Implications of Charles law in a biological matrix: farts

See note 3 for source.

Maggie Koerth-Baker has a great piece up at the 538 blog: "How Big Is A Fart? Somewhere Between A Bottle Of Nail Polish And A Can Of Soda."  It's well researched, digging into the biomedical literature with verve.  And it's great that she gives the answer a context, it's easier to visualize a bottle of nail polish than a 17 ml blob for most people, me included.

I'm not at all surprised at what you can find in the primary literature (I tracked down papers on exploding people and deuterated dogs¹ for my introductory chemistry class last spring). The piece is the first in a series Science Question From A Toddler, though I suspect that people somewhat past the target age group (5 and under) would be interested in the answer to this question, too.

In a footnote Koerth-Baker suggests that farts in the body would be smaller because the gas would be compressed inside the body.  But the pressure inside the human colon is the same as atmospheric pressure.  Farts and burps keep it that way. What's different is the temperature, higher inside the body by about 30^oF (17^oC).  Gases expand at higher temperatures. You can use Charles' law to figure out by how much the volume changes with changes in temperature:  V2=(T2/T1)V2

The researchers measured the volume of the farts at room temperature (I read the paper!), so the volume of a fart should be slightly larger in the body than the reported numbers by a factor of (310/293) or about 6% larger.  So how big is a fart?  Just before exit, it's about the size of a 14 ounce ketchup bottle for the largest one in the 1997 study.

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The details of the experiments are fascinating.  The technique for quantitatively² capturing flatus in the bathtub is elegant, and while a significant improvement over the method used for the studies in the 1860s³ you have to wonder how they got volunteers for either experiment.  And speaking of volunteers, the assessment of the "flatus perception threshold" was done by delivering 100 ml of an odorant mixture "from a large 250ml syringe in about 1s, 1 meter beneath the nose of the panel members, mimicking a flatus emission."

And just in case you don't think this is serious stuff: "The common tendency to treat rectal gas as a humorous topic has obscured appreciation of the complex physiology that underlies the formation of this gas." Suarez et al. American Journal of Physiology  272, G1028-G1033 (1997).

1.  The physiological effects of drinking heavy water, D₂O, on dogs.  If you've ever wondered what would happen if your poured that little vial of D₂O into your coffee, the answer is not much.  It's not great for the dogs as a steady diet, but a sip or two won't hurt.
2.  The fancy chemistry term for "we got all of it!"
3.  See the figure, from Tangerman, "Measurement and biological significance of the volatile sulfur compounds hydrogen sulfide, methanethiol and dimethyl sulfide in various biological matrices" Journal of Chromatography B, 877,  3366-3377 (2009).

Nitrogen in the snow

We are expecting another round of wintry weather tomorrow, and an article in the local paper noted that the snow and bitingly cold weather we have had recently are good for farmers.  The cold reduces the population of some pests, particularly the species making their way north.  The article also noted that snow contains nitrogen from the atmosphere, providing a little extra boost for lawns come spring.

The atmosphere is roughly 80% nitrogen, in the form of N₂.  The form matters.  Nitrogen gas is very unreactive, so much so that it many "air sensitive" materials are packed under pure nitrogen.  (The part of the air that is reactive is molecular oxygen, O₂.)  Snow certainly contains dissolved nitrogen gas.  Henry's law predicts the solubility of a gas in a solvent, water in this case, as a function of temperature.  It might seem at first glance counter intuitive, but gases are more soluble in cold solvents than in warm (the opposite is true of most solids, as anyone who has tried to dissolve sugar in cold ice tea knows).  An inch of snow contains about 7 milligrams of nitrogen gas per square foot, or about 1/3 of a kilogram in an acre of snow.  Given that fertilizers are spread onto fields at a field of roughly 300 kilograms per acre, it's not much.

The trouble is actually that this nitrogen isn't in a form that easily accessible to plants.  Nitrogen in the atmosphere must first be "fixed" or changed into a more reactive form, typically tetravalent nitrogen (ammonium) which is then converted to the nitrate ions that plants can use.  So where does the useful sort of nitrogen come from?

Industrially, nitrogen is fixed in the Haber process.  Since nitrogen is so unreactive, this requires pressures hundreds of times those of earth's atmosphere and temperatures more likely to be found on the surface of Venus (over 700^oF).  Nitrogen is fixed in the biosphere by microbes, which undertake an elaborate enzymatic dance to do this at low temperatures and pressures (and yes, scientists are on the job of trying to figure out how to get the enzymatic processes to work at industrial scales.)

Lightening strikes also convert minuscule amounts of N₂ in the atmosphere to nitrogen oxides, and industrial pollution has also injected nitrogen oxides into the atmosphere. Industrial pollutants are by far the biggest contributors. The nitrogen oxides become nitrate ions. These are the nitrogen sources that turn a blanket of snow into a gentle fertilizer.

To put it into perspective, snow and rain probably deposit about 5 kilograms total per acre over a year. It's not much, it's not quite all natural (the rates were much lower in pre-industrial days), but it's something.

Unbending the bends

Sometime before dawn this morning, we took our oldest son to the airport. He's bound for the Caribbean for a pre-orientation trip for college (learning to sail with a team of other freshmen). They will get the chance to do a little snorkeling, but when his dad asked him about whether or not they'd be doing any scuba diving, he replied enigmatically,"There is no hyperbaric chamber in the Virgin Islands. They'd have to fly you to Puerto Rico, I guess."

My first response was to wonder how they would do that, given that most aircraft are pressurized to something around 10,000 to 15,000 feet, which would certainly exacerbate the bends - the outgassing of nitrogen from the blood, which can cause embolisms (blockages) in your blood vessels and painful swelling in your joints.

Henry's law governs the amount of gas dissolved in a liquid: the amount of dissolved gas depends on the external pressure of the gas. For example as the pressure of carbon dixoide increases, so does the amount of dissolved carbon dioxide. Some portion of that dissolved CO₂ turns into carbonic acid (H₂CO₃), and lowers the pH, which gives soda water it's characteristic bite. It also means that acidification of the ocean is a risk of fossil fuel burning, and the resultant carbon dioxide in the atmosphere. Climate deniers will say that there is no data linking CO₂ levels with changes in the ocean pH, suggesting it's because the oceans aren't plain water, and that this will complicate the chemistry. True. But your blood is pretty chemically complicated, and this is essentially the system that is used to control your blood's pH.

So why would flying make the bends worse? As the external pressure of nitrogen falls with altitude, more nitrogren comes out of solution in your blood stream and joints. Neither are places where you want more bubbles. If possible, victims of the bends are evacuated on planes that can be pressurized to lower altitudes (an expensive proposition, and one often not covered by travel insurance).

Bariatric chambers allow the external pressure to be increased, and then slowly decreased to prevent the formation of large bubbles. It can take several "dives" to assuage the symptoms. I sat with my mother while she underwent treatment in a hyperbaric chamber, it's not for those with claustrophobia is all I will say.

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Photo is from Wikimedia.

Psychrometry - or how to tell when it's crazy hot out

The heat index is 107 ^oF (42^oC) at the moment. It's hot, and I'm procrastinating going outside by blogging.

My youngest son is doing summer theater, and their rehearsal space is not all air conditioned. So I bought him a cooling towel to help him stay comfortable. When he asked how it worked, I said it was like having a portable swamp cooler — a familiar item as my dad used one for years to cool his house.

The basic principle at work is that it takes energy to make water evaporate. Unless the relative humidity is 100% (in other words, the air has all the water it can hold), water will evaporate. If you keep running air past a wet surface (think a fan blowing past a damp towel, or the breeze blowing over your sweaty face), water will continue to evaporate as drier air is constantly being replenished. The energy to turn the water from a liquid into a gas has to come from somewhere, in this case, the surrounding air and the water itself. The air gets cooler. Whew!

The towel works similarly, there is a very large damp surface area (why the fancy $15 towel really does works better than a damp cotton lawn handkerchief, a much higher surface area than the smooth cotton weave) and as you move around, air moves past. The water evaporates, pulling energy from the water in the towel and makes it colder.

To get a sense of how much energy that is, it takes about 34,000 J to evaporate 15 grams of water (about a tablespoon). 34,000 J is roughly 8 nutritional calories. If you pulled all that energy out of a cup of water, the cup of water would cool off to about 41^o F. (In practice, you don't get things this cool!)

This whole endeavor depends on the air being able to soak up some water, so if the humidity is too high, you are going to be crazy hot towel or no. Swamp coolers work great in desert areas (where my dad lives, for example), and are pretty much useless in New Orleans.

So how cool can you get? To figure it out you need the dry bulb temperature and the wet bulb temperature of the air. The dry bulb temp is just the temperature of the air measured in the usual way (being careful to keep the thermometer out of the sun). The web bulb temperature is obtained by blowing air over a thermometer whose bulb is fitted with a tiny damp sock. For that you can use a sling psychrometer (see the video).

Too hot to be slinging thermometers around? Look up the dew point (your favorite weather app will likely have it) and you can estimate the wet bulb temp this way:

1. Subtract the dew point from the ambient temperature (what your regular thermometer reads)
2. Divide what you get in step 1 by 3.
3. Subtract the result in step 2 from the ambient temperature.

Right now the thermometer outside my window reads 100^o F, the National Weather Service says the dew point is 70^o F, so I take 100-70=30; 30/3 = 10; so the approximate wet bulb temperature is 100-10 or 90^o F.

Once you've got the wet bulb temp you can figure out just how much cooling you can get with a fan and a damp towel!

1. Subtract the wet bulb temp from the ambient temp (the dry bulb temperature)
2. Multiply the difference by 0.8 (assuming the process is about 80% efficient, which is a pretty reasonable estimate)

My calculations suggest that the best I could do to produce cool air in my study this afternoon would be 80% of *100-90) or 8 degrees of cooling. 100^o F or 92^o F? Both are way too hot...I think it's time to stop writing for the day and head for the pool!!

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There are more sophisticated ways to do this, talk to the meteorologists if you want to know more.

Psychrometry comes from the Greek for cold ("psuchron") and should not be confused with anything psychiatric (unless you are talking about mad dogs and Englishmen...)

A fluff piece on density

We're covering density in my introductory chemistry this week - which prompted this post.


Density is the ratio of mass to volume and often (though not always) one of the easiest physical properties of a substance to measure. Introductory chemistry labs often feature an exercise where the mass of an object is determined using an analytical balance or somesuch and the volume is determined by displacement (often in a graduated cylinder).

In certain of my teen-aged sons' circles it's in fashion to write in public - to take your notebook (computer or spiral bound) and head to the local coffee shop. You can write the scene while being seen. Personally, I write in public as a last resort. Last week, while waiting to meet a friend for coffee I did haul out my iPad to see if I could inhale some of the fumes of caffeine and inspiration wafting around and some first thoughts for a column hammered out. No coffee for me, hot chocolate - with a serious mound of whipped cream on top.

While I'm all for decadence when it comes to chocolate, hot or otherwise, the whipped cream was a practical touch. My friend is notoriously late, and I wanted the chocolate to stay hot until he arrived.

The ability of a material to conduct thermal energy - heat - depends to some extent on its density. On a molecular level, heat transfer is mostly about collisions between molecules. If you are a molecule with lots of thermal energy, you are generally stuck with it all until you collide with another molecule!

Air at 20^oC (68^oF) feels warm (yes, I know it's about 3^oC here right now, but a girl can dream, can't she?) while water at the same temperature feels refreshingly cool. Water is about a thousand times denser than air, so there are many more molecules in contact with your body surface. The more molecules boucing off a surface, the more opportunities there are for energy transfer. If you're hot, you'll get cooler faster by fully immersing yourself than by standing in a cool room. Conversely, if you want something to stay hot, surround it with air, not water. Air is a good thermal insulator, relative to water, because it is far less dense.

The whipped cream atop my hot chocolate is full of air, which lowers the density and so it floats on top of the cocoa. Heat transfer to the airy cream isn't very efficient due to the low density. Since the air trapped inside the cream isn't moving around (and thereby not presenting fresh molecules to take away the energy presently in the liquid in my cup), the system quickly equilibrates, with most of the heat in the system staying there.

Trapped air (or other gas) is a great insulator, but trapped nothingness works even better. Put my cocoa into a vacuum chamber and it should stay nice and toasty (though there would be other complications - but that is another post!).

The pressure to preserve

Stephen Davey, associate editor for Nature Chemistry, blogged at the Sceptical Chymist about visiting the National Archives and seeing the Declaration of Independence, the Constitution and the Bill of Rights. He was surprised to find that the documents were stored under helium as opposed to argon - and wondered why. That started me wondering as well, particularly since the inert gases are not interchangeable in all circumstances (you can use helium to dilute the air mixture for diving, but not argon, for example.)

Helium is both more expensive (not an issue in this context, the cost of the gas inside the cases has got to be the least expensive piece!) and difficult to work with than argon. It can leak out through materials that seem air and water "tight". That's why those latex balloons that looked so cheery on the day of the party are withered and droopy by the morning. They're waterproof, but not helium proof.

In the 1950s the US National Bureau of Standards (now NIST) was charged with deciding on the best way to preserve the Charters of Freedom (the three founding documents of the United States of America). (You can read the full report here.) Helium was chosen, despite its propensity to leak through many materials, partly because a high purity, local source was readily available but most because of its thermal conductivity.

The designers of the encasements wanted a way to measure the pressure of the helium within the cases without having to open them, or remove a sample. Since the thermal conductivity of helium is very different than that of air, changes in the thermal conductivity (how heat moves between the panes) could be used to detect leaks. Argon's thermal conductivity is similar to air, so if argon leaked out and air in, the change would be hard to detect.

New casements were designed about ten years ago, with argon as the gas of choice this time. Sapphire ports are embedded to allow the atmosphere inside the cases to be monitored spectroscopically - by passing a beam of light through the port. Since the new methods of monitoring don't require the inert atmosphere to have a different thermal conductivity, it allows argon - which can't wiggle its way out the way helium can - to be used.

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The photo is from The Science News-Letter, vol. 62 (Dec. 6 1952), p. 359.

The Grecian Bends: Ladies' Corsets and Henry's Law

In an earlier post I suggested there was a connection between ladies' corsets and Henry's Law. A general statement of Henry's Law is that the solubility of a gas in a liquid depends on the pressure of the gas above the liquid. An everyday example is soda. A can of soda is pressurized by exposing it to carbon dioxide having equivalent of about 2.5 times atmospheric pressure at room temperature. When you quickly lower the pressure of carbon dioxide over the liquid, say by opening the can, the solubility decreases and the gas adjusts by rapidly coming out of solution. Fizzing results (and eventually the soda goes flat).

When a diver dives the pressure of the gases breathed increases, and the amount dissolved in the blood increases. Diving to just 50 feet increases the total pressure to roughly that of the carbonated soda! Rapidly ascending reduces the pressure, just like opening the can of soda, and the gas rapidly comes out of solution - the diver's blood can "fizz". Bubbles in the blood and body tissues are clearly not a great thing, and the physiological effects range from the relatively minor (bubbles in the skin layers) and joint pain, to potentially lethal embolisms in the brain and lungs.

This phenomenon was first observed by Robert Boyle in 1670 who noted the formation of bubbles in the eyes of a snake that had been placed in a high pressure environment, then rapidly decompressed. "I once observed a viper furiously tortured in our exhausted receiver… that had manifestly a conspicuous bubble moving to and fro in the waterish humour of one of its eyes." Before the effects was widely understood, many construction workers suffered from "caisson workers' disease" while working in pressurized environments (caissons) under rivers.

Dive tables - a schedule for ascending from a dive that reduces the chance of decompression sickness - were first created for use by British Navy divers in the early 20th century. How do whales and dolphins cope without dive tables? Half-mile deep, hour long dives are not uncommon - and a rapid ascent from depth could cause a massive case of the bends. They may not be immune - recently researchers have found evidence for chronic decompression injuries in sperm whales. The whale bone in the photo above shows evidence of dysbaric osteonecrosis (bone death caused by rapid decompression).

What does this all have to do with ladies' corsets? In the 1870s tight corsets and big bustles were all the rage. The posture forced upon women wearing these fashionable undergarments was called the Grecian Bend. As decompression injuries caused a similar posture, workers on the Brooklyn Bridge christened the syndrome "the Grecian bends", soon shortened to "the bends".

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The photograph of the whale bone is by Tom Kleindinst, Woods Hole Oceanographic Institution and is used with permission.

The image of the Grecian Bends is from the Library of Congress