What are the key dependencies of the power of a fission bomb?
The type of fissile material and geometry( the arrangement in space).
Is it true that the power of a fission bomb depends linearly on the mass of the bomb? If so, why?
The energy available comes from nuclear transitions and is fixed for a specific interaction and isotope combination. It is proportional to the number of nucleons available, and thus to the total mass.
Is there a simple physical argument to estimate the magnitude of the total released energy of the bomb if you know the mass and the used isotope? Can you provide an example calculation?
No. It can be estimated after the fact. That is why there are always trials of all new weapons.
How can I estimate the power (released energy per time) from this information?
Is there a closed formula to calculate the power of a fission bomb.
Logarithmic scatterplot comparing the yield (in kilotons) and weight (in kilograms) of various nuclear weapons developed by the United States.
The power will depend on the geometry i.e. the arrangement in space of the fissile material. The energy released can be estimated after the fact, as is shown in this wiki article, although there are theoretical maximum yields that can be estimated.
This question can really be satisfied by taking a nuclear engineering course, not by asking questions here, imo.
All of it can be simulated to a certain level of precision - given enough computing power AND correct experimental values for all the parameters. The tricky bit without tests is to get experimental values for eg. the thermal conductivity of Plutonium at TPa of pressure.
Experimental tests can also only validate something to a certain level of precision - depending on the instrumentation and repeatability of the device.
edit: Yes, there are quantum effects that can't be predicted - which specific atom will fission first - but that isn't really important from an engineering perspective.
Best Answer
The sun and all other stars are in effect thermonuclear bombs. If they get heavier than about 10 times the mas of the sun they eventually blow up as a supernova, so there is a limit to the size but it's a lot larger than anything we will ever build.
In the wikipedia article, the yield limits have to do with deliverability. It's no good having a huge bomb if you can only explode it in the factory where it's made. They're talking about "6 megatons per metric ton" so a 60 megaton bomb would weigh 10 tons. The article gives examples of delivery, with the limit being a 1.3Gt bomb deliverable by an Antonov An-225.