# Is there a way to calculate the heat capacity of a solid or volumetric heat capacity of a solid oxide fuel cell?

I am working on a personal project and wanted to use a solid oxide fuel cell to power up a load (I have not decided what yet), so I am trying to find a way to estimate the power I would need to heat up my fuel cell to a working temperature, so I was considering calculating the heat capacity of the fuel cell. But as it turns out the fuel cell is composed of different materials. Should it be enough to obtain the heat capacity from each material and then add each value to compute the overall energy needed? Thanks!

This is a case where you want to determine a property in a composite using some form of a rule of mixtures.

$$P^n = \sum f_j P^n$$

Here, $$P$$ is the composite property, $$f_j$$ is typically the volume fraction, and $$P_j$$ is the property of the component $$j$$ in the mixture. When $$n = 1$$, this is the simple rule of mixtures. When $$n = -1$$, this is the inverse rule of mixtures.

An example of this rule applied to fiber composites is given at the link below.

https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Rule_of_mixtures.html

For heat capacity, the formulation is written using mass specific heat capacity and mass fraction. The link below gives an explanation and a calculator.

https://thermtest.com/rule-of-mixtures-calculator

• Thank you this is really helpful! – dareToDiffer07 Jun 11 '19 at 21:00
• As appropriate then please check that this answered your question. – Jeffrey J Weimer Jun 12 '19 at 12:07
• @dareToDiffer07 Thank you. – Jeffrey J Weimer Jun 20 '19 at 16:16