Under Pressure

The scourge of “terrorism” — for today’s purposes, let’s take the word to mean attacks on civilians perpetrated by individuals or by small, stateless groups — is a part of human existence going back as far as you want to look. If a person has what he or she views as a grievance, then attacking people who are loosely connected to that grievance, in order to kill and maim some of them and frighten the rest, is obviously one of the options, immoral and hideous as it may be. There’s nothing modern about the strategy of terror.

What’s new about terrorism in the modern world is science. Science, via the technology that it makes possible, is a great multiplier. It allows an individual, or a small group, to exploit power inherent in nature, turning a task that no human could perform, or that would take a cast of thousands, into something that can be done with ease by a few people, or even just one. Of course this multiplied power has many benefits for us as individuals and for society as a whole; think of trains, tunnel-boring machines, skyscraper cranes, snow-blowers, pneumatic drills, aircraft engines, power plants, and on and on. But it also poses many risks and challenges that we have to face, as individuals and as a global civilization.

I personally don’t think we can hope to eradicate terror; it’s too deeply ingrained in being human. The arms race between those who would carry out attacks and those who try to prevent them will never be won by either side. But every time the enemies of civil society develop a new tactic, it is important to respond by poking holes in it, to the extent possible. In fact it would be optimal to respond before that strategy actually gets used, though this never seems to happen in our culture. Still, better late than never, I suppose.

Enter the pressure cooker.

What is a pressure cooker? The basic scientific principle behind this device is very simple, and goes back at least as far as 1679. Denis Papin, a Frenchman (should we be surprised? bon appetit!), who was what we would today call a physicist and mathematician, is usually credited with its invention, though it didn’t become widespread until recent decades, when it became reliably safe for use in the home. I don’t know the precise history, but Papin, an expert on steam and its uses in engines, must have been among those who knew that under higher pressure, water boils at a higher temperature, as shown in the figure below. (Anyone who lives at high altitude, where the pressure of the atmosphere is lower than at sea level, knows the reverse is true; water boils at a lower temperature in Denver or Mexico City or Kathmandu than it does in New York or Shanghai or Cairo, so it takes longer to cook food in boiling water.) The hotter steam that emerges from the hotter boiling water can be used to cook food quickly and in a humid environment, keeping it moist.


How water’s boiling temperature is affected by the pressure of the gas (typically air mixed with steam) above the water. At sea level, the pressure of air is about 100 kPa, and water boils at 100 degrees Celsius, as marked by the red dot; the violet dot marks the maximum pressure and temperature of steam inside a standard pressure cooker.

The challenge for using high-pressure, high-temperature steam for cooking is that if the pressure in a gas is higher in one region than another, then the gas will move, if it can, in such a way as to equalize the pressure. Indeed, when you boil water in a tea kettle, the cool air outside the kettle has lower pressure than the hot steam in the kettle, so the steam rushes outward. And this flow of steam can be exploited to blow a whistle, alerting you that the water is boiling.  So high-temperature steam won’t stay where you want it to, unless you lock it inside a container.

A pressure cooker, therefore, has to be sealed tight when it is being used. You put the food above some water in the cooker; you close it; and you turn on the heat. The water boils a bit, and some steam forms above the water. In a kettle, the steam would escape and cause a whistle; but since the pressure cooker is sealed, the steam has no place to go, so the pressure of the air and steam inside the pressure cooker goes up a bit. This in turn increases the boiling point of the water. But the heat is still on, so the water gets hotter, boils a bit, more steam emerges, and as it has nowhere to go, the pressure again increases. And so it continues, moving the water and steam along the blue curve shown in the figure, until the desired pressure and temperature are reached.

Many pressure cookers can safely handle a pressure which is double the pressure that the atmosphere itself exerts on us down at sea level.  (“Safely” means the seal won’t break until the pressure reaches much higher levels.)   As seen in the figure, doubling the pressure found at sea level increases the boiling point of the water, and therefore the resulting steam, from 100 degrees Celsius to about 121 degrees (i.e. from 212 degrees Farenheit to 250 degrees).

Note that doubling the pressure means that the pressure difference between inside and outside is about the same magnitude, but opposite in direction, as would be found between ordinary sea-level air and a vacuum — i.e., a container out of which all the air had been pumped.  

Unfortunately the same tight seal that a pressure cooker requires is useful in multiplying the power of an explosive. The moment a material begins to explode, the chemical reaction it is undergoing creates high-pressure gases.  If the explosion begins in the open air, those gases begin to rush outward immediately. But if these gases are trapped — say, inside a pressure cooker — then they have nowhere to go, and so, in an instant, the pressure builds up. When finally the trapped gases are under so much pressure that they blast the containing vessel apart, they do so with a much more powerful explosion than would have occurred had they not been trapped. And of course, the broken pieces of the vessel, and any nasty materials stored inside the vessel, such as nails or metal balls, become deadly shrapnel.

It is unfortunate that a pressure cooker, a simple, useful and widely available device, based on such simple scientific principles, can be used just as simply to increase the killing power of a single vicious individual. And it’s even more unfortunate that terror networks have been encouraging people to use this method, without us doing anything to make pressure cookers more difficult to obtain.

But perhaps this tactic, at least, can be subverted?

To work properly, a pressure cooker needs to have a tight seal at 100 degrees Celsius and in the presence of steam.  The temperature and pressure build up slowly, over minutes. A bomber, by contrast, wants a vessel that has a tight seal at (initially) much lower temperatures, sustains that seal under a very rapid build up of pressure over a tiny fraction of a second, and does so even when there’s no substantial amount of steam, compared to other gasses released in the explosion. In short, the physical conditions encountered while cooking are very different from those in a nascent bomb.

So, inventors: can you design a pressure cooker that is safe and effective for cooking in the home, but has a seal that will instantly and completely fail if used in a bomb?

Of course, it’s not obvious a redesign is of much use. Perhaps there are many simple substitutes for pressure cookers that are only a bit more expensive and only a bit more trouble to obtain. But still, why make it easy for mass murderers?

Those in the United States will recognize some shards of irony embedded in this question.

36 responses to “Under Pressure

  1. Great comment and suggestion!

  2. Garcol Equphrates

    Thank goodness you didn’t mention g-ns; You would have been deluged with responses! :{}

  3. The other advantage pressure cookers hold for the terrorist is that they are so common they can’t be traced.

    It’s uncommonly easy to plan a small mass murder. What defends us is human nature. There are a number of bases to cover in addition to the weapon, such as privacy and availability.

    I think it is notable that in Boston, a large community was trained and prepared. Indeed, the civil response system was already mobilized and positioned. My personal hope is that the eventual outcome of the event will be to strengthen civic pressures against terrorism. It is these civic pressures that protect us better than most mechanical solutions.

  4. Regarding the invitation for inventors to propose ideas for pressure cookers that are not useful to develop homemade explosive devices, a simple idea to go after would be the rate of increase of the pressure, that is, at least the first derivative of the pressure as a function of time (the second derivative could also be useful, actually).

    As the pressure actually is a function a more variables and not only time, inventors should go after partial differential equations that could be interesting for the two types of problems at hand and specially, the differences between these two types of problems: how water turns into vapor within a pressure cooker, and how an explosion evolves within a pressure cooker.

    Any explosive based on TNT, gun powder, cordite or similar chemical compounds depends on chemical reactions that all share a similar kind of reaction kinetics, a chain reaction type of chemical kinetics (these are chemical chain reactions, not nuclear chain reactions).

    There are different varieties of chemical chain reactions, but all share a similar global structure of three general stages within the reaction mechanism:

    An initiation stage

    A propagation stage

    A finalization stage

    In general, it is the propagation stage that is the most significant (and characteristic) of chain reactions.

    So, it seems that inventors could exploit at least two different principles to consider (re)designs of pressure cookers that would be “terrorist-safe” (safe at least for some time): the rate of increase of pressure within the pressure cooker, and the telltails signs of a chain reaction from a physical perspective (temperature, pressure, etc.).

    For instance, the seal mechanism of the pressure cooker could work OK and reliably with a “slow” rate of increase of pressure, and break at a “fast” increase of pressure, very much like the release valves in a steam engine.

    Any steam engine is designed to work under a certain range of pressure, and any pressure above a certain threshold value is dangerous for the engine to substain, so, they have these valves that release steam when the pressure is above the threshold value to protect the engine.

    Kind regards, GEN

  5. By the way, how about that fertilizer plant?

  6. Richard Bauman

    Great Physics, so you are a Republican too ?

  7. Well, we should remember that Tim McVeigh (the attack at Oklahoma City) used a homemade explosive compound based on fertilizer.

    In fact, the first attack at the Twin Towers (the explosion at the garage) also depended on an explosive compound based on fertilizer.

    In Argentina we have suffered two major terrorist attacks (in 1992 and 1994) that also used explosive compounds based on fertilizer.

    The use of these types of homemade explosive compounds based on fertilizer are common all around the world.

    It all comes down to the fact that nitrates are important compounds in the chemical cycles of both fertilizers and explosives.

  8. It’s hard to express how mixed feelings I have about this.

    As technical challenge, it sure is possible to solve.
    Another thing is, how successful do you expect to be in convincing the whole world that they should throw out and scrap their current cheap pressure cookers and start using new, expensive, terrorist-proof ones. You may succeed in USA but I have my doubts about China, India and Africa, to name just a few. If you ban the cheap ones you’re just making the poor world even poorer. In total numbers your ban on cheap product may cause more deaths than what was caused by its terrorist abuse.

    The main problem about terrorism nowadays is its media popularity. If nobody was giving a damn about terrorist attacks and who’s behind them, of course there would still be a few sick individuals who would do that anyway but total numbers would go down significantly because terrorists would soon figure out that they’re accomplishing nothing. And what would remain would be much easier to handle.

    • Terrorism is singularly unsuccessful in resolving anything. The terrorist’s adversaries only become more determined.

  9. Perhaps a national registry of pressure-cooker owners and mandatory background checks for pressure-cooker purchases is in order?

    • Firearms are weapons, and their primary function is to kill (that’s what weapons do); pressure cookers are not weapons (they are kitchenware), and their primary function is to cook.

      It makes no sense to trivialize the importance of background checks for any firearm sale.

      • So that’s why Law Enforcement carries guns, so they can kill. Good to know. How about a knife? Kitchenware, weapon, or both?

        • Indeed, anyone with sense will tell you, if you use a gun, be prepared to kill. It’s nearly impossible to use a gun for anything else.

          • The local DA will have you for breakfast if that is your attitude. You use a gun to make the attacker stop, period. When the attack stops, you can no longer use deadly force. And if the attack stops without a shot being fired, so much the better.

          • Indeed, if the threat but not use stops the attack. But if I use the gun, if I shoot someone to stop an attack and deliberately intend to wound not kill I can be prosecuted.

            A gun, when used properly is intended to kill (even injury could be considered part of this.) there are few other things I can think of that have that as their primary purpose without which they would be of trivial use.

  10. The more common suggestion with fertilizer has been to suggest that something traceable that would survive an explosion allowing the source to be identified be included in the mix before sale – basically nano-VIN numbers that show locations and even particular batches of fertilizer (at least to a month or year) and that customers be logged (a bit like Sudafed purchases). This also has the virtue of allowing contaminated (e.g. biohazard or broken glass) or lots that are defective for any other reason to be tracked as well.

  11. Just like Prof Strassler mentioned, the higher the altitude, the lower is the atmospheric pressure (because you are closer to the edge of the atmosphere, so, you have less air on top of your head).

    But altitude is not the only factor that can change (decrease) pressure in a fluid. Speed can also decrease pressure, and this is something that has a rather negative effect on boat propellers.

    This effect is called cavitation, and this decrease of pressure can be such that water literally boils into bubbles of vapor around the blades of a propeller. As soon as the speed decreases enough, the pressure increases again and the bubbles collapse into a very distinct “pop” sound, very characteristic of this effect.

    This is a very negative effect, specially for submarines, so, the propellers for submarines are specially designed to avoid cavitation.

    Liquid water behaves like a non compressible fluid (when compressed it does not change its volume like a gas will do, even though water is not an ideal or perfect non compressible fluid), so, we can apply Bernoulli’s equation to water. This equation is a natural consequence of the conservation law of mechanical energy in classical (newtonian) mechanics:

    p + 1/2mV^2 + mgh = Constant

    If the height remains the same (so, the potential energy remains the same), when the kinetic energy increases (the kinetic energy increases when the speed increases), then, the pressure has to decrease. Through this equation is very simple to understand how cavitation could happen: all it takes is a speed high enough for pressure to go below the value of vapor pressure of water for the given conditions at sea.

    Kind regards, GEN

  12. I would think the major problem with a design like this would be kitchen safety; it is very hard to design a component that fails quickly under a given circumstance without its performance under less trying circumstances being compromised; a seal that was weak enough to fail under bomb pressure would likely have a shorter life than current seals and be prone to failure i ordinary circumstances.

    It reminds me of the current whooping cough vaccine. It is much safer in regards to side effects when being vaccinated, but as a result of this provides inferior protection compared to the old vaccine, something that has encouraged recent whooping cough epidemics.

  13. Frank Schwab

    I think the bigger problem is that the proposed solution won’t affect the problem. I’d submit that it’s likely that a pressure cooker with the seal removed (so no possibility of holding static pressure) would still amplify the effects of an explosive placed within it – the dynamic pressure rise from the explosion would still be effectively contained by the “impedance”, if you will, of the narrow obstructed slot between the lid and pot. Perhaps not as effective as having a seal, but still better than not having one.

    And I don’t understand why you’d bother with a pressure cooker when you have access to 2″ iron pipes at the local Home Depot (burst pressure measured in the hundreds of PSI).

    • A pressure cooker is much more effective than a pipe for at least three reasons:

      1) a pressure cooker can substain a much larger increase of pressure before breaking,

      2) for a given surface area, it can contain a much larger larger volume, which translates into a larger “payload” of schrapnel,

      3) and a pressure cooker has a shape closer to a sphere than a pipe does (a pipe is a cylinder), and the geometry, as well as the surface area, is a very important factor in the design of an “anti-personnel” explosive device. Other types of anti-personnel explosive devices are directional, and the geometry is clearly determined (and constrained) by this design attribute.

      Being myself a chemical engineer by training, I had to study how to design things like chemical reactors and heat exchangers, so, for many types of engineers (including mechanical engineers), it is crystal clear how behaviour and functionality of a certain type of machine may constrain its shape.

      Kind regards, GEN

      • It can be proven with simple calculus that the 3D shape that can contain the largest volume with the least surface area is a sphere, and that is the reason why liquids in the absence gravity shape into spheres.

      • An inferior bomb would produce mostly the same results, given the same context.

  14. This might sound stupid, but couldn’t you use the container’s material itself as a regulator?

    A pressure cooker makes a great bomb because its metal has the ability to maintain its structure past the 250’/15 psi needed to cook. Well, what for? Just make the cookers out of something that self-destructs beyond the required cooking point.

    To make a bomb with a cooker, you just bypass the safety mechanism to build the psi; but no matter how you rig it, a cooker can’t explode if the bottom melts out before psi reaches an explosive level.

    Help fight terrorism and save a few kitchens as well.

    Thanks for the article. Never used a pressure cooker. Had no idea they were death pots.

    Once you figure out the pressure cooker thing you’ll probably have to move on to microwaves. Ever see a hotdog blow up? Not pretty. Not pretty at all.

  15. Blaise Pascal

    There are a large number of readily available pressure containers out there, not counting things like the 2″ pipes from Home Depot mentioned earlier.

    Beer kegs, commercial soda containers (aka “Cornelius kegs”), propane tanks, fire extinguishers, commercial gas cylinders, etc are all designed to hold high pressures (most at much higher pressures than you’d find in a pressure cooker) at room temperature, and all are relatively easy to get ones hands on. Many of them have known hazards if mishandled in their normal operation (the stories of gas cylinders falling and breaking off their valve, or of LN dewars accidentally sealed until they explode, are easy to find). Heck, even a standard 2-liter plastic soda bottle has a burst pressure much higher than what you’d normally find in a pressure cooker. A SIGG bottle would be even higher.

    Today’s terrorist (or terrorist wannabe) used pressure cookers. It was easy and convenient. Tomorrow’s terrorist wannabe will use something else easy and convenient.

  16. Google “chemical explosives and propellants,” and “ballistics” and the physics of firepower.
    Before the later 16th century there was not much scientific examination of these, and surely not of the mathematics.There was always the work of Archimedes (his ‘claw’ – if real) and Leonardo da Vinci! Leonardo designed this (almost comically) oversized catapult. Yes he “designed” tanks and helicopters as well, but was not, AFAIK, a mathematician. It was more than the contemporary state of technology. The understanding of physical forces was still elementary. Chemistry was somewhat more advanced, but not much.
    Mathematics was, at that time, more applied to fortifications and their design (geometric considerations, and the limits of the range of artillery fire – pretty arithmetic). The OP seems to be thinking of physical forces and chemical understandings, as applied to military pursuits, that had minimal practical application before the later 16th century.
    Geometry, and the ability to count are far older skills. Soldiers and engineers understood how things affected military pursuits, but perhaps not so much why they did so.

    To bring the war to Quantum level ?
    Konfliktforschung: Die Physik des Krieges: Individuen wie Moleküle in einem Gas: file:///F:/BUS%2041/konfliktforschung-die-physik-des-krieges-1.963657.htm

  17. This is a terrifying blog Professor it goes differently inside my head, you described to me how to build a portable thermonuclear device with a plum-size plutonium. The objective of terrorism is to terrorize and they will find alternative ways to terrorize, 50 ways to skin a cat so to speak. Thus we need to think another 49 ways to circumvent their ways hoping we won’t create expensive and unnecessary legislation in the process.

  18. Dear Matt

    Many thanks for those very insightful comments. So true – unfortunately. Please allow me to try to add two remarks. 

    Firstly, you mention “The arms race between those who would carry out attacks and those who try to prevent them will never be won by either side”. I would like to add that the two parties mentioned, i.e. those “who would carry out attacks” on one and “those who try to prevent them” on the other side are usually *not* the two opposing  parties in the arms race itself. Instead, there are commonly two parties involved, who would *both* “carry out attacks”, while the party “try[ing] to prevent them” is commonly a third and unfortunately much weaker party. (Your wording does fully allow for the latter Interpretation and might indeed be, what you meant to imply. I would be happy, if my comment helps to clarify in that respect.)

    Secondly, although is is not yet clear whether the assault in Boston was somehow related to any kind of religious fundamentalism, it appears to me, that christian religion underwent a very similar phase of tremendous terroristic violence, through crusades, witch-burning and the like, at more or less precisely the same age, that the islamic religion has nowadays encountered. However as you mention, the current state of science & technology is a multiplier that greatly exacerbates the effects of contemporary terrorism as compared to those that cursed mankind several centuries ago. I do hardly dare to imagine, how earth would look today, had nuclear weapons been at the disposal of some medieval, crusading emperor?

    Provided that some underlying principles lead to those remarkarbly similar violent phases during evolution of a monotheistic world religion, I can only hope, that islamic religion will asap transform into a phase of peaceful coexistence with all other religions and societies, founded on “recognition of the inherent dignity and of the equal and inalienable rights of all members of the human family”, as stated in “The Universal Declaration of Human Rights”.

    Recent evidence [1] may indicate, that “Thinking about science leads individuals to endorse more stringent moral norms and exhibit more morally normative behavior.”. To me this does clearly show that all your work & unbelievable effort in maintaining this superb blog will also help in making this world a better place – even in areas, you might not at first expect to be influenced by it, like endorsement of moral norms. Many thanks also for that, Matt. 

    Imagine what will happen, if some new religion coming up during the next hundred years or so will go through its violent phase thousand years later? We better start to increase worldwide scientific literacy sooner than later, or mankind may not be able to survive then.

    [1] http://science.slashdot.org/story/13/03/30/1857216/does-scientific-literacy-make-people-more-ethical

  19. Even though this post in particular does invite to reflect on things beyond the realm of science, it is my understanding that it would help a lot to keep the discussions and its subjects close to the main theme of this blog, and which is science and, to some extent, its direct consequences, like technology, for instance.

  20. Richard Bauman

    Wow; that guy is not a Republican ! Oh, forgot, this is science.

  21. I think it would be less than meaningful to redesign the pressure cooker since almost any metal (or even plastic) container with a few liters of volume would work equally well as an low explosive device. And if the terrorists have access to high explosives, then the container has no function except to produce shrapnel.

  22. I pay a quick visit every day a few web pages and information sites to read content, but this weblog presents feature based articles.

  23. Thanks for another informative website. Where else could I am getting that
    kind of info written in such an ideal means? I have a undertaking that I’m just now running on, and I have been on the look out for such info.

  24. What i do not understood is actually how you are
    now not actually a lot more well-appreciated than you might be now.
    You are so intelligent. You recognize thus significantly in terms of this matter,
    produced me for my part believe it from a lot of numerous angles.
    Its like men and women aren’t interested until it’s one thing to do with Woman gaga!
    Your individual stuffs nice. Always take care of it up!

  25. I was suggested this blog by my cousin. I’m not sure whether
    this post is written by him as no one else know such detailed about my problem.
    You’re wonderful! Thanks!

  26. spider man hack

    When someone writes an article he/she maintains the idea
    of a user in his/her mind that how a user can know it. So
    that’s why this post is amazing. Thanks!