# Is an "instant ice pack" sword actually feasible?

Working on my world, I'm reminded of ice mages that can instantly freeze their opponent using an Ice Ray.

That got me thinking if this is possible in the real world. The most promising method of instant freezing is using an ice pack, which immediately absorbs heat when the chemicals are mixed.

However, I'm skeptic of the freezing part. The best I guess such mixture can do is sort of frostbite in an area around the wound. That is fine to me.

What I'm asking is whether utilizing an instant cold pack as a melee weapon to achieve that effect is possible or not?

If yes, in what form can such a weapon can be effectively used?

Right now I'm thinking about something similar to a poisoned dagger, but using a dagger with ammonium nitrate wrapped in plastic. On a successful full stab (the blade fully penetrates the flesh), the ammonium nitrate will dissolve and cause endothermic reaction, hopefully enough to cause the intended effect of frostbite to surrounding tissues.

• Possible duplicate of Making freezer arrows using endothermic reactions Oct 16 '17 at 14:10
• @sphennings that makes arrow and bow out. Is applying via melee weapon viable? And thanks for that! Oct 16 '17 at 14:20
• I wonder if there would be a point to supercool air so much that it is solid and then use it as projectiles. Maybe the projectiles could be stable enough to penetrate the target, sublimate back into gas and create an overpressure which does additional damage like an explosive shell. It might create frostbite around the wound, but most of the damage would be kinetic. Oct 16 '17 at 14:27
• +1 for asking instead of just using it ;) also, related: worldbuilding.stackexchange.com/a/70770/809 Oct 16 '17 at 15:03
• Some funny thoughts: Would not your dagger stick to the target? Or to it's sheet? Other problems might be accumulating ice out of air humidity and you might not want to swing it when it rains. If the effect is provided trough high heat conducting materials. If your dagger is only the tool to inject your target with your chemicals (like a bee or a snake it's venom) you might get interesting effects even some way downstream the blood vessels. thinking further: it might be possible like with acids to construct a biological agent more potent than some physical chemistry. With time delay e.g. Oct 16 '17 at 15:51

In short, no.

A human body is sitting at something like 300 Kelvins (K). A flamethrower might reach 1000°C, or 1270K - but the coldest an icethrower can ever get is 0 K. Even that flamethrower, which while very damaging isn't by any means the hottest flame we can make, has a higher temperature differential than the freezer.

If you can get your victim to breathe in ultra-cold air, you can freeze the lungs and kill them that way. If you can immerse them in an ultra-cold fluid, that'll work. But the frostbite you'll give them by spraying even liquid helium on them, while it will be nasty and maybe eventually fatal, is nothing like as effective as the damage from a heat weapon that weighs the same and is easier to use.

• On the other hand, a macroscopic boze-einstein condensate is likely to be stupid dangerous due to its high density combined with the cold permitting a much greater total heat transfer. Oct 16 '17 at 20:00
• @joshua High density, you say? And rapidly expanding under STP, I assume? BEC bombs! Oct 16 '17 at 21:15

You're talking about hitting someone with an instant cold pack. WebMD recommends keeping a cloth between the ice pack and the skin and limiting exposure to 15-20 minutes. As a weapon it's not going to be very effective.

I'm not sure why you'd want to in the first place. Even if you dumped a dewar of liquid nitrogen on someone you'd be looking at some added frostbite. This will be unpleasant to whomever has been stabbed, but the stab wound itself is of much greater and more immediate concern.

What you're talking about (seemingly, correct me if I'm wrong) is supercooling a blade to the point where contact with human skin would cause some kind of Ice Burn or other lasting cold damage.

Unfortunately, while it is possible to supercool something like a dagger blade by dipping it in liquid nitrogen, the process makes the metal incredibly brittle, so using a dagger wouldn't be practical. It would break apart into splinters if you struck anything with force.

However, you could press the flat side onto someone's skin and apply pressure to force the supercold metal into them (This might be easier with a larger block of metal on a stick, like a hammer). However, as mentioned previously, you wouldn't be able to actually strike anyone with it, because it would just break.

It would work quite well as a torture device, but not as a melee weapon, I'm afraid.

• I'm now imagining a super cooled dagger stabbing into someone and shattering inside them leaving small pieces of freezing metal stuck in the body like a weird, evil, hollow-point. Ouch. Oct 17 '17 at 18:08
• Definitely as a torture device. Oct 19 '17 at 19:04
• DEFINITELY. (That would hurt a LOT!) Oct 19 '17 at 19:04

TL;DR: This is possible.

## Damage from skin conduction (no penetration)

Ignoring real-world compounds for a moment, what could work is a really cold solid with a high specific heat capacity so that it can absorb a lot of heat energy without significantly reducing the temperature gradient, which would cause the cooling rate to fall more than it would otherwise.

To simplify calculations, let's assume that our ideal solid has a temperature of $0 K$ (absolute zero) and an infinite specific heat capacity, i.e. will suck heat away as fast as possible. According to this tabulation (which has a lot of useful values for other tissues and organs), the epidermal layer of the skin has a thermal conductivity of $0.209 W/(mK)$ (watts per metres per Kelvin). The dermis has a thermal conductivity of between $0.293 W/(mK)$ and $0.322 W/(mK)$ - I'll assume $0.308 W/(mK)$. The tabulation doesn't have information on the subcutaneous layer but this page says that this layer is mainly fat and collagen, so I'm assuming a value of $0.209 W/(mK)$. Assuming an epidermal thickness of $0.2 mm$, a dermal thickness of $2.5 mm$ and a subcutaneous thickness of $1mm$ (I have not found information on the latter value so it's a complete guess), the total thermal conductivity of the skin is:

$$\frac{0.209 W/(mK)}{0.2mm} + \frac{0.308 W/(mK)}{2.5mm} + \frac{0.209 W/(mK)}{1mm} = 1380 W/(m^2K)$$

(I initially got the units wrong for this - this Physics SE answer helped to straighten this out.)

Assuming that the internal tissues of the human body are constantly at $310 K$, the energy loss through the skin is:

$$(310 K - 0 K) * 1380 W/(m^2K) = 427800 J/(m^2s)$$

$427800$ joules per second per metres squared of contact surface. However, this is not taking into account that melee weapons generally cut or stab, not press against the skin of the opponent. Also, they tend not to be theoretically perfect energy vacuums. This value means, given a surface area of $10 cm^2$ (flat of a blade) and a contact time of $0.25 s$, the heat transferred through the skin is:

$$427800 J/(m^2s) * 10 cm^2 * 0.25s = 107 J$$

$$\frac{107 J}{3470 J / (kg K)} = 0.0308 kg K = 30.8 g K$$

This is starting to look promising. Of course, this is spread out across $10 cm^2$ of skin. To work out how much this skin weighs, the density and thickness of the skin can be used. I couldn't find a value for the density online, but this page suggests that it is less than that of water - I estimate $0.95 kg / l$. First, the conversion factor between skin area and mass needs to be determined:

$$0.95 kg / l \times (0.2 mm + 2.5 mm + 1 mm) = 0.95 kg / dm^3 \times 3.7 mm = 3.51 kg / m^2$$

Combining this with the energy loss through the skin and specific heat capacity, this gives:

$$\frac{427800 J/(m^2s)}{3470 J/(kg K) \times 3.51 kg / m^2} = 35.12 K/s$$

Note that this is through the skin, assuming that the specific heat capacity of whatever is under the skin is $3470 J/(kg K)$ and has no thermal capacity. As the threshold for ice crystal formation in cytoplasm is ~4°C, or a difference of $41 K$, this gives a contact time of $1.168 s$ for third-degree frost-bite. This is without penetration of the skin. Contrary to some other answers, this is possible.

• However the trick is the ability of the heat to be drawn out from deeper in the body. Unless the blood flow is sufficient to keep pumping heat to the site, this sudden local cooling would be short-lived. Local frost bite. Once the heat is taken from the contact site, then what? Oct 16 '17 at 23:58
• I'd like to see the calculations carried through, keeping in mind that a stabbing action probably keeps the blade in contact with the skin for less than a second. Unless the knife is being held in, in which case it's probably a killing stab, which would render freezing a moot point. Pre-emptive +1 though. Oct 17 '17 at 2:17
• @JustinThyme At present my calculations make unrealistic assumptions - if it still didn't work with these assumptions then it would not be possible just via conduction but if it is possible with these assumptions that says nothing about how possible it is without them. I'll have to factor in the specific heat capacity of human tissue, which I don't have at the moment, to answer your question and complete my answer. Oct 17 '17 at 6:59
• I now have a worldbuilder's search history. Oct 17 '17 at 7:01
• @wizzwizz4 - I think a quarter second would be a fair place to start. There is probably room for a macabre discussion on the topic, but it seems like a good rough value. Oct 18 '17 at 0:26

This type of melee weapon would have some odd effects in terms of the wound it would inflict.

As discussed in this question: Sealing a wound: ice or fire? The ice treatment would cool and possibly freeze the blood and tissues around the wound. If the wound itself is not fatal, the extreme cold at the wound site would act to limit the initial loss of blood, possibly allowing the injured person more time to get medical treatment than they would otherwise have had from a non-freezing weapon.

Of course freezing tissue damages that tissue, so when the area around the stab site thaws, the bleeding and infection would likely be worse than from a normal stab wound. So definitely a mixed bag in terms of lethality.

• Well, the lethality is not discussed here, but you raised a point here. Can suggest ways of how such melee weapon can utilize instant cold pack to achieve such effect? Oct 18 '17 at 2:10

This would do some damage. This is just a theory, but the “ice pack” would destroy surrounding tissue, which would slow down healing of the wound. It would also hurt a LOT, maybe disorienting the target enough for you to hit them again. I’m thinking you just leave the dagger in, not pull it out. The constant pain would hurt more, and tissue damage would be accelerated. While the victim is distracted, pull out another dagger and stab them again.

• Leaving the dagger in would allow much more of the energy stored in the temperature gradient to dissipate, almost certainly increasing the damage significantly. I'll have to remove the energy-vacuum assumption part of my answer but once that's sorted I'll have a formula you can use to work out how long would cause how much damage. You've got the added bonus that frozen skin expands trapping the dagger and making it harder for the victim to pull it out. Oct 19 '17 at 19:17

Can an ammonium-nitrate ice pack be used to instantly freeze an entire average sized human? Possible, yes. Feasible, no (It would take hundreds, or have to be huge, and it would take a very long time).

Assuming an average sized male weighing 62 kg, and an average specific heat capacity of 3470 J/kg•K, the minimum amount of energy required to completely freeze them is:

$q=mC\Delta T = 62kg\cdot 3470\frac{J}{kg\cdot K}\cdot\left ( 37-0 \right )\approx8000 kJ$

How much energy could be absorbed by an instant ice pack? The molar heat of solution is the amount of energy released or absorbed per mole of solute being dissolved, and is typically found experimentally. One source lists the molar heat of solution of ammonium nitrate as:

$\Delta H^o=25.41 \frac{kJ}{mol}$

With a molecular mass of 80.043 g/mol, how much ammonium nitrate would be required to achieve that much cooling?

$m_{NH_4NO_3} = 8000kJ \cdot \frac{1}{25.41\frac{kJ}{mol}}\cdot 80.043 \frac{g}{mol} \cdot \frac{1}{1000\frac{g}{kg}}\approx 25kg$

That's a big cold pack, and that doesn't include the mass of water required to dissolve that much ammonium nitrate. Furthermore, this is a lower bound on the mass and doesn't incorporate heat flux, or how long it would take.

A typical instant ice pack contains 40 g of ammonium nitrate and enough water to make 200 g of solution. (Means we're looking at ~625 ice packs to freeze a human in an perfectly insulated environment) This also doesn't account for the extra amount of heat being generated by the human - on the order of 100-120W.

Can an instant ice pack cause localized tissue damage due to cooling? Yes, but it takes a while.

An icepack can lead to serious burns and frostbite depending on duration of contact, size of contact, blood flow, and other factors like wind. The primary mechanism of injury is freezing the water in the blood cells. Secondary injury can be caused by lack of blood flow to an area of tissue.

Ice pack burns usually results from minutes of contact (e.g., 20 minutes), not the fractions of seconds that may be involved in a melee attack.

Is an instant ice-pack sword feasible? Possible, maybe. Feasible, not really.

See @wizzwizz4's analysis.

Melee cold damage requires large amounts of heat to be transferred quickly. This has two parts: how much heat can be transferred (heat transfer), and how quickly that heat can be transferred (heat flux).

The heat transfer depends on the mass, specific heat capacity, and temperature differential. The heat flux depends on conductivity, and gradient.

As tissue freezes, heat conduction is reduced. The frozen tissue tends to insulate deeper tissue from being frozen.

Relying solely on conduction (e.g. direct contact) for heat transfer is going to be limited, since any heat removed from the tissue is going to warm up the weapon, reducing the temperature differential. This means a massive weapon.

What form could an instant ice-pack weapon take to maximize damage?

Maximize heat transfer

• increase mass of weapon
• increase specific heat capacity of weapon
• reduce mass of tissue
• increase temperature differential
• increase contact time

Maximize heat flux:

• increase the surface area in contact
• increase temperature differential

In a melee context, maximizing the amount of time in contact with the tissue could be achieved with a blade that penetrates and stays, or something that is wrapped around a part of the target (like a whip).

To maximize the temperature differential between tissue and material, the weapon needs to be extremely cold (as close to 0K as possible). This needs to be balanced with the fact that many materials become more brittle at lower temperature.

Conduction could be increased on the weapon side if it was made of a material with high thermal conductivity (e.g. metal). This could be implemented as a hollow sword, with the instant ice pack material inside.

Local freezing could also make a penetrated blade more difficult to remove if it was frozen to the tissue.

EDIT: The original answer was based on super-cooled liquids as an alternative mechanism to get instant ice. A volume of super-cooled liquid could be nucleated and crystallized/frozen into the shape of whatever container it was in: basically an instant icicle. This could cause localized tissue damage using the same mechanism as an ice burn, especially if it was stabbed and remained in place.

• But this would in no way freeze the enemy, right? It would still only freeze wound? Oct 17 '17 at 19:38
• Freezing the enemy could mean different things - freezing solid is going to take a whole lot more energy than freezing a certain thickness of skin. This would likely be just a local effect.
– JDMc
Oct 17 '17 at 19:59
• The question asked for a feasibility assessment. Oct 17 '17 at 20:00
• @sphennings Supercooled liquids are also commonly used in reusable instant ice packs. This discusses whether a weapon made from one would be feasible. Open to suggestions for improvement.
– JDMc
Oct 17 '17 at 23:29
• Your 4th paragraph attempts to answer the question, although it requires feasibility test in itself (supercooled water will freeze upon firing or impact, making it impossible to "inject" water to the body). Your 3rd paragraph almost makes me hit "recommend deletion". I suggest you remove the 3rd completely. Oct 18 '17 at 1:17