For a commercial secondary cell, the polarization losses discussed in Section 7.4 are usually quite low when the cell is used as designed. Hence, most of the available chemical energy is converted into electrical work rather than heat. Nonetheless, heat generation plays an important role in cell performance, system design, battery safety, and useable cell life. This importance is partly due to the fact that, although the heat generation rates may be low, the thermal resistances of many cells and batteries are high. Thus, it is relatively difficult to remove heat from the interior of the cell. This challenge will be discussed in more detail as it relates to battery design in the next chapter. Here we address the fundamental processes.

Heat can be generated in electrochemical cells due to irreversible losses associated with kinetic and concentration overpotentials, by resistive or Joule heating associated with the flow of current in solution, and by reversible changes due to differences in the entropy of reactants and products. The expression used for heat generation in an electrochemical cell is

(7.20)

The first term on the right side is the current density multiplied by difference between the equilibrium potential and the cell voltage. All of the losses in the cell (ohmic, kinetic, and concentration) affect the cell voltage and therefore the rate of heat generation. As we have learned, these polarizations depend on the cell current and on the state of charge. The current is taken to be positive during discharge, and the cell potential is smaller than U. Therefore, the heat generation from this term is positive. During charge, the sign of the current changes (now negative) and the cell potential is larger than U, resulting again in a positive rate of heat generation. In other words, polarization losses in the cell always result in heat generation. The second term on the right side of Equation 7.20 is the entropic contribution, which can be negative or positive. This quantity can be determined from the change in the equilibrium potential of a cell with temperature.

Heat generation data, such as those shown in Figure 7.11, are generally the result of detailed experiments or models. Such data are critical for accurate simulation of battery performance. Another important point is that the heat generation rate increases nonlinearly. Heat generation is small at low rates of charge or discharge, but increases dramatically with current.

ILLUSTRATION 7.5

A small 1.6 A·h cell has a volume of 1.654 × 10⁻⁵ m³ and an internal resistance of 50 mΩ. Assuming that the cell is ohmically limited, calculate the rate of heat generation at 0.25, 1, and 5 C neglecting the entropic term.

If the cell is ohmically limited, then

The current is simply the capacity in A·h, Q, times the C-rate

Thus, the heat generation normalized by the volume of the cell is

Values for 0.25, 1, and 5 C are 0.48, 7.74, and 194 W L⁻¹. The rate of heat generation is quadratic function of the current or C-rate.

ILLUSTRATION 7.6

Calculate the cell potential that corresponds to zero heat generation for the LiSOCl₂ battery.

Data for the equilibrium potential for a primary lithium thionyl chloride battery are shown in the figure. A small decrease in U with increasing temperature is typical of most batteries. Based on a linear fit of the data, the slope of the curve is −0.228 mV·K⁻¹. Using Equation 7.20,

Therefore,

The potential is 3.723 V. This potential is called the thermoneutral potential and represents as condition where there is some current, but no heat flows into or out of the cell. At 25 °C, U is 3.657 V. This equilibrium potential is less than the thermoneutral potential, therefore a small charging current would be required to achieve the condition of zero heat generation. Since this is a primary cell, this condition would not occur.