number of electrons participating in the con-version
and F =96485 Coulomb/mol the Faraday constant.
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