# Measuring Specific Heat Capacity

Specific heat capacity (Cp) is a fundamental physical property that describes the amount of heat required to change the temperature of a substance by a given amount, typically per unit mass. Expressed in units like joules per kilogram per degree Celsius (J/kg°C) or calories per gram per degree Celsius (cal/g°C), it quantifies the thermal inertia of a material. In essence, specific heat capacity measures how much thermal energy a substance can store.

Specific heat is related to mass and temperature by following equation:

Note: In theory Specific heat is temperature dependent but for the purpose of this test and given the useful cell temperature window is very narrow (~-20°C to 60°C) we can assume Cp to be constant.

Specific Heat Capacity vs Temperature

For lithium iron phosphate cells we see a nominal heat capacity ~1110J/kg.K at 25°C and 50% SoC increasing to 1140J/kg.K at 60°C

A quick method to measure/estimate Specific heat which can be done in any lab setting is by using a well insulated (adiabatic) box.

### Construction of box:

Sample Container: At the heart of the chamber is a sample container where the material under investigation is placed.

Temperature Sensors: The chamber is equipped with fast response thermocouples to monitor the temperature of the sample continuously.

Heating System: A resistive heating system surrounds the chamber, capable of precisely controlling the temperature of the sample according to the experimental protocol.

Insulation: The entire assembly is heavily insulated to ensure adiabatic conditions, meaning that once the external heating is stopped, no heat should enter or leave the system.

## Steps to measure specific heat capacity

• Record weight of the cell
• Heat the cell to 20°C-35°C @ constant heating rate (this range to be determined based on cell chemistry, type, capacity)
• Record Temperature vs Time
• Typical Temperature vs Time plot

The setup is calibrated before each test run using a material of known specific heat e.g Aluminum block. This will provide us with a calibration constant, η

Since chamber is using resistive heaters we can compute Power input from from the electrical input P =V x I (equation 3).

Rearranging equation 1 and using calibration constant equation 2

### Accounting for Heat losses:

Capturing any heat losses from an adiabatic box, which by definition should minimize heat exchange with its surroundings, is crucial for accurate thermal measurements. While the ideal adiabatic box does not allow heat transfer, in practice, some minimal heat exchange may occur due to imperfect insulation or through the necessary openings for wires and sensors. Heat flux sensors can be used to monitor and quantify these heat losses, ensuring that your measurements of specific heat capacity or other thermal properties are accurate.

Here is an approach to get accurate Cp estimation of a li ion cell

#### Heat input to the cell:

Using equation 3, Compute total heat input into the cell over time period (t)

#### Heat loss to ambient:

Use the heat flux sensors to measure the heat flux() across the surface area (A) of the adiabatic box over the same period of time.

#### Net Heat Absorbed by the Li-ion Cell:

A modified final equation can be written as:

Typical specific heat capacities of different chemistries.