the ions ti is reduced, since ti = Ze/(Zi+Ze). This causes an additional reduction in
the output voltage.
In addition to a reduced output voltage, there will also be additional heat generation.
The total amount of Joule heating is the sum of that due to the passage of
current into the external circuit Iext and that due to electrochemical self-discharge.
Pth = I2
extZi+I2
e (Zi+Ze) (1.32)
In most cases, the first term is considerably larger than the second term.
Measured discharge curves vary with current density as conditions increasingly
deviate from equilibrium. This is shown schematically in Fig. 1.14.
A parameter that is often used to indicate the rate at which a battery is discharged
is the so-called C-Rate. The discharge rate of a battery is expressed as C/R, where
R is the number of hours required to completely discharge its nominal capacity.
For example, if a cell has a nominal capacity of 5 Ah, discharge at the rate of
C/10 would fully discharge it in 10 h. Thus the current is 0.5 A. And if the discharge
rate is C/5 the discharge current is 1 A.
Although the C-Rate is often specified when either complete cells or individual
electrodes are evaluated experimentally, and the current can be specified, this
parameter is often not time-independent during real applications. If the electrical
load is primarily resistive, for example, the current will decrease as the output voltage
falls. This means that the C-Rate drops as the battery is discharged. Nevertheless,
it is often important to consider the C-Rate when comparing the behavior of
different materials, electrodes, and complete cells.
It is obvious that not only the average voltage, but also the charge delivered, can
vary appreciably with changes in the C-Rate. In addition, the amount of energy that