Re: Physics 101
"What's its surface area ?"
You may assume the 1 cc object is made from carbonized coconut, and has a surface area that is vast (Wales sized) on the microscopic scale, if you think it'll help. The area at the macro scale is on the order of 6 cm^2 (if we assume a cube for simplicity).
"Thermal conductivity ?"
Feel free to browse the Periodic Table. Help yourself.
"...in a vacuum ... or liquid sodium ?"
Help yourself. Anything you want. Your goal it bring the temperature down to, heck, 4 digits would be a major accomplishment.
The point of the 1 cc Thought Experiment is to assist those with poor conceptualizing skills to catch-on to the fact that moving power as heat implies temperature. 100MW is a lot of power. Size matters. It cannot be made arbitrarily small with practical materials.
Back to the LM example, at some point in the future the Steam Turbine folks are going to knock on the reactor room door, with their 1m diameter 100MW class steam pipe in tow, and everyone will be left wondering where they're supposed to connect the 1m diameter pipe to the wee cute little 100MW reactor.
I can sense some problems with the plumbing. It's because I tend to pay attention to numbers, such as (for example) 100,000,000 joule per second.
Biting the hand that feeds IT
