Sorry for the late answer, I intended to write this 2 weeks ago but couldn’t find the time.
OK, so let’s look at the amount of potential energy locked up in our configuration of water spheres: I calculated the radius to be r=√34π⋅117⋅1.35⋅1018m3=266.644 km. By symmetry, the potential energy would be the same if all the water were located at the center of these spheres, i.e. 133.322 km above ground. Add negative potential energy of Earth’s oceans in its equilibrium state (1.844 km, half the average ocean depth), and we get a total of g⋅h=9.81ms2⋅135166m=1.325MJkg
That’s a lot of energy. Let’s assume the water is at 0°C initially (most ocean water is in the cold deep layers). To bring all this water to the boiling point, we’d need 100K⋅4.186kJkg⋅K=0.4186MJkg. That leaves us 0.9064MJkg to boil the water. Given the latent heat needed, we can boil 906.4kJkg2257.92kJkg=40.14% of the water.
Since Earth’s oceans is 262 times as massive as the atmosphere and we boiled almost half of it, we now have an atmospheric pressure of 105 bars, exceeding that of Venus. Of course, the boiling point of water increases with pressure, but the latent heat of vaporization decreases and these two effects pretty much cancel each other out. It does mean however that we’ll have a surface temperature of 315°C, approaching that of Venus. In other words, all life on Earth’s surface, including the hardiest extremophile bacteria, is toast (or rather steam buns). Absolute overkill actually, since DNA itself disintegrates completely at around 200°C. The only safe place would be deep underground where the heat can’t penetrate until it is radiated off into space.
What about seeking refuge in the ISS? Let’s see what the atmospheric conditions are at its orbital height of 400 km. We’ll use the barometric formula without temperature lapse because this isn’t an equilibrium state anyway. ρ400km=ρ0⋅exp(−g⋅M⋅hR⋅T0)=58.94kgm3⋅exp(−9.81ms2⋅0.018kgmol⋅400000m8.314JK⋅mol⋅588K)=58.94kgm3⋅e−14.44=3.14⋅10−5kgm3This is equivalent to the air density of our current atmosphere at 60 km height.
Woah, tks a bunch man. But exactly what happens starting from t=0? I suppose that at 1st the water must be falling down, right? How will the Earth’s surface be altered by the tremendous force of water? How will the potential energy from height turn 40% of water into vapor? I mean, how will it happen over time? If it takes time, then maybe some people will have a chance to understand what’s going on & run into the nearest underground mine, no?
Regarding the ISS, I suppose that even at the hypothetical altitude of 460km, it will still burn. But as the above paragraph mentioned, I guess that the boiling process will not be instantaneously, or even fast, so the astronauts will have plenty of time to watch the horrors unveil below. With maximum number of ships (I forgot, 4?) on board, can they use them to boost the ISS up to, say, 1000km? Or if time doesn’t allow, can they manage to load supplies into a ship & launch it into some orbit far from Earth & return after maybe 2 years? You know, doing whatever to preserve the human race long term.
These follow-up questions pertain to a dynamic context, and I’m afraid I’m not equipped to answer them. Moreover, I would also claim that not even Randall Munroe himself would be able to answer these questions, or anyone who hasn’t got a supercomputer and a team of physicists at disposal.
I bought the What If book myself and loved every chapter of it. But if you look closely, you will notice that basically every analysis in that book was made from a static context or a dynamic one that has ridiculously simple solutions (i.e. linear or exponential). Even exotic topics like neutron star matter and supernova neutrinos can be analysed with ease under a static context; just a matter of typing large numbers into a calculator. But as soon as dynamics is involved, even mundane things like Earthly weather or air flow over ailerons are going to require a supercomputer.
It doesn’t help to analogize the problem with more familiar scenarios, either. Quantity has a quality of its own, as Stalin famously said. Things like the cube-square law make big things behave very differently than small things even if they’re made out of the same material or undergoing the same basic process. Nuclear explosions and supernovas are not hard to understand because of the extreme energies involved per se. Nuclear interactions relevant to these processes are many orders of magnitude lower than the energies achieved in particle accelerator experiments. What macroscopic effect a gargantuan amount of these simple interactions can produce, however, is a different matter.
That’s why you need lots of brute force computational power as well as a team of physicists doing clever simplifications just to get a general understanding of the problem at hand, not even a precise prediction of a specific problem instance like weather forecast. And I’m afraid they won’t let you borrow their precious compute for a fun thought experiment.
Worse yet, in the case of real phenomenons like nuclear explosions and supernovas we at least get to observe their aftermaths (bomb yield/supernova remnant) to set a few boundary conditions on our analysis. For completely hypothetical scenarios, we can’t even check our predictions against reality. Can we, for instance, safely ignore temporary phase changes into exotic ice forms? How about nuclear interactions triggered by locally extreme heat and pressure?
Though this particular curiosity will never be satisfactorily quenched, at least I know when to stop pushing it further and try to put it into the back of my mind. You know, acting rationally :)
I think I won’t be able to express enough gratitude.
Sorry for the late answer, I intended to write this 2 weeks ago but couldn’t find the time.
OK, so let’s look at the amount of potential energy locked up in our configuration of water spheres: I calculated the radius to be r=√34π⋅117⋅1.35⋅1018m3=266.644 km. By symmetry, the potential energy would be the same if all the water were located at the center of these spheres, i.e. 133.322 km above ground. Add negative potential energy of Earth’s oceans in its equilibrium state (1.844 km, half the average ocean depth), and we get a total of g⋅h=9.81ms2⋅135166m=1.325MJkg
That’s a lot of energy. Let’s assume the water is at 0°C initially (most ocean water is in the cold deep layers). To bring all this water to the boiling point, we’d need 100K⋅4.186kJkg⋅K=0.4186MJkg. That leaves us 0.9064MJkg to boil the water. Given the latent heat needed, we can boil 906.4kJkg2257.92kJkg=40.14% of the water.
Since Earth’s oceans is 262 times as massive as the atmosphere and we boiled almost half of it, we now have an atmospheric pressure of 105 bars, exceeding that of Venus. Of course, the boiling point of water increases with pressure, but the latent heat of vaporization decreases and these two effects pretty much cancel each other out. It does mean however that we’ll have a surface temperature of 315°C, approaching that of Venus. In other words, all life on Earth’s surface, including the hardiest extremophile bacteria, is toast (or rather steam buns). Absolute overkill actually, since DNA itself disintegrates completely at around 200°C. The only safe place would be deep underground where the heat can’t penetrate until it is radiated off into space.
What about seeking refuge in the ISS? Let’s see what the atmospheric conditions are at its orbital height of 400 km. We’ll use the barometric formula without temperature lapse because this isn’t an equilibrium state anyway. ρ400km=ρ0⋅exp(−g⋅M⋅hR⋅T0)=58.94kgm3⋅exp(−9.81ms2⋅0.018kgmol⋅400000m8.314JK⋅mol⋅588K)=58.94kgm3⋅e−14.44=3.14⋅10−5kgm3This is equivalent to the air density of our current atmosphere at 60 km height.
Here’s a video of the Mir space station at 80 km height.
Woah, tks a bunch man. But exactly what happens starting from t=0? I suppose that at 1st the water must be falling down, right? How will the Earth’s surface be altered by the tremendous force of water? How will the potential energy from height turn 40% of water into vapor? I mean, how will it happen over time? If it takes time, then maybe some people will have a chance to understand what’s going on & run into the nearest underground mine, no?
Regarding the ISS, I suppose that even at the hypothetical altitude of 460km, it will still burn. But as the above paragraph mentioned, I guess that the boiling process will not be instantaneously, or even fast, so the astronauts will have plenty of time to watch the horrors unveil below. With maximum number of ships (I forgot, 4?) on board, can they use them to boost the ISS up to, say, 1000km? Or if time doesn’t allow, can they manage to load supplies into a ship & launch it into some orbit far from Earth & return after maybe 2 years? You know, doing whatever to preserve the human race long term.
These follow-up questions pertain to a dynamic context, and I’m afraid I’m not equipped to answer them. Moreover, I would also claim that not even Randall Munroe himself would be able to answer these questions, or anyone who hasn’t got a supercomputer and a team of physicists at disposal.
I bought the What If book myself and loved every chapter of it. But if you look closely, you will notice that basically every analysis in that book was made from a static context or a dynamic one that has ridiculously simple solutions (i.e. linear or exponential). Even exotic topics like neutron star matter and supernova neutrinos can be analysed with ease under a static context; just a matter of typing large numbers into a calculator. But as soon as dynamics is involved, even mundane things like Earthly weather or air flow over ailerons are going to require a supercomputer.
It doesn’t help to analogize the problem with more familiar scenarios, either. Quantity has a quality of its own, as Stalin famously said. Things like the cube-square law make big things behave very differently than small things even if they’re made out of the same material or undergoing the same basic process. Nuclear explosions and supernovas are not hard to understand because of the extreme energies involved per se. Nuclear interactions relevant to these processes are many orders of magnitude lower than the energies achieved in particle accelerator experiments. What macroscopic effect a gargantuan amount of these simple interactions can produce, however, is a different matter.
That’s why you need lots of brute force computational power as well as a team of physicists doing clever simplifications just to get a general understanding of the problem at hand, not even a precise prediction of a specific problem instance like weather forecast. And I’m afraid they won’t let you borrow their precious compute for a fun thought experiment.
Worse yet, in the case of real phenomenons like nuclear explosions and supernovas we at least get to observe their aftermaths (bomb yield/supernova remnant) to set a few boundary conditions on our analysis. For completely hypothetical scenarios, we can’t even check our predictions against reality. Can we, for instance, safely ignore temporary phase changes into exotic ice forms? How about nuclear interactions triggered by locally extreme heat and pressure?
This. Is an eye-opening answer. I see now.
Though this particular curiosity will never be satisfactorily quenched, at least I know when to stop pushing it further and try to put it into the back of my mind. You know, acting rationally :)
I think I won’t be able to express enough gratitude.