Modern Engineering Thermodynamics

638 CHAPTER 15: Chemical Thermodynamics
WHO INVENTED THE FUEL CELL? Continued
ax
hy
ax hy ax hy ax hy ax hy
FIGURE 15.14
Grove’s fuel cell/battery.
Fuel cell technological development continued sporadically throughout the 19th century until the dramatic technological
developments produced by the American inventor Thomas Alva Edison (1847–1931). Edison’s development of the lightbulb
and associated electrical generating and distribution system technology completely dominated the development of
electrical technology for 50 years. Beginning in the 1960s, with the emergence of the United States space program, interest
in fuel cell technology was rekindled and its development continues today. The outstanding energy conversion capability of
fuel cells plus their low pollution potential and wide variety of operating fuels make fuel cells one of the leading contenders
for heat engine replacement in the 21st century.
and if the system has isothermal boundaries at temperature T b , then the entropy rate balance gives its heat transport
rate as
_Q = T b
∑
out
_m i s i −∑
in
! !
_m i s i − _S P = T b ∑ _n i s i −∑ _n i s i − _S P
out in
Combining these two equations and using the definition of the molar specific Gibbs function, g = h − Ts, gives
_W = ∑
in
= ∑
in
= ∑
in
_m i ðh − T b sÞ i
−∑
out
_m i ðh − T b sÞ i
− T b
_S P
_n h − T b s −∑ _n
i i h − T b s i − T b S _ P
(15.40)
out
_n i g i −∑ _n i g i − T b
_S P
out
where we assume that the temperature of the fuel cell reactants and products are the same as the system boundary
temperature (i.e., T R = T P = T b ). Note that the second law of thermodynamics requires that _S P ≥ 0:
We can now calculate the “reaction efficiency,” η r , with the following general formula:
η
The desired result
_W
_W
r = =
=
What it costs
_m i h i
or
η r =
∑
in
_m i g i −∑
out
_m i h i −∑
out
∑
in
∑
in
_m i g i − T b
_S P
_m i h i −∑
out
_m i h i
=
∑
in
∑
in
∑
in
_n i h i −∑ _n i h i
out
_n i g i −∑ _n i g i − T b
_S P
out
(15.41)
_n i h i −∑ _n i h i
out