How To Calculate Internal Heat Generation In Batteries

 
Internal heat generation during the operation of a cell or battery is a critical concern for the battery engineer.

If cells or batteries get too hot, they can rupture or explode.  And Lithium and Lithium-ion cells/batteries can catch on fire when they rupture, creating even more of a safety hazard.

To ensure safe operation over the entire intended operating range of a cell or battery, it is crucial that the battery engineer understands the fundamentals of internal heat generation and be able to calculate the expected adiabatic temperature rise of a cell or battery under any operating condition.  The objective of this article is to provide that fundamental understanding and the methodology for making those calculations.

Once the quantity of generated heat and the adiabatic temperature rise of the cell/battery have been determined, methods can be devised and implemented to reject the heat and maintain safe operating temperature levels.  This is the essence of safe cell/battery design, especially when high charge or discharge rates are to be employed.
 

Sources Of Heat Generation In a Battery:

There are two primary sources of internal heat generation in electrochemical cells and batteries during their operation:

● Heat from the electrochemical reactions

● Heat from polarization

In the following discussions, batteries are defined as being made up of multiple electrochemical cells. Thus, the cell is the basic building block.

The cell is also the entity to which the thermodynamic principles apply. Thus, the derivation of the fundamental equations will focus on the individual cell, recognizing that the quantity and rate of heat generation or absorption ultimately calculated can be readily scaled to multi-cell batteries. Examples will be provided to show how this is done.
 

Heat Generated By the Electrochemical Reactions:

The electrochemical reaction of a cell can either evolve heat or absorb heat depending on whether it is exothermic or endothermic. This heat is the result of the entropy change occurring during the course of the reaction. The quantity and rate of heat evolution/absorption can be calculated from thermodynamic principles, as follows.

The maximum electrical work obtainable from a cell is equivalent to the free energy of the electrochemical reaction at the reversible EMF. The free energy, in turn, is given by the following equation.

ΔG_r^o = ΔH_r^o – TΔS_r^o  [1]

where

ΔG_r^o = Standard free energy change of the electrochemical reaction (J/mol or cal/mol)

ΔH_r^o = Standard enthalpy change of the electrochemical reaction (J/mol or cal/mol)

T = Temperature (^oK)

ΔS_r^o = Standard entropy change of the electrochemical reaction (J/mol ^oK or cal/mol ^oK)

TΔS_r^o is a measure of the energy which is unavailable as electrical work and which appears as evolved or absorbed heat, depending on the direction and thermodynamics of the electrochemical reaction involved.  This heat is often called Entropic or reaction heat.

The Entropic heat evolved or absorbed per mole of the cell reactant(s) at the reversible EMF is:

Q_r = TΔS_r^o = ΔH_r^o – ΔG_r^o    [2]

where

Q_r = Quantity of Entropic heat generated or absorbed per mol of reactant by an electrochemical reaction at the reversible EMF (J/mol or Cal/mol)

The reversible EMF (E^o) of an electrochemical cell is related to its free energy by:

ΔG_r^o (J/mol)= -nFE^o      [3]

where

E^o = Reversible EMF (Open Circuit Potential) of an electrochemical cell (V)

n = Number of equivalents per mol of reactant involved in the electrochemical reaction

F = Faraday’s constant (96,485 coulomb/eq)

The negative sign in Equation [3] reflects the fact that (ΔG_r^o) is negative for spontaneous reactions, such as the discharge of an electrochemical cell.

Differentiating Equation [1] with respect to (T) yields:

(dΔG_r^o/dT)_P = -ΔS_r^o    [4]

Differentiating Equation [3] with respect to (T) yields:

(dΔG_r^o / dT)_P = -nF(dE^o/dT)_P     [5]

Equating Equations [4] and [5] yields a relationship for (ΔS_r^o) in terms of (E^o):

ΔS_r^o (J/mol ^oK)= -(dΔG_r^o/dT)_P = -[ -nF(dE^o/dT)_p] = nF(dE^o/dT)_p   [6]

Equation [6] now allows (ΔH_r^o) to be defined in terms of (E^o).

ΔH_r^o (J/mol) = ΔG_r^o + TΔS_r^o = -nFE^o + nFT(dE^o/dT)_P [7]

The total quantity of Entropic heat (Q_r) evolved or absorbed by the cell reaction is now given by:

Q_r (J/mol) = TΔS_r^o = ΔH_r^o – ΔG_r^o = -nFE^o + nFT(dE^o/dT)_P + nFE^o  =
nFT(dE^o/dT)_P    [8]

and

Q_r (cal/mol) = 0.239nFT(dE^o/dT)_P    [9]

The quantity (Q_rt) and rate (q_rt ) of Entropic heat generation/absorption from the electrochemical reaction during a period of operation can now be determined from the time and current as follows (note: by convention, the current is positive for the discharge reaction (spontaneous process) and negative for charging (non-spontaneous) process.  This convention maintains (ΔG_r^o) negative for the spontaneous discharge process).

First, (n) is defined as a function of current and time:

n = It / F      [10]

where

I = Current (A)

t = Time (sec)

Next, Equation [10] is substituted into Equation [9] to yield the equation for (Q_rt ) for the discharge reaction (positive I):

Q_rt (cal) = 0.239nFT(dE^o/dT)_P  = (0.239ItFT/F)(dE^o/dT)_P = 0.239ItT(dE^o/dT)_P   [11]

where

Q_rt = The quantity of Entropic heat generated or absorbed by an electrochemical reaction over (t) seconds of operation at current (I) (cal or J)

The rate of heat generation or absorption is determined by differentiating Equation [11] with respect to time:

q_rt (cal/sec) = (dQ/dt) = 0.239IT(dE^o/dT)_P      [12]

where

q_rt = The rate of Entropic heat generated or absorbed by an electrochemical reaction when operating at current (I) (cal/sec or J/sec)

If the electrochemical reaction is reversible, the Entropic heat generation or absorption and the rate of Entropic heat generation or absorption for the charging process can be determined by changing the sign of Equations [11] and [12] above from positive to negative.  This is due to the fact that, by convention, the charging current is negative. The equations then become:

Q_rt (charging, cal) = -0.239ItT(dE^o/dT)_P     [13]

q_rt (charging, cal/sec) = -0.239IT(dE^o/dT)_P     [14]

For both the charge and discharge process, if (Q_rt) is negative, heat is evolved (reaction exothermic) and heat is absorbed if (Q_rt) is positive. Under the latter conditions, the cell reaction would have a cooling effect on the cell.
 

Heat Generated By Polarization:

Polarization represents the voltage drop caused by the current flowing through the internal resistance of a cell and always results in heat generation (i.e. it is always exothermic).

The quantity and rate of heat generated by polarization is calculated as follows:

Polarization (η) is given by:

η = (E^o – E_L)      [15]

where

η = Cell polarization (V)

E_L = The potential of a cell under load (V)   

During discharge, the total heat generated by polarization (Q_Pt) over time (t) at current (I) is given by:

Q_Pt (J) = -It(E^o – E_L)    [16]

and

Q_Pt (cal) = -0.239It(E^o – E_L)    [17]

where

Q_Pt = Quantity of heat generated from polarization in a cell over (t) seconds of operation at current (I) (cal or J)

Here, once again by convention, the discharge current (I) is taken to be positive. The negative sign reflects the fact that polarization is always an exothermic process (negative value of (Q_Pt)). The discharge heat generation rate (cal/sec) from polarization is given by:

q_Pt (cal/sec) = (dQ_Pt/dt) = -0.239I(E^o – E_L)    [18]

where

q_Pt = Rate of heat generated from polarization in a cell when operating at current (I) (cal/sec or J/sec)

During charging, by convention, the current is given a negative value which changes the sign of equations [16] – [18] from negative to positive. Since, during charging, the load voltage (E_L) will be greater than (E^o), (Q_Pt) and (q_Pt) will both be negative, consistent with the fact that polarization is always exothermic. This is ohmic heating, just like what occurs in a light bulb or electric stove, and it doesn’t matter which way the current is flowing; heat will always be generated. The charging equations, expressed in (cal), are:

Q_Pt (cal) = 0.239It(E^o – E_L)    [19]

q_Pt (cal/sec) = (dQ_Pt/dt) = 0.239I(E^o – E_L)    [20]

 

Total Heat Generation/Absorption In an Electrochemical Cell:

The total rate of heat generation or absorption (q_Tt) during discharge of an electrochemical cell is equal to the sum of the rates of polarization heat generation and Entropic heat generation or absorption:

q_Tt (cal/sec) = q_Pt + q_rt = -0.239I(E^o-E_L) + 0.239IT(dE^o/dT)_P  =
-0.239I [(E^o – E_L) – T(dE^o/dT)_P ]   [21]

where

q_Tt = Rate of total heat generated or absorbed during the operation of an electrochemical cell at current (I) including both polarization heat and Entropic heating or cooling (cal/sec or J/sec)

The total heat evolved or absorbed by the cell (Q_Tt) during discharge over time (t) is given by:

Q_Tt (cal) = q_Ttt = -0.239It [(E^o – E_L) – T(dE^o/dT)_p ]  [22]

where

Q_Tt = Total quantity of heat generated or absorbed during the operation of an electrochemical cell for (t) seconds at current (I) including both polarization heat and Entropic heating or cooling (cal or J)

For charging, the rate and quantity of total heat generated or absorbed are obtained simply by changing the sign of Equations [21] and [22] from negative to positive, again reflecting the fact that the charging current is negative by convention. That is:

q_Tt (charging, cal/sec) = 0.239I [(E^o – E_L) – T(dE^o/dT)_P ]   [23]

Q_Tt (charging, cal) = q_Ttt = 0.239It [(E^o – E_L) – T(dE^o/dT)_p ]  [24]

lf a multicell battery is involved, then the total heat is the heat generated or absorbed by each cell multiplied by the number of cells in the battery (N). For example, during discharge, the total heat for a battery would be given by:

Q_Tt (cal) = -0.239ItN [(E^o – E_L) – T(dE^o/dT)_P ]  [25]

where

N = Number of cells in a battery

To be able to calculate the heat generated or absorbed during charge or discharge of a cell or battery, the following parameters must be known:

● I (A) (operational current flowing through each cell)

● t (sec) (operational time)

● E^o (V per cell) (average value over range of operation)

● E_L (V per cell) (average value over time of operation)

● (dE^o/dT)_p for the cell reaction (V/^oK)

● N (number of cells in battery if calculation is for a battery)
 
Example Calculation:
Consider discharge of a Li/SOCl₂ battery consisting of 5 individual cells in series. The input values for the calculation are:

● E^o = 3.65V per cell

● E_L = 3.20V per cell

● l=75A

● Run Time (t) = 48O sec (8 min)

● T = 344 ^oK (71 ^oC)

● N=5cells

● (dE^o/dT)_p = -0.0009705 V/^oK (Calculated from thermodynamic principles, as discussed later)

Since ((dE^o/dT)_p) is negative, the discharge process of this battery will be exothermic. The total heat generated during the 480-second discharge is calculated as follows:

Q_Tt (cal) = -0.239ItN [(E^o – EL) – T(dE^o/dT)_p ]

= -0.239*75* 480*5[(3.65-3.20) -(344) (-0.0009705) ]  = -33,721 cal

Breaking this down, the Entropic heat was -14,362 cal and the polarization heat was -19,359 cal. In percentages, the Entropic heat was 42.6 percent of the total heat and the polarization heat was 57.4 percent.

Unfortunately, some battery engineers neglect the Entropic heat, either because they think it is negligible or because they don’t know the value of (dE^o/dT)_p. However, this is a mistake.

As shown later in this article, (dE^o/dT)_p can be readily calculated from thermodynamic principles. And when the discharge is exothermic, the Entropic heat can be very significant, as shown in this example for a Li/SOCl₂ battery. Neglecting this heat can cause the total heat generation to be grossly underestimated, possibly leading to catastrophic results.

If the five cells in the battery were connected in parallel, the current would be divided equally among the five cells, resulting in less current per cell, a lower polarization level, and less heating.

In this case, the heat calculation would be as follows:

The input parameters would be:

E^o = 3.65V per cell

● E_L = 3.56V per cell

● l=75A / 5 = 15A per cell

● Run Time (t) = 48O sec

● T = 344 ^oK

● N=5cells

● (dE^o/dT)_p = -0.0009705 V/^oK

Here, the total heat generated during the 480-second discharge is calculated as follows:

Q_Tt (cal) = -0.239ItN [(E^o – EL) – T(dE^o/dT)_p ]

= -0.239*15* 480*5[(3.65-3.56) -(344) (-0.0009705) ]  = -3,647 cal

As can be seen, this heat is only about one tenth that of the series connected battery, thus demonstrating the significant benefits of lower currents. Putting cells in parallel is a great way to reduce heating if space allows for a larger battery.
 

Calculating the Bulk Adiabatic Temperature Change Of a Cell Or Battery From the Total Generated Or Absorbed Heat:

The bulk adiabatic temperature change of a cell or battery during operation is given by:

ΔT = -Q_Tt / m_TC_pT = -Q_Tt/C_T  [26]

where

ΔT = Adiabatic temperature change of the cell or battery (^oK)

C _PT = Weighted average specific heat of the cell or battery (cal/g^oK )

m_T = Total mass of cell or battery (g)

C_T = m_TC_PT = the overall heat capacity of the cell or battery  (cal/^ok)

The overall heat capacity (C_T) of the cell or battery is determined by summing the products of mass times specific heat for each component that makes up the cell or battery.  That is:

C_{T =} SUM(m_iC_pi)  (Summed over i=1 to n_c)   [27]

where

n_c = Number of components in the cell or battery

m_i = Mass of component (i) of the cell or battery (g)

C_Pi = Specific heat of component (i) of the cell or battery (cal/g^oK or J/g^oK)

 
Example Calculation:
The bulk adiabatic temperature rise for a single Li/SOCl₂ cell discharged under the conditions given in the previous example involving the series-connected cells is calculated as follows.

The first step is to calculate the heat generated per cell in the battery.

Q_Tt = -33,721 / 5 = -6,744 cal per cell

Next, the total heat capacity of the cell is calculated from the mass and specific heat of the individual components that make up the cell, as shown in the following table.

Component	Material	Mass (g)	Specific Heat (CPi) (cal/g oK)	Heat Capacity (Ci) (cal / oK)
Current Collectors	Nickel	284.8	0.106	30.19
Anode	Lithium Metal	9.56	0.849	8.12
Separator	Glass	5.52	0.265	1.46
Cathode	Carbon	7.02	0.160	1.12
Electrolyte Solution	1.5M LiAlCl4/SOCl2	41.4	0.202	8.36
Cell Case	Nickel	500	0.106	53.0
TOTAL (CT)				102.25

 
The bulk adiabatic temperature rise of the cell is then calculated as follows:

ΔT = -Q_Tt / C_T = -(-6,744) / 102.25 = 66.0 ^oK

 

Calculating (dE^o/dT)_P From Thermodynamic Principles:

(dE^o/dT)p can be calculated from thermodynamic principles as follows:  (note: Equations [1], [3], [4], [5], [6] and [7] are repeated here to show the complete derivation of (E^o/dT)_p ).

ΔG_r^o = ΔH_r^o – TΔS_r^o   [1]

(dΔG_r^o / dT)_p = -ΔS_r^o  [4]

ΔG_r^o (J/mol) = -nFE^o      [3]

(dΔG_r^o / dT)_P = -nF(dE^o/dT)_P  [5]

ΔS_r^o (J/mol ^oK)= -(dΔG_r^o/dT)_p = -[ -nF(dE^o/dT)_p ]= nF(dE^o/dT)_p [6]

ΔH_r^o (J/mol) = ΔG_r^o + TΔS_r^o = -nFE^o + nFT(dE^o/dT)_p [7]

Solving Equation [7] for (dE^o/dT)_p yields:

(dE^o/dT)_p = [ΔH_r^o + nFE^o ] / nFT =
(1/T) [E^o + ΔH_r^o / nF ]   (ΔH_r^o in joules) [28]

and

(dE^o/dT)_p = (1/T) [ E^o + 4.184 * ΔH_r^o / nF ]   (ΔH_r^o in calories)  [29]

 
Example Calculation:
Consider a Li/SOC1₂ cell, assuming the following electrochemical reaction.

4Li + 2SOCl₂  —-> 4LiCl + S + SO₂

The standard Enthalpy of Reaction (ΔH_r^o ) is calculated as follows:

First, the equation is rewritten in terms of one mol of lithium because lithium is the reactant typically tracked in lithium cells.

Li + 0.5SOCl₂  —-> LiCl + 0.25S + 0.25SO₂

The Heats of Formation (ΔH_f^o ) for the reactants and products are as follows (1):

● Li = 0 (Element)

● SOCL₂ = -49,200 cal/mol

● LiCl = -97,700 cal/mol

● S = 0 (Element)

● SO₂ = -70,960 cal/mol

The standard Enthalpy of Reaction (ΔH_r^o ) is then calculated as the sum of the Heats of Formation of the products minus the sum of the Heats of Formation of the reactants, with each Heat of Formation value multiplied by its stoichiometric coefficient.  That is:

ΔH_r^o  = [(1.0)(-97,700) + (0.25)(0) + (0.25)(-70,960)] – [(1.0)(0) + (0.50)(- 49,200)] = -90,840 cal/mol Li

The input parameters for the calculation of (dE^o/dT)_p are:

● E^o = 3.65V (open circuit potential of a Li/SOCl₂ cell)

● ΔH_r^o = -90,840 cal/mol Li

● T = 298 ^oK

● n=1 eq/mol Li

● F=96,485 coulomb/eq

● 4.184 J/cal (conversion factor to convert calories to joules)

● Volts = Joules/coulomb

(dE^o/dT)_p is then calculated as follows:

(dE^o/dT)_p = (1/T) [ E^o + 4.184 * ΔH_r^o / nF ]

= (1/298) [ 3.65 + 4.184 * -90,840 / (1 * 96,485) ] = -0.0009705 V / ^oK = -0.9705 mV / ^oK

This result is in good agreement with the value of -1.026 mV/^oK measured in a high precision calorimeter at Honeywell (1).  Again, the negative value of (dE^o/dT)p indicates that Entropic heat will be evolved during discharge and will contribute to cell heating.
 

Calculating the Thermoneutral Potential:

The Thermoneutral Potential (E^H) of an electrochemical cell is the potential where there will be no Entropic heating or cooling from the electrochemical reaction, thus rendering the cell thermally neutral with respect to that reaction.

The significance of the Thermoneutral Potential is that, during discharge, any load voltage occurring below the Thermoneutral Potential during operation will cause heat be evolved from the cell (i.e. be exothermic) and any load voltage above the Thermoneutral Potential will cause heat to be absorbed by the cell (be endothermic). For charging, the reverse is true: Load voltages below the Thermoneutral Potential are endothermic and load voltages above the Thermoneutral Potential are exothermic.

The Thermoneutral Potential is calculated as follows:

From Equation [1] we know:

ΔG_r^o = ΔH_r^o – TΔS_r^o    [1]

We also know that Entropic heating/cooling is given by (TΔS_r^o).

At the Thermoneutral Potential, there is no Entropic heating or cooling.  Thus, TΔS_r^o  = 0.

Therefore, the standard free energy change at the Thermoneutral Potential (ΔG_r^H ) is equal to the standard enthalpy of the electrochemical reaction:

ΔG_r^H  = ΔH_r^o  – TΔS_r^o  =  ΔH_r^o  – 0 =  ΔH_r^o  [30]

where

ΔG_r^H = The standard free energy change of an electrochemical reaction at the Thermoneutral Potential (J/mol or cal/mol)

In terms of potential,

ΔG_r^H (J) = -nFE^H  [31]

where

E^H = The Thermoneutral Potential (V)

From Equation [7], we get

ΔH_r^o  (J) = nFT(dE^o/dT)_P -nFE^o   [7]

Therefore, Equation [30] becomes:

-nFE^H = nFT(dE^o/dT)_P – nFE^o  [32]

Solving for (E^H) yields the equation for the Thermoneutral Potential:

E^H = E^o – T(dE/dT)_P  [33]

The total internal heat generation or cooling in a cell can now be expressed in terms of the Thermoneutral Potential, as follows:

Equation [22] gives the general expression for the total internal heat generated or absorbed during discharge:

Q_Tt (cal) = q_Ttt = -0.239It [(E^o – E_L) – T(dE^o/dT)_p ] [22]

Rearranging slightly gives:

Q_Tt (cal) = q_Ttt = -0.239It [-E_L + E^o – T(dE^o/dT)_p ] [34]

Substituting Equation [33] into Equation [34] gives:

Q_Tt (cal) = -0.239It [-E_L + E_H] = -0.239It [E_H – E_L] [35]

This equation shows that any discharge load voltage below the Thermoneutral Potential will be exothermic (negative Q_Tt) while any discharge load voltage above the Thermoneutral Potential will be endothermic (positive Q_Tt)

The rate of heat generation is obtained by differentiating Equation [35] with respect to time (t), thus giving:

q_Tt (cal/sec) = dQ_Tt/dt = -0.239I [E_H – E_L] [36]

For charging, the sign of Equations [35] and [36] is changed from negative to positive, reflecting the convention of charging current being negative. This gives:

Q_Tt (charging, cal) = 0.239It [E_H – E_L] [37]
q_Tt (charging, cal/sec) = 0.239I [E_H – E_L] [38]

Thus, for charging, any load voltage below the Thermoneutral Potential will be endothermic (positive Q_Tt) and any load voltage above the Thermoneutral Potential will be exothermic (negative Q_Tt).
 
Example Calculation:
The Thermoneutral Potential for a Li/SOCl₂ cell is calculated as follows:

The input parameters are:

● E^o = 3.65V

● T = 298 ^oK

● (dE/dT)_P = -0.0009705 V/ ^oK

Therefore,

E^H = E^o – T(dE/dT)_P = 3.65 – 298(-0.0009705)  = 3.939 V

Since this value is greater than the open circuit potential of a Li/SOCl₂ cell, the discharge process will be exothermic at all levels of current (i.e. at all polarization values).

Because the Li/SOCl₂ system is not reversible, charging currents do not apply.
 

Wrapping Up:

High energy batteries have become an integral part of modern-day life with just about every electronic device on the market using a Lithium-ion cell or battery of some type. Lithium-Ion batteries are now even the battery technology of choice for electric vehicles.

With this proliferation of Lithium-Ion cells and batteries in larger and larger numbers and sizes, thermal management becomes more important than ever.

Safety must be the number one priority for all cells and batteries used in consumer products and it is hoped that this article will give the battery engineer the knowledge and understanding to design and develop cells and batteries that are thermally safe and robust.
 

Nomenclature:

ΔG_r^o = Standard free energy change for a given reaction (cal/mol or J/mol)

ΔG_H^H  = Standard free energy change of an electrochemical reaction at the Thermoneutral Potential (cal/mol or J/mol)

ΔH_r^o = Standard enthalpy change for a given reaction (also called the Heat of Reaction) (cal/mol or J/mol)

ΔH_f^o  = Standard Enthalpy of Formation (also called the Heat of Formation) for an element or compound (cal/mol or J/mol)

ΔS_r^o  = Standard entropy change for a given reaction (cal/mol^oK or J/mol^oK)

T = Temperature (^oK)

ΔT = Adiabatic temperature change of a cell or battery (^oK)

E^o = Reversible EMF (Open Circuit Potential) of an electrochemical cell (V)

E^H = Thermoneutral Potential of an electrochemical cell (V)

n = Number of equivalents per mol of reactant involved in a reaction

F = Faraday’s constant (96,485 coulomb/eq)

I = Current (A)

t = Time (sec)

Q_r = Quantity of Entropic heat generated or absorbed per mol of reactant by an electrochemical reaction at the reversible EMF (cal/mol or J/mol)

Q_rt = Quantity of Entropic heat generated or absorbed by an electrochemical cell over (t) seconds of operation at current (I) (cal or J)

q_rt = Rate of Entropic heat generated or absorbed by an electrochemical cell when operating at current (I) (cal/sec or J/sec)

η = Cell polarization (V)

E_L = Potential of a cell under load (V)

Q_Pt = Quantity of heat generated from polarization in a cell over (t) seconds of operation at current (I) (cal or J)

q_Pt = Rate of heat generated from polarization in a cell when operating at current (I) (cal/sec or J/sec)

Q_Tt = Total quantity of heat generated or absorbed during the operation of an electrochemical cell for (t) seconds at current (I) including both polarization heat and Entropic heating or cooling (cal or J)

q_Tt = Rate of total heat generated or absorbed during the operation of an electrochemical cell at current (I) including both polarization heat and Entropic heating or cooling (cal/sec or J/sec)

N = Number of cells in a battery

n_c = Number of components in a cell or battery

C_Pi = Specific heat of component (i) of a cell or battery (cal /g^o K or J/g^oK)

C _PT = Weighted average specific heat of a cell or battery (cal/g^oK  or J/g^oK)

m_T = Total mass of cell or battery (g)

C_i = Heat capacity of component (i) of a cell or battery (cal/^oK or J/^oK)

C_T = m_TC_PT = Overall heat capacity of the cell or battery (cal/^oK or J/^oK)

m_i = Mass of component (i) of a cell or battery (g)
 

Conversion Factors:

● cal = 0.239 * Joules
● Joules = 4.184 * cal
● Volts = Joules / Coulomb
● 1 Coulomb = 1 amp-sec
 

References:

1. Values taken from the Handbook of Chemistry and Physics
2. Private communication