explosionspressure
I would like to know, if given a TNT equivalent of explosive (or its Energy) is it possible to determine what would be the initial pressure that will be the result of that explosion ?
To be more precise let's say I have a vessel and given the vessel volume can I determine pressure inside that vessel (assuming vessel won't break).
OK, I did some more research on this and I think I have an answer, but I would still appreciate someone who actually knows what they're doing checking my math.
First, I used the Sadovsky equation to calculate the increase in pressure in atmospheres. The equation is here:
https://www.metabunk.org/attachments/blast-effect-calculation-1-pdf.2578/
The explosive mass has to be multiplied by a relative effectiveness factor (REF) to account for the type of explosive. For example, the REF of ammonium nitrate is .42, because it has 42% of the explosive power of TNT.
Second, I found that pressure can be converted to decibels with the equation:
Db = 20*log(P/Pref) where:
P=The pressure caused by the explosion
Pref-The reference pressure for 0 decibels, which is the threshold for human hearing. It's 20 microspascals, or about 1.97 EXP-10 atmospheres.
So using a distance of 1.5M, a REF of .42, and a mass of 4.5 grams, the Sadovsky equation tells me the air pressure will be increased by about .091 atmospheres. Plugging that into the equation above yields a decibel level if 173.3, which is right in line with the specification.
So I guess the takeaway is that it takes very little explosive to make a major noise if you're close enough to it. Thanks everyone for your help.
In my view the water isn't really the thing to focus on here. The real energy reservoir was the partially-melted core; the water wasn't dangerous because it held energy, but rather because it had the potential to act as a heat engine and convert the thermal energy in the core into work. We can therefore calculate the maximum work which could conceivably be extracted from the hot core (using exergy) and use this as an upper bound on the amount of energy that could be released in a steam explosion. The exergy calculation will tell us how much energy an ideal (reversible) process could extract from the core, and we know from the Second Law of Thermodynamics that any real process (such as the steam explosion) must extract less.
Using exergy, the upper bound on the amount of work which could be extracted from the hot core is
\begin{align} W_\text{max,out} &= X_1 - X_2 \\ &= m(u_1 - u_2 -T_0(s_1-s_2)+P_0(v_1-v_2)) \end{align} If we assume that the core material is an incompressible solid with essentially constant density, then \begin{align} W_\text{max,out} &= m(c (T_1 - T_2) -T_0 c \ln(T_1/T_2)) \end{align} where $T_0$ is the temperature of the surroundings, $T_2$ is the temperature after energy extraction is complete, and $T_1$ is the initial temperature. At this point you just need to choose reasonable values for the key parameters, which is not necessarily easy. I used:
This gives me $W_\text{max,out} = 6.23 \times 10^{11}\,\text{J}$ or 149 tonnes of TNT equivalent. This is several orders of magnitude lower than the "megatons" estimate provided in your question, but does agree with your gut response that "megatons" seems unreasonably high. A sanity check is useful to confirm that my result is reasonable...
With the numbers I used, the system weights 1 kiloton and its energy is purely thermal. If we considered instead 1 kiloton of TNT at SATP, the energy stored in the system would be purely chemical. Chemical energy reservoirs are generally more energy-dense than thermal energy reservoirs, so we'd expect the kiloton of TNT to hold far more energy than the kiloton of hot core material. This suggests that the kiloton of hot core material should hold far less than 1 kiloton of TNT equivalent, which agrees with your intuition and my calculation.
One factor which could increase the maximum available work would be the fact that the core was partially melted. My calculation neglected any change in internal energy or entropy associated with the core solidifying as it was brought down to ambient conditions; in reality the phase change would increase the maximum available work. The other source of uncertainty in my answer is the mass of the core; this could probably be deduced much more precisely from technical documents. A final factor that I did not consider is chemical reactions: if the interaction of corium, water, and fresh air (brought in by an initial physical steam explosion) could trigger spontaneous chemical reactions, then the energy available could be significantly higher.
Although addressing the limitations above would likely change the final upper bound, I doubt that doing so could change the bound by the factor of ten thousand required to give a maximum available work in the megaton range. It is also important to remember that, even if accounting for these factors increased the upper bound by a few orders of magnitude, this calculation still gives only an upper bound on the explosive work; the real energy extracted in a steam explosion would likely be much lower. I am therefore fairly confident that the megaton energy estimate is absurd, as your intuition suggested.
Best Answer
According to New Energetic Materials, table 1.2, 19.5 GigaPascals (GPa) is the initial pressure.