# Specific Heat Capacity of Lithium Ion Cells

The specific heat capacity of lithium ion cells is a key parameter to understanding the thermal behaviour. From literature we see the specific heat capacity ranges between 800 and 1100 J/kg.K

Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. Specific heat is the amount of heat per unit mass required to raise the temperature by kelvin (one degree Celsius).

The specific heat capacity of a cell is likely dependent on:

• chemical composition
• production processes
• chemical reactions and hence SoC and SoH
• temperature

For the main lithium ion chemistries the following generic heat capacities for a cell are:

• Lithium Nickel Cobalt Aluminium Oxide (NCA) = 830 J/kg.K
• Lithium Nickel Manganese Cobalt (NMC) = 1040 J/kg.K
• Lithium Iron Phosphate (LFP) = 1130 J/kg.K

These numbers are for cells operating at 30°C to 40°C and 50% SoC.

### Components

The heat capacity of a mixture can be calculated using the rule of mixtures. The new heat capacity depends on the proportion of each component, the breakdown can be expressed based on mass or volume. The following breakdown of the components of a cell is based on an NMC chemistry [Ref 4].

Electrolyte increases the specific heat capacity as the electrolyte fills in voids [Ref 3].

• Graphite changes from a specific heat capacity of 632 J/kg.K dry to 1437 J/kg.K wet.

This shows that the rule of mixtures cannot be applied to the values of the dry components.

### State of Charge

Tests of a Sony US-18650 cell [Ref 2] showed that the specific heat capacity was dependent on SoC:

• NCA
• 848 J/kg.K @ 100% SoC
• 835 J/kg.K @ 50% SoC
• 825 J/kg.K @ 0% SoC
• NMC
• 1040 +/-34 J/kg.K @ 50% SoC
• 960 +/18 J/kg.K @ 0% SoC
• LFP
• 1150 J/kg.K @ 100% SoC
• 1145 J/kg.K @ 50% SoC
• 1138 J/kg.K @ 0% SoC

The change in specific heat capacity of the LFP cell versus SoC is very small and can easily be ignored for most of the charge and discharge scenarios.

### Temperature

Murashko et al [Ref 5] show the specific heat capacity of the NCA 18650 cell increasing with temperature.

Murashko et al [Ref 5] show the specific heat capacity of an LFP 26650 cell increasing with temperature.

### Conclusions

The generic heat capacity values for cells of different chemistries are a good starting point for a thermal model. However, as the specific heat capacity is such a key parameter it is important to measure the actual cell being used under different operating conditions.

1. Y. Tang, T. Li, X. Cheng, “Review of Specific Heat Capacity Determination of Lithium-Ion Battery”, Energy Procedia, Volume 158, February 2019, Pages 4967-4973
2. H. Maleki et al, “Thermal Properties of Lithium-Ion Battery and Components”, Journal of The Electrochemical Society, 146 (3) 947-954 (1999)
3. A. Marconnet, R. Kantharaj, Y. Sun, “Characterization of thermal conductivity and thermal transport in lithium-ion battery”, Thermal & Fluids Analysis Workshop, TFAWS 2018, August 20-24, 2018, NASA Johnson Space Center
4. M.V. Morganti, S. Longo, M. Tirovic, C.Y. Blaise and G. Forostovsky, “Multi-scale, electro-thermal model of NMC battery cell”, IEEE Transactions on Vehicular Technology, Volume 68, Issue 11, 2019, pp. 10595-10606
5. Murashko, Kirill & Pyrhönen, J. & Jokiniemi, Jorma, “Determination of the through-plane thermal conductivity and specific heat capacity of a Li-ion cylindrical cell”, International Journal of Heat and Mass Transfer. 162. 120330. 10.1016/j.ijheatmasstransfer.2020.120330.

#### Heat Generation in a Cell

The heat generation equation has two terms: Joule heating which is the irreversible term and Entropy change that is the reversible term.

At high currents Joule heating dominates as it is I2Rint. However, charging from low states of charge at lower currents and the entropy change is very significant.

This means that each battery needs to be fully characterised so that it can be modelled and optimised.