Science question for the brainy among us

BVB said:
Quick recap: magically miniaturized volume of liquid sealed in a (non-magical) metal sphere.

Our final step is to cancel the shrinking spell cast on the water.

What will the effect be?

Let's see here - we'll keep things to an order of magnitude.

1 gallon = 231 cubic inches.

Assume a sphere of one-inch internal diameter. Its volume is 4/3piR^3 or about 1/2 of a cubic inch.

That means, to an order of magnitude, we are compressing the water to 1/500th its normal size.

Let us further assume that water behaves "only" as an ideal gas (obviously, it exerts a lot more push than a gas does, but let's play with this for a moment). A sudden expansion (not out of line with reduce/expand spells) means that there is no time for the temperature to adjust initially.

Ideal gases obey the law PV=kT. Since k is a constant, and we are holding T constant for the moment of expansion, we know that since the water is contained in a container that is 500 times too small for it, the pressure must by 500 times greater than normal (again, one order of magnitude here).

Now, we'll hold V constant when compared with a sphere filled with 1/2 cubic inch of water and see what will quickly happen to temperature in the instant after the water "expands." Since P is 500 times that of a sphere with 1/2 cubic inch of water, and we are holding V constant, that means the temperature will rapidly rise - in fact, it will increase 500-fold since P(magically uncompressed water) = 500 P (water). Room temperature is around 300 degrees K, so this leads us to a result of about 150,000 degrees K - or ten times hotter than most stars!!! This would (obviously) immediately boil the metal away and allow the water to escape long before it hit star-like temperatures - which would mean you would get a spray of hot liquid metal (OUCH!) immediately followed by immersion in superheated water if you were holding the sphere. If you were not within a few feet of the sphere, you'd still be in danger of being hit with the liquid metal, but the water temperature would cool rapidly (back to room temperature) as it expanded - meaning by the time the water had created a globe sufficient to hold its 231 cubic inch size (roughly 3.75 inches in diameter), it would be back to normal temperatures.

Result: Effectively a painful "chrome plating bath" (or whatever metal is used) for anyone in the vicinity, a wickedly burned hand and lower arm for the person holding the globe, and a big "splash" of water drenching that hand and the as the water returns to normal size and falls to the ground.

If (using magic) you instead "unshrank" the water in an impenetrable globe of force 1 inch in diameter (the force will not melt, etc.) you would produce a body so hot (150,000 K, remember?) that it would instantly sear your hand and then drop to the floor, melting its way all the way through to the center of the planet (probably doing slight oscillations once it got there) and heating the planet from the interior. The intense heat and light thusly emitted (yes, it would emit some light as a black body) would cause severe planetary problems. I haven't done the math to figure out how long it would take such an object to "burn down" to normal temperatures, but it's a good bet that life on the planet would be summarily toasted - if not blown away entirely by the prospect of having something far hotter than a star sitting in the center of the planet.

And that's just with water "pressing back" with the force of a gas. My guess is that water actually "pushes back" with at least 1,000 times as much force as a gas (a conservative estimate) which would peg the temperature of the object created in the 150,000,000 degree range - which is so hot it's just stupid. It would vaporize the entire planet instantly.

NOW, if by some quirk you were able to do this in an isolated area so as to not destroy the world (a bag of holding or portable hole, perhaps?) and let the thing blast that destructive energy out over a long period of time (eventually, it will cool down, but it will likely take hundreds to millions of years), and THEN pull it out when it has cooled to room temperature and then crack it open...

Well, the exact reverse of the process will happen... you'll have to "put back" all the heat that you radiated away earlier. If the heat you had before was enough to vaporize a planet, what you wind up with is instant deep-frozen planet (we're talking the entire planet instantly goes to within a degree or two of absolute zero). Again, completely impractical for making ice armor or anything else.

Long story short... there are not a lot of possible outcomes for this.

1.) The ball almost instantly cracks and water sprays out. Ball is launched in the opposite direction at high speed, possibly with a spin (different coefficient of friction at spots where you were holding it). Unless all the water is out almost instantly, it will heat up too fast and turn into #2 (below).

2.) The ball holds together long enough to get so hot that the metal vaporizes - it only has to hold for a few hundredths of a second, so I think this is the most likely scenario - the water simply can't escape fast enough to stop the superheating. You get an explosion of liquid metal in every direction at once, anything within about 2 inches is hit with superhot water, and then the 4" water ball (assumes it expands in all directions at once) drops onto the ground, making a big wet splash (at normal temperatures).

3.) The ball is made of force (or other material) and is not compromised. Instant "mega-hot-to-the-tune-of-ten-times-hotter-than-a-star" ball that vaporizes the planet.

4.) The ball is not compromised per #3 above and is allowed to "burn out" of temperature changes. Then the ball is cracked open. Instant deep freeze of entire planet.

#2 is the most likely - and will do more damage to the poor sap holding the ball than anyone else. #1, though MUCH less likely, is a vague possibility - but you'd probably need to have a sizable hole in the sphere to get it to work. #3 and #4 are, quite simply, apocalyptic planet-destroyers either way. :-)

Those are really your only four choices. No matter what, the person most likely to suffer any damage is the poor sap trying this stunt... though taking out the planet as collateral damage is not great either.

I'm in the camp of "expand/reduce in D&D stops before damage accrues" so you'd wind up with a sphere of "partially unshrunk" water - it unshrinks until it fills the sphere but does not exert abnormal pressure on the sphere.

Again, my calculations were with a GAS - a LIQUID will have FAR more pressure (and far more heat).

--The Sigil
 

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Aaron L said:
It could break the electron shells of the water molecules and make neutron star material.

This water isn't dense enough for neutral star material. A neutron star has a density 10^14 times that of normal (uncompressed) water. The density we are talking about here is more like that of a white dwarf.

I would guess that the water would pressure ionize (meaning you don't have water anymore) and the sphere would explode. If the sphere was magically unbreakable, it would probably initially become extremely hot. After the heat radiated away, the material inside would probably form a crystal formed of the hydrogen and oxygen nuclei.

- Kusuf
 

Re: Re: Science question for the brainy among us

The Sigil said:



Again, my calculations were with a GAS - a LIQUID will have FAR more pressure (and far more heat).

--The Sigil

And there should be more than one quantum effect to further complicate this. By far I prefer you explanation the most. It's still purely science-fictional.
 
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Re: Re: Science question for the brainy among us

The Sigil said:



If (using magic) you instead "unshrank" the water in an impenetrable globe of force 1 inch in diameter (the force will not melt, etc.) you would produce a body so hot (150,000 K, remember?) that it would instantly sear your hand and then drop to the floor, melting its way all the way through to the center of the planet (probably doing slight oscillations once it got there) and heating the planet from the interior. The intense heat and light thusly emitted (yes, it would emit some light as a black body) would cause severe planetary problems. I haven't done the math to figure out how long it would take such an object to "burn down" to normal temperatures, but it's a good bet that life on the planet would be summarily toasted - if not blown away entirely by the prospect of having something far hotter than a star sitting in the center of the planet.


--The Sigil

While this scenario sounds exciting, it isn't very plausible. First off, 150000 K is hot, but not that hot. Nuclear explosions are much hotter. The center of the sun is 15 Million degrees. The real issue, is how much of a heat capacity this weird ball has. Its not that large. This ball will probably hit the ground and slag a few feet of soil at the most before it cools down.

- Kusuf
 

I love this kind of stuff. Just like in Dragonstar, where archmages hover off the horizon of black holes to study them, using antigravity magic.
 

Bastoche said:


If you mix them together, you don't have "science" anymore. So in that sense it's magic only. No arguments will be logical in such a mindset. ... any answer would be as false, right and/or arbitrary (all at the same time) as any other.

... Which also reduces the value of your dismissals of others' pseudo-scientific proposals given here. (shrug) If anything is possible in a fantasy, then you can't exert the true constraints of science as we know it.

This was supposed to be a fun little game of supposition. "Brainy" is obviously a relative term.
 

Probably something that someone else mentioned so here's my thoughts.

Supercondensed water would very much be heavy water tho not radioactive but that's a 'duh'. The sphere won't necessarily explode. However it may expand rapidly like a balloon, possibly evenly, especially if in some sort of antigravity situation. More stress in one spot, more likely it is to rupture there. It all depends on how stretchable the metal is.
 

Re: Re: Re: Science question for the brainy among us

Kusuf ibn Zaid said:


While this scenario sounds exciting, it isn't very plausible. First off, 150000 K is hot, but not that hot. Nuclear explosions are much hotter. The center of the sun is 15 Million degrees. The real issue, is how much of a heat capacity this weird ball has. Its not that large. This ball will probably hit the ground and slag a few feet of soil at the most before it cools down.

- Kusuf
Not as hot as the CENTER of the sun, no... but considerably hotter than the sun's surface ( http://hypertextbook.com/facts/2001/AsserEstriplet.shtml ) - most stars have a surface temperature in the tens of thousands of degrees.

BUT... point well taken on the heat capacity. And that's simple to calculate. The heat capacity is the amount of heat required to change an object's temperature by one degree.

We have one gallon of water at 150,000 K. Fortunately, water is laughably simple to check the heat capacity of... 1 calorie per gram per degree K. Since we're only working in orders of magnitude guesstimates here, 150,000 minus 300 K (room temp) might as well just be 150,000. So we have:
150,000 times 3785 grams (Mass in grams of a gallon of water) times 4.184 joules per calorie = 2,375,466,000 J. We'll round that to 2.4 billion joules.

1000 kg of TNT has a "punch" of 4 billion joules, so in rough guesstimates, this is the equivalent of the heat released by detonating 500 kg (or about half a ton for the imperial system of units) of TNT.

I guess that's not enough to obliterate a planet - but it's sure not gonna be comfortable for anyone in the immediate vicinity.

Though again, if you assume liquid water has a pressure 1,000 times that of an ideal gas (and I think that estimate is on the low side by several orders of magnitude), you get the same heat as a 500 ton bomb - not as much heat as in a nuclear blast, but as much heat as is on the order of the largest recorded non-nuclear explosions.

And yes, at that sort of compression, there would be all sorts of weird quantum effects. ;) I'm just throwing out some "order of magnitude" guesstimates. All of the compression necessary to overcome Electromagnetic and Quantum forces, let alone the lack of viscosity in compressed water, would add even more energy to the "blast."

--The Sigil
 
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I don't believe for a second that the ball of steel wouldn't explode as soon as the spell ended, but if it didn't, and assuming the <i>Shrink</i> spell is diabatic, looks like you would get a hunk of ice-VII at a pressure on the order of 10 GPa, storing something like 30-40 MJ of potential energy.
 


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