E10
Materials Science and Engineering Module:
Batteries and Fuel Cells
Fall Semester 2010
Thomas M. Devine
Department of Materials Science and Engineering
University of California, Berkeley
INTRODUCTION
The performance of a battery is largely described by plots of charging and discharging
curves.
The discharge curves were introduced in the second lecture.
“Discharge” means that
the battery is providing energy.
“Charge” means that energy is being stored in the
battery.
Both charging and discharging curves are graphs of voltage (vertical axis) vs
charge (horizontal axis;
units of amp hr or coulombs).
As shown in
Figure 1
, a discharge curve is a plot of the instantaneous cell voltage (e.g.,
V
cell
= V
1
) at a given value of the amount of charge (e.g., Q
1
) that has been discharged
by the operation of the battery at a constant value of cell current(I
1
).
There is a different
discharge curve for each value of cell current.
Note that the total amount of charge that a battery can provide decreases as the
discharge current increases.
In other words, the faster you discharge a battery, the less
is the total amount of charge the battery provides.
A charging curve graphs the instantaneous cell voltage at a given value of the amount
of charge that has been stored in the battery as a consequence of a constant value of
charging current.
As shown in
Figure 2
, there is one charging curve for each value of
charging current.
(Note: the curves should be smooth  I
!
m not a good artist.)
The higher the current used to charge the battery the larger is the total amount of
charge supplied to the battery.
Note that the maximum value of cell voltage, V
cell
max
, is identiFed in both Fgures.
The
numerical value of V
cell
max
is the same in both Fgures.
±urther on in these notes we
!
ll
discuss how V
cell
max
is calculated.
One of the objectives of the Materials Science and Engineering module is to explain the
shapes of the charge/discharge curves and the effects of cell current on the charge/
discharge curves.
1
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View Full DocumentThe selection of the most appropriate battery for a particular application is made by the
use of the charge/discharge curves and our discussion begins with analysis of the
charge/discharge curves.
DISCHARGE CURVES
Discussing the shape of a discharge curve is best done by comparing a “real” discharge
curve, such as that presented in
Figure 1
, to the “ideal” discharge curve.
The
comparison between real and ideal is presented in
Figure 4
.
First, note that the “ideal”
battery
!
s cell voltage is the maximum possible value, V
cell
max
, independent of the
battery
!
s state of charge (i.e., independent of how much charge the battery has already
provided). Second, in the “ideal” discharge curve, the total energy that the battery can
provide (i.e., the total amount of work that the battery can do) is independent of the rate
at which the battery provides the energy.
That is, for the “ideal” battery there is only one
discharge curve; it is that same curve independent of the value of the discharge current.
The total amount of work that the battery can do is equal to the area underneath the
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