Direct Energy, 2018a

9 BATTERIES AND FUEL CELLS 221
quotient, and its natural log is between zero and one.
( )
[products]
0 ≤ ln
≤ 1 (9.34)
[reactants]
When a battery is rst set up, there are many reactants but fewproducts
present, and
( )
[products]
ln
≈ 0. (9.35)
[reactants]
In this case, the activity quotient is very small, so the practical cell voltage
between the terminals is very close to the theoretical cell voltage. After a
battery has been discharging for a long time, the activity quotient is large
because many products are present.
( )
[products]
ln
≈ 1 (9.36)
[reactants]
As expected, this model shows that as a battery discharges, the dierence
between the theoretical and practical cell voltage grows. We cannot ever
use the entire capacity stored in a battery. As the battery discharges, the
voltage between the terminals drops. At some point, the voltage level is
too lowto be useful, and the end voltage is reached. At this point, the
battery should be replaced even though it still has some stored charge.
The Nernst equation is useful to chemists because it can be used to
solve for the amount concentration of reaction products and reactants.
The theoretical cell voltage can be calculated or found in a table, and the
practical cell voltage can be measured with a voltmeter. Reference [137]
tabulates components of the activity quotient as a function of temperature
for various reactions.
Electrical engineers may be more interested in the Nernst equation because
it gives information on the eciency of batteries and fuel cells. Eciency
is dened as the output power over the input power or the output
energy over the input energy.
η eff = E out
E in
(9.37)
Energy stored in an electrical component is given by Eq. 2.8 where Q is
charge and V is voltage. The amount of charge involved in each reaction is
given by number of electrons involved times their charge for each, Q = qN v .
E in = 1 2 qN vV cell theor (9.38)