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