Current Related Heat Effects

Current flow through any conducting object generates heat proportional to the

voltage drop caused by the current itself according to

dQJoule=dt . DU? i e35T

with Qj: generated heat (Joule effect) (J); t: time (s); DU: Lenovo 57Y6309 battery voltage drop caused by the

current (V); i: current (A). This heat is called the Joule effect; it always means loss of

energy.


Note: Strictly speaking, the negative absolute value should be used in Eq. (35) for

consistency with the arithmetical sign of the Lenovo L09S6D21 thermodynamic parameters (lost energy

always has the negative sign).

In an electrochemical cell, the voltage drop caused by the current is represented by

the difference between the cell voltage under current flow (U) and the open circuit

cell voltage (Uo). Then the Joule effect reads according to Eq. (35):

dQJoule=dt . eU UoT ? i =W e36T


or its integrated form for a period t (in hours):

QJoule . Z t

0feU UoT ? igdt =Wh e37T

Note: U Uo means polarization. It includes the voltage drop caused be current flow

through electronic resistance as well as the FUJITSU FPCBP119 electrolyte, but also overvoltage caused by

kinetic hindrance of the reaction. For heat effects this is not relevant, since heat

generation is proportional to polarization. U Uo does not remain constant during


charging or discharging, because it is related to the internal resistance, which usually

increases with proceeding discharge, because of the lower conductivity of the discharged

products.



1.4.3 Heat Generation in Total

Summation of the Joule effect and the reversible heat effect gives the total heat

generated in the cell or the battery, which means

Qtotal . QJoule t Qrev =Wh e38T

as energy, e.g. Wh, or as work per time unit:


dQtotal

dt .

dQJoule

dt t

dQrev

dt

=W e39T

Depending on the sign of dQrev=dt, the total energy generation may be larger or

smaller than the Joule effect.


According to Eq. (36), dQJoule=dt can be substituted by eU UoT ? i and gives

dQtotal

dt . eU UoT ? i t

dQrev

dt e40T

Substitution of dQrev=dt through Eq. (32) and application of Eq. (33) results in the

simple relation that is convenient for heat calculations:

dQtotal

dt . eU UcalT ? i e41T


Note: Strictly speaking, Eq. (41) should have the negative sign according to

thermodynamic parameters, since the Joule effect is always lost energy, as mentioned

in connection with Eq. (35). To overcome this difficulty, Qgen . Qtotal is introduced

in Section 1.4.5.

1.4.4 Examples for Heat Generation in Lenovo 51J0499 Battery

To illustrate the possibility of heat calculations, four examples will be shown in this

section, concerning lead-acid and nickel/cadmium batteries. The thermodynamic

data that determine the equilibrium values are listed in Table 1.3. The Toshiba PA3788U-1BRS also


Table 1.3 Thermodynamic data of lead-acid and nickel/cadmium batteries and water decomposition.

1 2 3 4 5

1 System Lead-acid battery Ni/Cd batterya Water decomposition

2 Cell reaction Pb t PbO2 t 2 ?H2SO4 ) 2 ? PbSO4 t 2 ?H2O

NiOOH t Cd ) NieOHT2 t CdeOHT2

H2O ) H2 t 1=2O2

3 DHs Eq. (4) 359.4 kJ & 282 kJ 285.8 kJ

4 DGs Eq. (4) 372.6 kJ & 255 kJ 237.2 kJ


5 TDSs . Qrev Eqs. (4), (31) 13.2 kJ & 27 kJ 48.6 kJ

6 Uo;s Eq. (5) 1.931V &1:3V 1.227V

7 Qrev=DGs 3.5% &11% 20.5%

8 Ucal Eqs. (33),

(34)

Uo 0:068V &1:44V 1.48V

a Actually these reactions are much more complex, and exact values of the thermodynamic data are not available (cf., e.g.


Section 5.2.2.1 in Ref. 5).



shows corresponding data of water decomposition that always occurs in batteries

with aqueous electrolyte as an unavoidable secondary reaction when the voltage of

1.227V is exceeded. In toshiba PABAS22 valve-regulated lead-acid and sealed nickel/cadmium

batteries, instead of water decomposition the internal oxygen cycle is the important

reaction that carries most of the overcharging current (cf. Sections 1.8.1.5.2, 1.8.3.2

and 1.8.5.2.6).

Heat generation in a battery is decisively affected by the distribution of the

charging current between the various reactions, because of 9 Cell SONY VGP-BPL12 specific heat

generation. This is illustrated in Fig. 1.10.

In a vented lead-acid battery heat effects during charging are caused by the


charging reaction itself and by water decomposition that accompanies the charging

process at an increasing rate with increasing cell voltage. The charging reaction is a

very fast one which means that overvoltage is small. At an assumed internal

resistance of 4.5 mV/100 Ah, a charging current of 1A causes polarization of only

4.5mV and the resulting heat generation would be DU? i . R? i2 . 4:5mW, which is

represented only as a line at the bottom of the left column in Fig. 1.10. The reversible


heat effect, on the other hand, is determined by the amount of converted material

(formula mass that is proportional to current) and amounts to 0.07W/A.

Most of the energy that is employed for water decomposition escapes from the

cell as energy content of the generated gases. This energy consists of the two

components:

1. The ‘decomposition energy of water’, which means the product current


times 1.23 V.

Figure 1.10 Heat generation in a vented lead-acid battery by the charging reaction and by

water decomposition, relative to a current of 1 A. Assumed internal resistance 4.5mO per

100 Ah of nominal capacity as in Fig. 1.11.



2. The reversible heat effect, which amounts to about 20% of the Dell XX327 converted


energy and means cooling of the cell during electrolysis (Column 5 in

Table 1.3), and a corresponding increase of the XX337 energy content of the gas.

Both shares are proportional to the amount of decomposed water, which again is

only determined by the current i as the product Ucal ? i . 1:48Wh=A.

The portion of heat that remains within the cell is generated by Joule heating


and determined by polarization of the water-decomposition reaction, i.e. by eU 1:48T ? i eWhT and increases with cell voltage as shown in Fig. 1.10.

As an example Fig. 1.11 shows current distribution and heat generation in the

course of a charging/discharging cycle as it is customary for vented lead-acid

batteries in traction applications.

The voltage curve is shown at the top of the figure. The current-limited initial

step of charging is followed by a constant-voltage period at 2.4 V/cell. Equalizing


charging up to 2.65 V/cell is the final step of the charging schedule. Discharge is

assumed at constant current (I5.20 A/100 Ah). The broken line represents the

calorific voltage Ucal, the full line the actual discharge voltage U.

Figure 1.11 Charging/discharging cycle of a vented traction battery.

Lead-acid with tubular positive plates (Varta PzS), 500 Ah. Heat-generation values

referred to 100 Ah of nominal capacity. The figures in the bottom part represent heat


generation in total. The sum of the whole charging period amounts to 28.7 Wh/100 Ah.

Internal resistance 4.5mO per 100 Ah of nominal capacity.



The center part of Fig. 1.11 shows how the current is distributed to charging,

water decomposition, and discharging. During the initial stage, practically only

charging occurs; water decomposition can be neglected on account of the flat current


voltage curves for gas generation (cf. Fig. 1.19). Only when theAcer TravelMate 5100 Battery voltage approaches

the 2.4V level, the onset of water decomposition becomes noticeable. The broken

horizontal line marks the average voltage during this initial step. When subsequently

the cell voltage remains at 2.4 V, gas evolution is maintained at a roughly constant

rate (assuming that the potentials of the positive and negative electrodes do not


change too much). During the equalizing step, nearly all the current is used for water

decomposition on account of the progressively reduced charge acceptance. During

discharge, water decomposition again can be neglected because of the reduced cell

voltage.

At the bottom of Fig. 1.11, the heat generation is drawn as blocks that

represent average values for the corresponding sections of the charging/discharging


process. The distribution between reversible heat effect, charging, and water

decomposition is marked by different patterns of the areas concerned. The Acer Asprie 5050 Battery value

above each block is the total heat generation in Wh.

During the first stage of the charging process, gas evolution can be neglected.

The heat is mainly generated by the Joule effect, on account of the high current and


the rather high internal resistance of 4.5mO assumed for this example, which

corresponds to a battery with widely spaced tubular plates and causes a voltage drop

(polarization) of 180 mV. But the reversible heat effect also contributes noticeably to

heat generation, on account of the converted active material. (40Ah&85Wh is

Figure 1.12 Heat generation in valve-regulated lead-acid batteries by charging and

overcharging, referred to a current of 1 A.

When the Acer Asprie 3680 Battery internal oxygen cycle is established, almost all the overcharging current is

consumed by the internal oxygen cycle (center bar in the graph). The bar on the right

corresponds to a vented battery. Internal resistance assumed as 0.8mO per 100Ah of nominal

capacity, as in Fig. 1.13.




charged during this period, which means a reversible heat effect of about

3Wh.11 kJ.)

When 2.4V is reached, the current is reduced and, as a consequence, Joule

heating and the reversible heat effect caused by the charging reaction are reduced

too. But now the approximately constant gas evolution causes most of the generated

heat eeU 1:48T ? iT.

During the equalizing step, gas evolution (required for mixing of the

electrolyte) dominates. On account of the notebooks battery large difference between the actual

charging voltage and the calorific voltage of water decomposition, heat generation is

considerable, although the current is rather small (cf. Fig. 1.10).

During discharge, due to the small overvoltage, heat generation is also small,


and further reduced by the reversible heat effect that now causes cooling.

Heat generation in a valve-regulated lead-acid battery (VRLA battery) is

mainly determined by the internal oxygen cycle that characterizes this design. It

means that the overcharging current is almost completely consumed by the internal

oxygen cycle formed by oxygen evolution at the positive electrode and its subsequent

reduction at the negative electrode (cf. Section 1.8.1.5A)

Battery for notebook reversible heat effect equals that in Fig. 1.10, but Joule heating is much

smaller because of the lower internal resistance assumed in this example, which

corresponds to a modern valve-regulated lead-acid battery designed for high loads.

The most effective heat source is the internal oxygen cycle, since it converts all the

electrical energy employed for overcharging into heat within the cell, because the


reaction at the positive electrode is reversed at the negative one, and thus the

equilibrium voltage of this ‘cell’ would be zero. As a consequence, the cell voltage in

total means polarization that produces heat. For this reason, overcharging of valveregulated

lead-acid batteries must be controlled much stronger than that of vented

ones to avoid thermal problems.

The charging behavior of a valve-regulated type is shown in Fig. 1.13 that


corresponds to Fig. 1.11. The calculation assumes an initial charging period at

constant current of 40 A/100 Ah (26I5; voltage drop 32 mV), limited by the

charging device, and subsequent charging at 2.4V per cell. As an DELL Latitude D610 Battery

overcharging for 1.5 hours at 2.5V at a maximum current of 5 A/100 Ah is assumed,

which corresponds to the usual operation of a cycle regime of valve-regulated leadacid


batteries.

In the center of Fig. 1.13 the distribution of the current between charging and

internal oxygen cycle is shown. The current share, consumed by the internal oxygen

cycle is magnified by 10 during the initial phase and by two during equalizing. The

sum of charging current and internal oxygen cycle represents the charging current

(hydrogen evolution and grid corrosion equivalents are not considered, since they


are two orders of magnitude smaller than that of the internal oxygen cycle).

Actually, the current would slightly be increased by heating of the battery. This

increase also is not considered in Fig. 1.13.

The bottom part of Fig. 1.13 shows the heat generation by the various

processes. At the beginning, the reversible heat effect dominates heat generation due

to the high amount of material that is converted. Joule heating is proportional to the


voltage drop, caused by the current flow. The m1210 battery relation between the reversible heat

effect and Joule heating is determined by the internal resistance of the battery. With

batteries of higher internal resistance, Joule heating would dominate during this

initial stage of the charging process. This applies, for example, to Fig. 1.11 where the


calculation is based on an internal resistance of 4.5mO/100 Ah, corresponding to a

larger traction battery with tubular plates.

When the charging voltage is reached, the current decreases and this applies

also to heat generation due to the reversible heat effect and Joule heating, while heat

generation by the internal oxygen cycle remains constant, according to the constant

cell voltage (which actually would slightly be increased by heating up).

Figure 1.13 Charging of a VRLA battery at 2.4 V/cell, calculated curves, constant

temperature, and 100% of recombination efficiency assumed. Internal resistance 0.8mO (single

cell). 1.5 hours equalizing at 2.5 V/cell at a current limit of 5 A. Heating of the battery during

charging is not considered. Heat generation: reversible heat effect 5.7 Wh; Joule heating

2.3 Wh; internal oxygen cycle 23.2 Wh; in total: 31.2 Wh.

Figure 1.13 shows the strong heating effect caused by the internal oxygen cycle.

The current share consumed by this reaction is very small and had to be magnified to

be recognized in the current comparison. But the total heat generation is largely

determined by the internal oxygen cycle, especially during the equalizing step that in

Fig. 1.13 causes 13.5Wh of heat, and so nearly half of the lenovo x200 battery heat generated in total.


Actually, an even larger heat generation is to be expected, since, as already

mentioned, the calculation did not consider the heat increase within the cell during

charging that again would increase the rate of the internal oxygen cycle.

In nickel/cadmium batteries the reversible heat effect is larger than that in leadacid

batteries and has the opposite sign, i.e. it acts as a cooling effect during charging

and contributes additional heat during discharge (cf. Table 1.3). As a consequence,


vented nickel/cadmium batteries are more in danger of being overheated during

discharging than during charging. This is different for sealed nickel/cadmium

batteries where the internal oxygen cycle is a most effective heat source when the

battery is overcharged (cf. Fig. 1.15).

Figure 1.14 shows heat generation in a vented nickel/cadmium battery when

charged and discharged with a constant current (5 hour rate) and the charging


voltage is limited to 1.65 V/cell. The calculation is based on the equilibrium voltage

Uo.1.3V (Table 1.1) and the latitude d830 battery calorific voltage Ucal.1.44V (Table 1.3). Due to the

uncertain thermodynamic data, these calculations are only rough approximations,

but correspond with practical experience.

During the initial two sections of the charging period, slight cooling is observed


on account of the reversible heat effect that consumes heat at a constant rate

proportional to the current. With increasing cell voltage, Joule heating is increased,

and when the charging voltage exceeds 1.48 V/cell, water decomposition contributes

an increasing amount of heat, since its calorific voltage is exceeded (Column 5, Line 8

in Table 1.3 and Fig. 1.10). Thus, during the final sections of the charging period, a

growing amount of heat is generated.

In total 12.3Wh were generated during discharging, while heat generation

during charging only amounted to 9.25 Wh. The main reason is that the reversible

heat effect generates additional heat during discharge, while it compensates for heat

generation during charging.

The latitude d800 battery is different for sealed nickel/cadmium batteries, due to the


internal oxygen cycle. Figure 1.15 illustrates the heat evolution of a sealed nickel/

cadmium battery during constant-current charging with a charge factor of 1.4 (such

an amount of overcharge is usual for conventional charging methods but can only be

applied to comparably small batteries <10 Ah).

. The voltage curve at the top shows the gradual increase of charging voltage


with charging time. The generated heat is calculated as an average value for

different sections of this curve. The numbers beside the charging curve are

the average voltages (V per cell) for the corresponding section.

. The middle figure shows the (constant) current and its distribution between

charging process and internal oxygen cycle.

. The bottom figure shows the heat generation as average value for the


different sections. The numbers are the heat in kJ (for comparison,

converted to 100 Ah of nominal capicity). During the first 2 hours, the



reversible heat effect exceeds the Joule effect and cooling is observed. So the

number for this section is written below the zero line.

When the charging process approaches completion, nearly all the current is used for


the internal oxygen cycle, which causes much heat generation.

Battery manufacturers usually strongly advise the customer not to charge

sealed nickel/cadmium batteries at constant voltage without monitoring, because of

this heat generation on account of the internal oxygen cycle. Since this cycle can

attain extremely fast rates, the situation is very dangerous in regard to thermal

runaway.

Altogether 264.7 kJ.73.53Wh of heat are generated, referred to a nominal

capacity of 100 Ah. These figures are much larger than the 31.2Wh/100 Ah of the

valve-regulated lead-acid battery in Fig. 1.13. The main reason for the high heat

generation of the sealed nickel/cadmium battery in Fig. 1.15 is the high charge factor

of 1.4. The charging factor for the FUJITSU FPCBP119 lead-acid battery in Fig. 1.13 is only about 1.10.


Figure 1.14 Heat generation during charge and discharge of a vented nickel/cadmium

battery. Charging with constant current I5 (5 hour rate) until 1.65 V/cell is reached. Discharge

also with I5.

In the top part, sections are shown that were used to calculate the average heat

generation, shown in the bottom part. The calorific voltage of 1.44V is shown as the broken

line. The difference U Ucal determines the effect of heating or cooling. (Calculation based on


Uo.1.3 V; Ucal.1.44 V.) VARTA TS-type values referred to 100 Ah of nominal capacity.

This indicates the strong influence of overcharging on heat generation in sealed or

valve-regulated batteries caused by the internal oxygen cycle.

Figure 1.15 shows that this heat is generated practically during the last 3 hours

of the charging process, and means an average heat generation of 24.51W/100 Ah


for these 3 hours. The conclusion can be drawn that sealed nickel/cadmium batteries

can be charged at a high rate as long as the current is actually used for charging and

not for the internal oxygen cycle. Rapid charging methods, as described in Section

13, are always based on this principle.

Figure 1.15 Charging of a sealed nickel/cadmium battery with constant current 0.2 C(A).

During 7 hours 140% of the nominal capacity are recharged, which corresponds with a charge


factor 1.4. For comparison, all values are converted to 100 Ah of nominal capacity. Actually,

batteries of this type and for such a charging schedule are only available in sizes <10 Ah.

Middle: current distribution between charging and internal oxygen cycle.

Bottom: heat generation as an average of the different sections (slight cooling during the

first 2 hours).

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