How much liquid ice is in one unit?

[felinoel]

http://www.d20pfsrd.com/equipment---final/goods-and-services/herbs-oils-other-substances#TOC-Liquid-Ice

Obviously this is liquid nitrogen, it says it can be used to freeze liquids but I want to know how much liquid it can freeze.
To do this I need to know how much is in one unit, thoughts?

[Oracle_of_Void]

Well, since the item description has no rules for freezing liquids, we are entirely in "ask your DM" territory. However, we can make some educated guesses. I assume that a jar of liquid ice is similar in volume to a potion bottle. I would estimate that it would be able to freeze maybe 2 or even 3 times its volume in liquid. Of course, the purpose of this item seems to be intended to be used as an improvised cold weapon or maybe a quick grease effect. Really, if I was DM, I would just be reasonable on the amount frozen. You know, freeze a whole keg of beer solid? Sure, why not. Freeze a whole lake? With only 1 jar? Get outta here.

[deuxhero]

Unfortunately there is no "jar" item like there is "flask"

[atemu1234]

Unfortunately there is no "jar" item like there is "flask"

It's magical, so I'd say either five gallons or five cubic feet, depending on your DM and what you're basing it off of.

[felinoel]

Well, since the item description has no rules for freezing liquids, we are entirely in "ask your DM" territory. However, we can make some educated guesses. I assume that a jar of liquid ice is similar in volume to a potion bottle. I would estimate that it would be able to freeze maybe 2 or even 3 times its volume in liquid. Of course, the purpose of this item seems to be intended to be used as an improvised cold weapon or maybe a quick grease effect. Really, if I was DM, I would just be reasonable on the amount frozen. You know, freeze a whole keg of beer solid? Sure, why not. Freeze a whole lake? With only 1 jar? Get outta here.
My DM said that there wasn't enough in three of them to freeze a floating orb of water that had a medium sized fish thing with tentacles. He never determined how much would be.


It's magical, so I'd say either five gallons or five cubic feet, depending on your DM and what you're basing it off of.Five gallons of liquid nitrogen would be too heavy to carry.

...

...wait...

What is the weight of the unit!?!! Lemmie see...


EDIT:
Two pounds! Now to see just how much liquid can be frozen from two pounds...

[Spore]

I'd say a 5 foot cube with possible splash. The reagent works that it evaporates quickly pulling the heat from the surface making it (or the moisture in the air) freeze instantly. For rivers I'd say a possible "ice cube" of 5x5x5.

[deuxhero]

You could look at the Quick Freeze Oil from Dungeoneer's Handbook which has rules on pooring it out on stuff

[felinoel]

I'd say a 5 foot cube with possible splash. The reagent works that it evaporates quickly pulling the heat from the surface making it (or the moisture in the air) freeze instantly. For rivers I'd say a possible "ice cube" of 5x5x5.

My DM disagreed that any sizeable amount would not be possible to freeze with three units which is why I am trying to get the real world physics involved.

Based on the weight it would have to be about 40 ounces for one unit.

[Knaight]

Technically we don't know that the substance in question is liquid nitrogen - it could easily be something like liquid helium instead. With that said, working off the assumption that it is liquid nitrogen, there are a few things to look at. One is that it evaporates instantly - presumably it isn't subcooled. I'm going to assume that the atmospheric pressure is 1 atm, for convenience. The latent heat of vaporization of nitrogen is 200 J/g. The latent heat of fusion of water is 334 J/g. Nitrogen has a boiling point of -196 C, water has a freezing point of 0 C. The specific heat of nitrogen gas is 1.039 J/gK, liquid water is 4.186 J/gK.

If we assume that the water is initially at 25 C (picked as STP), and the nitrogen is initially at -196 C (it isn't subcooled), we get 403.7 J/g Nitrogen. Water takes 438.7 J/g. We get 837 mL of water, which is .227 gallons.

Given how unimpressive this is, I'd be inclined to conclude that the substance is not supposed to be liquid nitrogen. There are a lot of much more impressive substances which would work better. For instance, liquid ammonia has a latent heat of 1369 J/g, though this runs into issues with being dissolved in the water instead of freezing it (which does cool the solution, but it's pretty negligible). Alternately, a magical substance can be used. Something like a magically induced reversed combustion reaction (to create a natural opposition to alchemist's fire) could be fun, along with very endothermic.


My DM disagreed that any sizeable amount would not be possible to freeze with three units which is why I am trying to get the real world physics involved.
Well, the real world thermodynamics above were not exactly impressive. Real world physics are not on your side here, for the simple reason that water is a ridiculously good heat sink. Liquid nitrogen is also really not that impressive here.

[felinoel]

Technically we don't know that the substance in question is liquid nitrogenWell there is also this thread that was likely the cause of the item coming into game existence:
http://paizo.com/threads/rzs2kmeu?Alchemists-Ice#1


working off the assumption that it is liquid nitrogen, there are a few things to look at. One is that it evaporates instantly - presumably it isn't subcooled. I'm going to assume that the atmospheric pressure is 1 atm, for convenience. The latent heat of vaporization of nitrogen is 200 J/g. The latent heat of fusion of water is 334 J/g. Nitrogen has a boiling point of -196 C, water has a freezing point of 0 C. The specific heat of nitrogen gas is 1.039 J/gK, liquid water is 4.186 J/gK.

If we assume that the water is initially at 25 C (picked as STP), and the nitrogen is initially at -196 C (it isn't subcooled), we get 403.7 J/g Nitrogen. Water takes 438.7 J/g. We get 837 mL of water, which is .227 gallons.

Given how unimpressive this is, I'd be inclined to conclude that the substance is not supposed to be liquid nitrogen. There are a lot of much more impressive substances which would work better. For instance, liquid ammonia has a latent heat of 1369 J/g, though this runs into issues with being dissolved in the water instead of freezing it (which does cool the solution, but it's pretty negligible). Alternately, a magical substance can be used. Something like a magically induced reversed combustion reaction (to create a natural opposition to alchemist's fire) could be fun, along with very endothermic.


Well, the real world thermodynamics above were not exactly impressive. Real world physics are not on your side here, for the simple reason that water is a ridiculously good heat sink. Liquid nitrogen is also really not that impressive here.Huzzah thank you for the math!
What happens when you apply one more unit, and one more, and one more, etc? Does the exponential growth favor me in any way?

[Knaight]

Well there is also this thread that was likely the cause of the item coming into game existence:
http://paizo.com/threads/rzs2kmeu?Alchemists-Ice#1
Yeah, but they might still have gone with a different interpretation.


Huzzah thank you for the math!
What happens when you apply one more unit, and one more, and one more, etc? Does the exponential growth favor me in any way?

Nope. 837 mL 25 C water frozen per usage, and that's assuming that you don't waste energy cooling the ice further. If the nitrogen is subcooled you get somewhat better yields, but the description doesn't favor that, and it's fairly minor unless it gets really, really cold.

It's a linear system, essentially. You have the energy transfer to 1 gram of nitrogen heating it to 0 C and evaporating it (403.7 J), and the energy transfer from 1 gram of water cooling it to 0 C and freezing it ( 438.7 J). So, each gram of nitrogen freezes 0.92 grams of water. It's a linear system, not an exponential one.

I'm also neglecting the mass of the jar itself here - presumably it's fairly low. Still, it could be used to get a 1/5 of a gallon even per jar, which is a somewhat nicer number to deal with.

[felinoel]

837 mL
So just under one liter of water freezes per unit of liquid ice with no exponential growth?

That isn't too bad...

EDIT:
I assumed there would be exponential growth because the water surrounding the water getting frozen would cool the water before the next unit of liquid ice was applied.

[Knaight]

So just under one liter of water freezes per unit of liquid ice with no exponential growth?

That isn't too bad...

EDIT:
I assumed there would be exponential growth because the water surrounding the water getting frozen would cool the water before the next unit of liquid ice was applied.

The cold can propogate through the water, so the liquid ice wouldn't necessarily need direct contact with what it freezes (though given the volumes involved, direct contact is probably happening). Exponential growth isn't happening though, as the cooling of the water also heats the liquid ice, they reach equilibrium, and nothing interesting happens from there. The calculations I did were basically all simple calorimetry that works from that.

Basically, the system works like this.
1) Liquid nitrogen is put into water.
2) The liquid nitrogen evaporates, which sucks a lot of energy out of the water, which cools (some freezes).
3) The gaseous nitrogen is extremely cold and heats up, sucking a lot of energy out of the water, which cools (some freezes).
4) Everything involved reaches the same temperature, and the process stops.

The vast majority of the energy involved in evaporating the nitrogen and heating it comes from freezing the water. It takes the same amount of energy to melt ice as it does to heat the resulting melted ice to 80 degrees C.

[georgie_leech]

So just under one liter of water freezes per unit of liquid ice with no exponential growth?

That isn't too bad...

EDIT:
I assumed there would be exponential growth because the water surrounding the water getting frozen would cool the water before the next unit of liquid ice was applied.

Look at it this way. If it was exponential, an ice cube would freeze everything because it would freeze the area around it which would freeze the area around that bigger area which would freeze an even bigger area...

[felinoel]

The cold can propogate through the water, so the liquid ice wouldn't necessarily need direct contact with what it freezes (though given the volumes involved, direct contact is probably happening). Exponential growth isn't happening though, as the cooling of the water also heats the liquid ice, they reach equilibrium, and nothing interesting happens from there. The calculations I did were basically all simple calorimetry that works from that.

Basically, the system works like this.
1) Liquid nitrogen is put into water.
2) The liquid nitrogen evaporates, which sucks a lot of energy out of the water, which cools (some freezes).
3) The gaseous nitrogen is extremely cold and heats up, sucking a lot of energy out of the water, which cools (some freezes).
4) Everything involved reaches the same temperature, and the process stops.

The vast majority of the energy involved in evaporating the nitrogen and heating it comes from freezing the water. It takes the same amount of energy to melt ice as it does to heat the resulting melted ice to 80 degrees C.Cool stuff, thanks again!


Look at it this way. If it was exponential, an ice cube would freeze everything because it would freeze the area around it which would freeze the area around that bigger area which would freeze an even bigger area...But... an ice cube is not much colder than ice water?

[dascarletm]

You also have to account for the fact that as the nitrogen boils it goes into the atmosphere cooling the air around the water. You lose quite a bit of cooling potential this way.

I use Liquid N2 in lab to flash-freeze aqueous solutions, and from first-hand experience I can tell you that it takes more than an equivalent amount of N2 to freeze water, and what we use is sub-chilled.

Sad, I know.

[georgie_leech]

But... an ice cube is not much colder than ice water?

Right. There's a finite amount of heat it can absorb from the surrounding area. Changing how cold the substance is doesn't change that; the colder it is, the bigger the area of ice it will make, but that ice won't then go on to freeze an already bigger area.

[felinoel]

There's a finite amount of heat it can absorb from the surrounding area.OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH.

Yes that is right, my mistake it all makes perfect sense now.