I make an effort to say nice things about pop-science books that I read, whether for book research or blog reviews. Every now and then, though, I hit a book that has enough problems that I have a hard time taking anything positive from it.
I got David Bodanis's E=mc2: A Biography of the World's Most Famous Equation from Union's library because I like the subtitle, and plan to reference it in the relevant chapter of the book-in-progress. I figured that, if I'm going to swipe his subtitle, I should at least be able to say something substantive about the book.
Bodanis takes pains to say that this isn't a book about the science of Einstein's equation, but rather a "biography" of it, basically a collection of interesting historical anecdotes about the equivalence of mass and energy. The problem is, on the occasions when he does talk about the science, it's always a bit off, by enough that I'm not sure I trust his historical anecdotes, either.
In an effort to find something good to say, though, I'll say that he at least managed to stimulate some physics-y thought with one particular paragraph. Toward the end of the section about the sinking of the Lake Tinnsjo ferry to prevent a shipment of heavy water from reaching the Nazi atomic bomb program, he writes:
A few of the barrels that had been only slightly purified bobbed on the top of the lake, and the passengers who'd managed to get off but hadn't made it onto lifeboats... grabbed on till a rescue boat came. But the barrels that contained the concentrated heavy water demonstrated, in slow-motion free fall, what they contained. Since the H2O molecules are composed of a nucleus heavier than ordinary water, the barrels sank as if weighted, swirling around the ferry and its innocent trapped passengers down to the bottom.
You can see what I mean by the science being a little off-- he uses "H2O" as if it was something different than "ordinary water" (usually, heavy water is written "D2O," from the name "deuterium" given to heavy hydrogen), he talks about a water molecule as if it were a thing with a single nucleus (which might arguably make sense at a coarse enough approximation, but just sounds wrong), and most of all, the way he talks about the sinking of the barrels makes it sound like heavy water is double the mass or ordinary water, when in fact it's only about 10% heavier (most of the mass of a water molecule comes from the single oxygen, with a mass of 16 atomic units; hydrogen adds 2 for a total mass of 18, deuterium adds 4 for a total mass of 20, so an increase of 1/9 the original mass).
But is the picture described plausible? That is, would it be reasonable to think that a barrel full of heavy water would sink, where a barrel full of ordinary water would float?
My first reaction was "That's ridiculous. They sank because the water was in barrels. It's the mass of the container, not the mass of the contents that makes the difference."
The key factor in determining whether an object sinks or floats is whether the mass of that object is greater than the mass of an equal volume of water (for the details, look up buoyancy) as has been known since the time of Archimedes. This is why ships float when all goes well-- the air inside the ship has basically no mass compared to water, so while the hull materials are all heavier than water, the total mass of the ship is less than the mass of an equivalent volume of water-- but sink when they hit an iceberg and fill up with water-- once there's enough water in the hull to make up for the mass difference, the whole thing goes straight to the bottom. You can demonstrate this for yourself with a cake pan and a sink full of water-- an empty pan will float, but if you start pouring water in from a glass, the pan will sink below the surface, long before you have filled it from the glass.
So, if you have a barrel that is entirely full of water, it will sink, whether it's heavy water or ordinary water. The mass of the water inside the barrel is obviously equal to the mass of the same volume of water outside the barrel, while the mass of the metal making up the barrel itself is far greater than the mass of the same volume of water-- around 8 times greater, for most useful metals.
But is it possible that you could have a situation where a barrel containing ordinary water would float, while a barrel of heavy water would sink? That is, what would you need to do for that 10% difference in mass to make the difference between sinking and floating?
Well, if you want a barrel of water to float, you need to not fill it up all the way. How much space do you need to leave? To know that, you need to know the volume, and the weight of the barrel. If we assume the barrel to be the canonical 55 gallon drum, the volume is around 200 liters, and the mass of an equivalent volume of water is about 200 kg. So, what's the mass of a 55 gallon drum? A little Googling turns up this hilarious page which boldly states a value for the weight, and then gives a bunch of examples, none of which are anywhere near as large as the first number. People selling steel drums claim a mass of about 50lbs, while the lightest mass claimed at WikiAnswers is around 20 lbs, so let's say between 10-20 kg total mass.
If you want a steel barrel of water to float, then, you need to leave out at least enough water to add up to the mass of the metal. At the high end of barrel masses, that's about 10% of the mass of the full volume of water, so you would only fill the barrel to 90% of its total capacity. The same volume of heavy water would be about 10% heavier, so if you got the percentages exactly right, there probably is a point where a barrel of ordinary water would float while a barrel of pure heavy water would sink (these are very rough numbers, but I'm only after a back-of-the-envelope estimate of the plausibility).
Is that a reasonable fill level? My first inclination would be to say no, at least not for a resource that was sufficiently valuable to the Nazis for the allies to sink a ferry with innocent passengers on board to stop it from reaching Germany. You would think that they would fill those barrels right to the top.
However, if you look at that link all the way back up at the top, you'll see that the ferry sinking took place in February. In Norway. Given that water expands when it freezes, you would need to leave a little extra space inside the barrels so that the water would have room to expand, should it freeze along the way. How much space? Well, an iceberg is famously 9/10th below water, which tells you that the mass of a given volume of ice is about 90% of the mass of the same volume of water. So, the expansion during freezing must be about 10% of the volume, which means you would want your barrels to be at most 90% full.
So is it plausible that barrels of heavy water might've sunk, while barrels that contained ordinary water floated? Yes, barely. It would depend on the details of the barrels-- their exact dimensions and mass-- and how they were filled and shipped. With slightly lighter barrels and a 90% fill, the 10% mass difference between heavy water and ordianry water might make the difference between sinking and floating. You'd need to do the math a little more carefully than I did above, but there's a reasonable chance that it might work.
I suspect, though, that the fill fraction is still a bigger factor than the mass difference. That is, the barrels that floated on the surface were probably not filled up to the same level as the ones that sank. (We'll also ignore the fact that most of them were probably tied onto something so they didn't roll around loose, and thus they went down as one unit with the ferry...) While it's plausible that the mass might've made the difference, the numbers are close enough that it would seem kind of a big coincidence for that to be the determining factor. Particularly since they were supposedly incompletely purified, not pure light water, which would imply some increase in mass, of not the full 10%.
But, hey, on the bright side, I passed a few amusing hours thinking about the physics of buoyancy. And time spent thinking about physics is never completely wasted...
- Log in to post comments
You can add in confounding factors like maybe the heavy water barrels were filled so they WOULD float in case some clumsy guy knocked one off the deck while loading. So they wouldn't lose their precious cargo. In which case maybe all the floating barrels were heavy water barrels.
Are you confusing steel drums with barrels? For all you know, the barrels could have been made of wood, which is lighter than water.
@Mana Towoc: You would be taking the chance of water exchange between the wood and the contents diluting (slightly) your very expensively obtained D2O. Or worse - springing a leak....
If I were transporting it then I would have put it in the most robust container I could find - steel drums.
It gets even worse I think. If you had a barrel riding this 90% full fine-line of sinking and floating, then tried to use it to buoy a person in the water as the author claims, wouldn't you have to count part of the person's mass as well in your calculations? How much will this be?
I know it won't be the full weight of the person, but I think it makes the whole situation a little less plausible.
@andre3,
No, you don't really have to count the person. The weight will make the barrel ride a bit lower in the water, but since the person is also buoyant, the exterior addition of the person cannot possibly sink it.
In the extreme case, imagine the person climbing on top of the barrel, putting their full weight on it and completely submerging it. As the person sinks into the water, they become buoyant and reach the situation where the person is floating high in the water, and the barrel is trapped beneath them pushing up. The person cannot continue pushing the barrel down into the water at this point because they do not have the traction against the water to do it.
Another way to look at it: when the person grabs onto the barrel, yes, the person's mass becomes relevant, but you also have to add the person's volume into the system. Since the barrel is lighter than water, and the person is lighter than water, the aggregate of the two cannot be denser than water.
From Wikipedia, that infallible source of all knowledge:
http://en.wikipedia.org/wiki/Norwegian_heavy_water_sabotage#Sinking_the…
"Witnesses reported seeing steel drums floating after the sinking, leading to speculation that they did not really contain heavy water, but an examination of records after the war showed that some barrels were only half full, and therefore would have floated."
Are you confusing steel drums with barrels? For all you know, the barrels could have been made of wood, which is lighter than water.
True. I think Benjamin's point about contamination is a good one-- you'd want something impermeable for your extremely valuable heavy water. Also, I saw a History Channel program on it a few years back (one of the experts interviewed is my colleague Mark Walker, in the History department at Union), and they had some shots from divers visiting the wreck, which was full of metal drums, not wooden barrels.
As anyone north of South Carolina knows this year: *ALL* water is heavy.
Badum bum.
Sorry, making bad snow-jokes is a defense mechanism.
Nice discussion. However, if the barrels were made of wood, which might be less dense than water, the buoyancy has to account for that as well. I agree it seems intuitively pretty unlikely that everything else factored in, a 10% difference in density would be just enough. One other question though, even though the deuterium versus hydrogen is easily calculable in terms of mass, are there significant effects on water density due to isotopic effects on hydrogen bonding between D20 vs H20 molecules? My understanding is that hydrogen bonding is a major factor in water colligative structure and properties.
As an aside, the Norwegian commandos that bombed the train had previously bombed the factory, which was a converted Haber process plant producing D20 as a side-product of ammonia synthesis. The factory is in Rjukan, a lovely small town in the center of the country, and some years ago there was a 50th anniversary celebration of the event, which I attended while doing some x-country skiing in Norway (the anniversary, not the bombing!). Most of the original commando team were still alive and were the stars of the show. Many years ago, the whole operation was made into a pretty weak movie starring Kirk Douglas, called Heroes of Telemark.
Much of this density difference is because the iceberg is mostly fresh water if it calved off of say the Greenland ice sheet and floating in salt water. If you look at an ice cube floating in glass, the amount sticking out of the water is much less than 10%.
Was the ferry crossing salt water? If the barrels contained fresh water, they could conceivable float in salt water.
Even without the freezing it's not inconceivable that the barrels would only be 90% full. I'm guessing the limiting factor in supplying the heavy water would be in the preparation rather than transportation. There would be no need to pack the barrels as tightly as possible.
Also, it doesn't make much sense to me to be sending barrels of regular h2o. In the Wikipedia article it states that some of the barrels were half full. This seems to me a much better explanation of why they were floating.
Yes, why isn't the density of salt water addressed?
German industrialists working in Norway in the 1940s would not have used wooden barrels. trust me on this; such things were notably obsolete even back then.
Yes, why isn't the density of salt water addressed?
From the article: "Toward the end of the section about the sinking of the Lake Tinnsjo ferry..." (emphasis mine) Salt water lakes do exist, but the lake in question is a fresh water body.
-- Steve
It's quite reasonable that there would be some partially-filled barrels, but they would contain a variety of enrichment levels.
The production process for heavy water is multi-stage. At each stage, deuterium-enriched output goes on to the next stage while depleted output goes back to the previous stage. When the process is stopped, each stage has a certain level of enrichment, and these must be kept separate during transport so the process can be restarted without starting all over.
Since the tanks at each stage would not necessarily hold an even multiple of 55 gallons, there would be at least one partially-filled drum for each stage. That number could be multiplied if the plant had multiple lines running in parallel.
IIRC, the Norsk Hydro plant had something on the order of 20 stages, so there would have been a fair number of positively-bouyant barrels aboard the ferry.
Mark @10,
I had that same thought. The macroscopic density isn't just a function of the molecular weight, so it's plausible that the substitution could change the hydrogen bonding enough to have the density of D2O be significantly different than 1.10. I've even seen some papers in my field where that substitution has noticeable effects on solution properties of polymers.
I checked my boss's CRC, though, and it appears that the density of D2O is 1.10, with all the temperature variation in the next digit.
I think Donnie B. hit the nail on the head. Exactly what I was thinking.
I read another book by Bodanis, _Electricity_, and had problems with his confusing metaphors. The atoms of a material are like the pillars of an Egypt temple, and the photons are like archeologists being pulled in behind the pillars... What, exactly, does that mean?
Segue into other interesting properties of heavy water: it doesn't support life. Rats given only D2O will eventually die although it isn't toxic in the usual sense of I suppose drinking a glass cause some serious problem. Having double weight hydrogen is enough difference to make it not fit well enough in to biological needs. Also, many drugs work differently with D-substituted molecules. The below, from the Wikipedia article, is interesting and I wonder why some eccentric billionaires etc. haven't tried it (perfect concept for MJ if he'd thought of it, certainly better than what he ended up indulging in):
It has been proposed that low doses of heavy water can slow the aging process by helping the body resist oxidative damage via the isotope effect.[11] A team at the Institute for the Biology of Ageing, located in Moscow, conducted an experiment to determine the effect of heavy water on longevity using fruit flies and found that while large amounts were deadly, smaller quantities increased lifespans by up to 30%.[12]
I don't know how relevant this is, but heavy water freezing point is about +3.8 degrees C
Therefore it would have been good practice to not fill the drums
Michael
I don't know how relevant this is, but heavy water freezing point is about +3.8 degrees C
Therefore it would have been good practice to not fill the drums
Michael
Donnie B @17 -- It's quite reasonable that there would be some partially-filled barrels, but they would contain a variety of enrichment levels.
Exactly. In fact, that's what I heard was actually the case (I believe it was during a Nova program about the incident). The sinking of the ship wasn't as harmful as it could have been to the Nazi cause. It was the minimally enriched water which sank in the lake, as they had enough of it to completely fill the barrels. The highly enriched water was actually among the floating barrels, as they had less of it, so the barrels were mostly filled with air.
If the cargo was really precious, such as this, perhaps more robust barrels were used. There are certainly different classes of barrels today, and I am just guessing that in that time there were probably a few classes too.