Wikipedia:Reference desk/Archives/Science/2019 April 4

= April 4 =

Origin of "natural history"
Our page Natural history states that the term natural history is a calque from the Latin phrase historia naturalis. But why was this phrase used in the first place? Specifically, what does the Latin word historia have to do with the study of nature? Qzekrom 💬 theythem 00:53, 4 April 2019 (UTC)
 * As opposed to "human history"? Also, here's EO's take on it. ←Baseball Bugs What's up, Doc? carrots→ 05:30, 4 April 2019 (UTC)


 * Contrast natural philosophy, which is an archaic name for physics (and science at large). For example, Isaac Newton was termed a "natural philosopher," and his most famous book was titled Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).  In those old days of academic study in the Western world, one either specialized in "natural" subjects, or one specialized in theology or divinity.
 * By extension, natural history would be in stark contrast to the alternative theological views - ergo, reading eleven pages of Genesis and interpolating the rest of the primeval history consistent with religious doctrine.
 * This arcane distinction between the "natural-" and the "super-natural-" versions of all subjects of academic study has been widely meta-researched, and it is deeply connected with the history of the University as an institution, particularly in the Western and European spheres of cultural influence. Our article lists many great books on this topic, written from a lot of different perspectives.  Among them is the book series A History of the University in Europe, which I seem to recall reading many years ago during a college class about the history of ancient and modern science.  It is a very boring and thorough book series, targeted at members of the social-sciences community, and while it is scientifically and historically accurate, its authors are not really even aiming to please the physicists, geologists, and biologists in the room; we're a stubborn bunch, and we tend to draw only one very clear distinction between "natural-" science and "wrong-" science...;  but we can all do with a little mind-expanding, every once in a while.
 * Nimur (talk) 12:10, 4 April 2019 (UTC)
 * The natural history/natural philosophy distinction largely mirrors the more modern primary division of the sciences into techne and episteme, or what is also called the "practical sciences" and the "theoretical sciences", though such divisions are not a neat one-to-one correlation, but it does represent part of the human tendency to categorize things. By the 20th century, the "natural history"/"natural philosophy" distinction had become a categorization that was not as popular as other ways of dividing up the sciences (such as "hard" or "soft", or "practical" vs. "theoretical"), but it lives on a bit in things like the many "Museums of Natural History", which tend to focus on exactly what they describe: those aspects of science that focus on the history of nature, so things like palentology, archaeology, geology, evolutionary biology, etc.  -- Jayron 32 15:08, 4 April 2019 (UTC)
 * Beside wisdom Greek historia means something like knowledge, investigation, survey 89.204.139.99 (talk) 15:15, 4 April 2019 (UTC) Marco Pagliero Berlin

Crystal structure of a gas
If we take the molar volume of an ideal gas at STP, 22.4 liters, and divide by Avogadro's number, 6.022E23, then we get (22.4/6.022)E-23 L = 3.72E-20 cm^3 = (33.4 A)^3. (confirmed) By comparison, butane gas has an effective length of 8.24 A.   This makes me start to wonder... if the butane molecules are at a criss-cross they ought to run into each other within just a few "unit cell" distances, rather than going through 100,000 unit cells like an an argon example at the first link. Is there a tendency of the gas to adopt some kind of statistically more regular structure in space, akin to a crystal structure? Is this a source of non-ideality? Wnt (talk) 10:27, 4 April 2019 (UTC)
 * You can get the Angstrom by using this symbol: Å. In a gas not only are those molecules moving, they are also spinning. So there will not be much chance of any grid shape hanging around to affect the result. If you could make a Bose-Einstein condensate out of butane, then this could be relevant. But I think the most complex molecule formed into a condensate like this is RbCs, and humans are not close to getting a 14 atom molecule collection all into the same quantum state. Graeme Bartlett (talk) 12:21, 4 April 2019 (UTC)
 * Graeme Bartlett has the right idea here. The relevant article is the Equipartition theorem, which says that thermal kinetic energy is always equally distributed among every Degrees of freedom in a molecule.  Thus, each individual butane molecule will be, simultaneously and with equal energy, flying in a straight line, spinning around each of three axis, stretching along each bond, flexing around each bond angle, etc. etc.  A molecule that large has a STUPIDLY large number of degrees of freedom, so there's a high amount of entropy in the gas anyways, and the positions of each individual atom are in constant motion, even within a molecule.  The reason why solids form crystals is that the bonding in the solid restricts the degrees of freedom of the individual molecules; solids basically only have vibrational modes of motion; they don't translate or rotate.  Since gases do both as well as vibrate (and indeed, you cannot have a gas that, even partially, restricts any modes; the equipartition principle means that any energy is always equally distributed among available modes.) you can't have the sort of restricted motion you describe.  By definition if you had restricted motion, you don't have a gas.  -- Jayron 32 12:31, 4 April 2019 (UTC)
 * I don't understand it well, but the equipartition theorem article gives a formula for a non-ideal gas based on radial interactions only:

H = \langle H_{\mathrm{kin}} \rangle + \langle H_{\mathrm{pot}} \rangle = \frac{3}{2} Nk_{B}T + 2\pi N \rho \int_{0}^{\infty} r^{2} U(r) g(r) \, dr. $$
 * What strikes me is that the potential energy doesn't look like it becomes another "degree of freedom" in the sense that they don't say that's equal to 4/2 NkBT. Also, I would have thought that they're saying that yes, non-ideal gases can be spaced out more (or is it less?) regularly than random ... and therefore that they could also perhaps be aligned in a more regular way than random? Wnt (talk) 12:43, 4 April 2019 (UTC)
 * There are edge cases at extreme conditions; for example supercritical fluids which are something of a transitional situation kinda sorta like a gas with some condensed properties. But for normal, near-room-temperature conditions, the boundary conditions between gases and condensed phases are fairly sharp.  -- Jayron 32 12:55, 4 April 2019 (UTC)


 * The original question is (reformulated with some jargon) "since the molecular radius of gas particles is not much larger than the mean distance between two molecules, how come the ideal gas approximation is valid?". I do not think the considerations above address it entirely.
 * An ideal gas is a gas in which:
 * Molecules do not have long-distance interactions
 * Molecules do interact frequently by elastic collisions
 * The first point requires that the energy of interaction between the particles is low compared to inner energy. For the latter, see the answers above about equipartition theorem etc.; for the former, see for instance Lennard-Jones potential, but it is a vast topic. It turns out that this assumption is reasonable for most (electrically neutral) gases at room temperature and pressure.
 * The second point requires that the gas is "not too sparse", which means that the Knudsen number is low. The mean free path of molecules (i.e. the average distance travelled before a collision) is a few tens of nanometers (which can be decently estimated as follows: imagine you spherical molecule of radius r travels alongs an axis, on average, it will run FMP before meeting another molecule, which means there must be one molecule per a volume of FMP*r^2), which is quite short compared to the size of most physical systems. So it is actually required that the mean free path is low - otherwise, you do not have a gas, you have a set of independent molecules. Tigraan Click here to contact me 16:01, 5 April 2019 (UTC)
 * Sort of; it's one of those things where the boundary is not sharp. There isn't a phase of matter which is "a set of independent molecules", and any definition thereof does not have a sharp boundary with that of a "gas".  This is evident in both a theoretical sense (there is no theoretical threshold where on one side of the line are "gases" and on the other side of the line is "a set of independent molecules") and in a real physical sense.  Actual phases have phase boundaries.  For example, between a liquid and a gas will always exist a physical surface that marks where the liquid ends and the gas begins.  This is true even of phases that are of the same state (for example, a substance with different solid phases will have a clear phase boundary between those phases).  However, there is no "phase boundary" between a gas and a putative "set of independent molecules" phase.  You see this problem with defining the upper limit to the Earth's atmosphere.  That's because the atmosphere doesn't have an upper limit.  It just gradually bleeds away into space, and nothing magical happens at any one distance.  Any "set of independent molecules" will have the same properties as a gas, it's just that gas-like things happen on longer time scales (like thermal transfer or propagation of sound waves), often too long for a human time scale, but that doesn't mean that they don't happen.  For example, people often say there's "no sound in space", but that isn't true, sound waves propagate through deep space the same way they do through the earth's atmosphere.  They just do so at time scales and pressure differences too small to make sense to us puny humans.  Soundwaves in space have gigantic wavelength, but that's still sound and the interstellar medium is still a gas.   discusses that aspect well. -- Jayron 32 16:18, 5 April 2019 (UTC)
 * You are right that at Knudsen numbers close to 1 it's neither entirely "gas" nor "independent molecules". But the point is that the Knudsen number for most gases at room temperature and pressures in most physical systems is very low. It is also true of interstellar gas because even though the mean free path is much larger, so is the scale of the physical system.
 * The important point is that a "set of independent molecules" cannot be described by an equation of state because it does not have a well-defined thermodynamic temperature or pressure. Each molecule has a momentum and kinetic energy of its own, but the distribution of those does not follow the statistical laws that allow to summarize the information on many molecules by a single temperature or pressure in the later mathematical treatment. Tigraan Click here to contact me 10:10, 8 April 2019 (UTC)


 * The interaction between molecules will cause correlations between positions and orientations of molecules to appear. You can calculate such things from first principles using the virial expansion method, see e.g. here. You can evaluate the thermal average of a function that measures how well molecules within some radius of some given point are sticking to a certain crystal structure using the same formalism. Such thermal averages will be very small, but they won't be exactly equal to zero. Count Iblis (talk) 21:11, 5 April 2019 (UTC)


 * The first sentence in the Crystal article says a crystal is a solid. By implication, not a liquid or a gas. ←Baseball Bugs What's up, Doc? carrots→ 05:46, 6 April 2019 (UTC)
 * There are Liquid crystals, and also Time crystals. {The poster formerly known as 87.81.230.195} 90.200.138.194 (talk) 13:07, 9 April 2019 (UTC)