# Determining the Energy Density of a Battery given the anode and cathode

everyone, I'm using nanohub's introduction to the material science of rechargeable batteries course to do some self-studying until I can go back into the lab. On one of the practice problems, it asks to calculate the energy density of a given battery system. For the first problem, it asks this for a lithium metal anode, LiCoO2 cathode system. We are asked to assume an electrode thickness of 100 micrometers and a porosity of 35%. I assumed no porosity contributions from other components such as binders. When I calculate the value I don't get something close to the answer given in the solution which is 453.6 J/kg.

I have tried calculating this and the other problems a few different ways with different units but I am not getting the correct answer. The formula I am using is

Energy density = (potential difference between anode and cathode) * cathode charge (capacity)* electrode thickness (this was given in the PS)*(1-porosity(this was also given)) below is an image of what the given information and potential answers looks like

This is the equation to find the energy density of a battery: $$E=VC/m$$
$$E$$ is energy density in Wh/kg, $$V$$ is nominal voltage in volts, $$C$$ is capacity in Ah and $$m$$ is mass in kg. Why are you multiplying this equation with thickness and porosity?
Keep in mind that not all electrodes will be porous (for example for Li metal you can assume porosity is 0%). Also, you will have to report results in $$J/kg$$, so make sure you keep track of your units and convert if necessary.