Welcome to the forum. Yes there is a direct correlation between volume to cool and degrees of temperature drop per minute/hour/whatever.
There will be a coefficient of thermal conductivity to consider for the losses between inner and outer temps. Unless you have the perfect insulation, (not yet invented) there will be a small, but steady heat gain to compensate for.
Yes, you will need to ascertain a size to contain 105-Qt. That could range from a piece of 1" PVC pipe 14-feet long (internal volume 105-Qt) to a small cubic container that would contain 105-Qt. More importantly, what are you trying to contain? Is it a liquid you just pour into the "box" is it in some form of container? Are there multiple containers?
Converting an existing cooler wold be very difficult as you would need to bend and manipulate the evaporator coils and they are not built with that in mind.
If you can find an evaporator from a conventional refrigerator at will fit neatly inside the box YOU have designed to fit the contents, then you may be on the way.
This is not a trivial design project unless it is all theoretical.
Finally, MHz will almost certainly not figure into any of your design considerations.
Don't give up, but there is a ton of research you need to do to understand the refrigeration design and principles.