Also, just to add it, the relevant energy quantity in this problem is probably best described as
enthalpy,
,
, where- is internal energy;
- is pressure;
- is volume.
In this case, the volume of the void is filled in at, let's say, constant atmospheric pressure. So the enthalpy change is roughly
.
This enthalpy change can effect vaporization to an extent with a limit estimable in terms of the
enthalpy of vaporization.
Naively (lazily) estimating the enthalpy of vaporization for water to be constant at the STP value over the domain of interest, e.g.
,
then for the sphere given in the problem, there's enough enthalpy to, theoretically, drive
.
Assuming
then that's about 0.0103 moles of water that theoretically could be evaporated, as
calculated by WolframAlpha. That's roughly 0.19 grams of water. Using
Wikipedia's value for the density of water vapor at STP as
, that'd be a total potential bubble volume of about 0.23L, which is about 5.5% (
WolframAlpha) of the original void's volume.
In short, the theoretical maximum bubble size under these simplifying assumptions is about 5.5% of the void's original volume. However this assumes that all of the enthalpy generated goes entirely into vaporizing water, which is at the dynamic extreme limit. At equilibrium, the enthalpy will be dispersed throughout the body of water as a slight increase in overall temperature. Any vapor generated will condense, releasing heat, until equilibrium is reached. So, will any bubbles reach the surface of the water before fully recondensing? That's the dynamics problem that the above post concluded with.
This post was mostly just to show how we might naively estimate the generated bubbles' total volume, which appears to be thermodynamically limited to 5.5% of the void's original volume. It wouldn't be too difficult to perform this logic more rigorously (e.g. consider pressure, enthalpy, vapor density, etc. using more detailed correlations than just the simple constant estimates), though if I had to solve this problem in a professional setting, I'd likely have to make a simulation program to attack is numerically. It's really a dynamics problem, so these simple, assume-pseudo-equilibrium calculations that I've been showing here are insufficient for good estimation.
In summation:
- Bubbles will be generated.
- How many bubbles, and how large they are, depends largely on the void's original size and how water floods into it at the start time that it "bursts".
- Total bubble volume is thermodynamically limited to about 5.5% of the void's original volume.
- If I had to guess, the actual initial bubble volume would probably be much smaller.
- After the bubble(s) are generated, they will begin to recodense back into the body of water while also generally moving upward.
- Bubbles may be observed at the surface of the body of water if they get there before recondensing back into the water.
- There are many complicating factors involved, including stuff like what gases and salts are already in the water.
- A good solution to this problem would require numerical simulations or extremely rigorous/advanced analytical calculations.