Make a crucible, using steel pipe. Drill a hole in one of the end caps so as to not make a pressure vessel that could come apart at the extreme temperatures a fireplace's coals can reach.

Then fill it with dryer lint and dog hair, packing it as tight as you can and saturate the packed nastiness with extra strength cleaning ammonia.

Wait for snow and cold.

Fire it in a fireplace until the pipe glows red. Leave it there for one hour.

Let the pipe crucible cool and extract the shrunken mass of reduced carbon, oxygen, nitrogen, and sulfur. The picture below is a small peice broken off of one end. The entire mass will be about 75% of the volume of the original lint/hair pack.

Mix the electrolyte. 2.0M LiSO4 and 0.1M KI. This works out to 21.998 grams LiSO4 and 1.25 grams KI in 100mL of distilled water.

Assemble a cell by sawing a few millimeter disks off of the carbon rod. Then place a piece of shop towel between the disks.

Add electrolyte, it will readily be absorbed by the incredibly porous carbon.

And finally sandwhich between two stainless steel charge collectors.

Test!

Do the maths and graphs.

You can use my ods file to get her done. Farads are simply Coulombs divided by Volts or (Amps x Seconds)/Volts