Wikipedia:Reference desk/Archives/Science/2011 October 26

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October 26

Phase space

How to calculate number of quantumstaes or unit cells within energy range E and E+dE in the phase space to prove the eqn: g(E)dE=[(8π√2V)/h^3]*m^(3/2)√EdE — Preceding unsigned comment added by Intr199 (talk • contribs) 13:41, 26 October 2011 (UTC)

The number of states in a volume d^3p of momentum space is

V/h^3 d^3p

You can write this in terms of dE by integrating over all angles. This leaves you with:

V/h^3 4 pi p^2 d|p| = V/h^3 4/3 pi d|p|^3 =

(using E = p^2/(2m))

V/h^3 4/3 pi d (2 m E)^(3/2) =

V/h^3 4/3 pi (2m)^(3/2) 3/2 E^(1/2) dE =

V/h^3 4 sqrt(2) pi m^(3/2) E^(1/2) dE

If the particles have spin 1/2, then you need to multiply this by 2. Count Iblis (talk) 15:34, 26 October 2011 (UTC)

"using E = p^2/(2m)"

why kinetic energy is being considered only?Intr199 (talk) 16:40, 26 October 2011 (UTC)

This is for free particles. There is actually a potential, the particle is confined to a volume, so you can consider the case of a particle in a box, solve the Schrödinger equation and then derive this result. Count Iblis (talk) 23:22, 26 October 2011 (UTC)

Can just anybody get fat?

I'm not sure how to search for this, so I'll just throw out as a question and see what I get: can a great majority of average men of normal height reach BMI of 45/body weight of 150 kg or so (330 pounds) simply by eating a lot, if they tried? Or would many of them develop type II diabetes and just pee out the sugar or otherwise run into obstacles preventing the attempt? (I'm not interested in psychological/social factors here, only the metabolism) Wnt (talk) 17:28, 26 October 2011 (UTC)

Sure, when energy input exceeds energy used you gain weight. It's a simple equation. You can also get type II diabetes. It isn't like an either/or proposition. --Jayron32 17:43, 26 October 2011 (UTC)

There are a few people whose metabolism doesn't allow them to get fat, whatever they eat. This seems particularly true during growth spurts in the teenage years, and for those who are athletic. However, the majority of people seem to pack on pounds quite easily. The only question, then, is if they could reach that weight without dying first. Diabetes doesn't keep you from gaining further weight, but it could kill you. However, due to modern medicine, insulin should keep them alive until they reach the weight you want. (Planning a cannibal feast ?) StuRat (talk) 17:55, 26 October 2011 (UTC)

I know some people can get a lot of junk and don't seem to get fat. This doesn't mean they have a metabolism that doesn't allow them to get fat. It's possible if they really tried, e.g. if someone forced them to eat 10 Big Mac combos and a 10 pack of KFC a day, they would get fat. They may vomit or have other problems at first but it wouldn't surprise me if they would eventually learn to adapt. Nil Einne (talk) 18:22, 26 October 2011 (UTC)

StuRat: I'm wondering if there is any real difference between a highly obese person with type II diabetes, and a normal person with no propensity to become overweight, except for the obesity. It seems like what would be called insufficient insulin production from the pancreas for an obese person would still be enough to provide for all the cells of a person of normal weight; likewise the insulin resistance would likely be much reduced or eliminated for such a person at normal weight. If that is true, then in overweight people, is type II diabetes a disease at all, or merely a symptom of obesity? To take this reasoning to the furthest extreme, what if hyperinsulinism is the real disease, leading to the excessive weight gain (as suggested by places like [1]) - is it possible that the subsequent onset of type II diabetes in obese people actually represents the remission of the condition of excess insulin production, so that it is then possible to lose weight more readily and avoid all adverse health effects? Wnt (talk) 19:50, 26 October 2011 (UTC)

You might be interested in a documentary called "Why Thin People are not Fat. I believe it is available online for free. From memory they said it was largely genetic and it's not easy to get some people to put on weight, even when they're trying to force it. Vespine (talk) 21:16, 26 October 2011 (UTC)

I saw that documentary, but I think that most people would fall in that category if they only made sure they were physically very fit well before they reached adulthood and stayed that way. The real problem is that the Western way of living has been made the standard for healthy living, while it is actually the cause of problems. Things are slowly changing, it has recently been realized that walking alone is not good exercise (unless you are past 75 years of age), you really need to exercise intensely, (at a heart rate of 140 bpm or higher). Count Iblis (talk) 23:37, 26 October 2011 (UTC)

To pick up on one point above, I read over and over again that a modest amount of walking IS good exercise. Is giving this advice an act of desperation to try to encourage ANY level of activity? Wanderer57 (talk) 04:28, 27 October 2011 (UTC)

Hmmm. I have need of such information myself, so searching exercise "beats per minute" on PubMed and just dumping the results in reverse chronological order: PMID 19501315 prescribes 110 to 130 bpm for pregnant and perhaps postpartum women for up to 150 minutes/week of aerobic activity. [2] tests an exercise regimen for "beneficial autonomic effects on the heart" using a formula of 70% * (220 (+6 if female) - age) bpm; however no evidence is given that this remarkable formula is better than others. Another study [3] also uses this and shows results on cardiovascular scores. [4] showed that exercise reaching a peak of >150 bpm reduced snoring in obese children, with 40 minutes being roughly twice as effective as 20 minutes. Osteogenic index and ground reaction force improve when exercise is over 135 bpm ( PMID 16920771 ) ... if only I understood what that means. Now [5] starts to get down to brass tacks in their discussion - apparently there is a problem, chronotropic incompetence, where people fail to reach the expected bpm in a treadmill exercise test (which I assume is equal exercise for anyone doing it) - in a test group of heart failure patients they came out 10 bpm slower than the others; then they take longer to return to normal heart rate afterward. This illustrates a potential problem with studies of the effect of 140 bpm exercise, because people who can't reach 140 bpm will be excluded from the group, reducing the observed mortality in that group. Prescribing a set 20 bpm increase in heart rate is unsatisfactory in cardiac rehabilitation in terms of the total oxygen reserve. (PMID 15235299) Exercise at 163 bpm but not 132 bpm in women caused a decrease in body fat and a decrease in the intake of saturated fat and cholesterol in a test group of women (PMID 9013436). Both aerobic exercise and weight training caused decrease vascular resistance in the forearm (PMID 9004105). Exercise at 120 bpm improved glucose readings and C-peptide levels in type II diabetics (PMID 8911982). "50-70% maximal effort" reduces abdominal fat and improves cardiovascular risk factors in type II diabetics (PMID 8582541 - also PMID 2019225 for 60-80%). VO2max can be improved by 166 bpm exercise in children (PMID 7567326 - also PMID 2007150 for 151 bpm in obese children). Jogging at 70-75% of maximal heart rate in coronary heart patients increased muscle and decreased fat by about a pound (PMID 666558).

Looking at all this, what I'm seeing is that a) there are many different criteria for whether exercise "works", depending on the health and what you're using it for; b) there is an overreliance on witchy formulas that equate years of age with bpms, which reminds me of the now-discredited "120+age" formula for high blood pressure; c) frustratingly, while studies use all different standards of exercise, nobody wants to compare X bpm with Y bpm and see how effective they are toward a specific measurement. The result is a situation where it looks like the individual pretty much has to try and see for himself, or rely on anecdotal evidence from internet forums. I'm rather disappointed by the low quality and disorganization of scientific study of what is probably the leading health issue of this era. Wnt (talk) 16:38, 27 October 2011 (UTC)

A person's metabolism, diet, and constitution type all affect one's initial "natural" body weight. There are also the "skinny fat people", who have a high body fat ratio but are slim in complexion. ~AH1 ^(discuss!) 20:25, 29 October 2011 (UTC)

Photon to electron

Can a photon be converted into an electron, neutron or proton?--195.94.11.17 (talk) 18:30, 26 October 2011 (UTC)

Sort of. There are certain conditions where a photon may spontaneously produce an positron-electron pair, see Pair production. Pair production is used in the explanation of Hawking radiation and Pair-instability supernova. As far as my limited understanding of particle physics tells me, it wouldn't work with neutrons or protons because those are composite particles, not fundemental particles. That is, protons and neutrons are themselves composed of smaller particles, called quarks. Electrons, however, are fundemental particles, and may be produced as via pair production, as may other fundemental particles. --Jayron32 19:05, 26 October 2011 (UTC)

Composite particles can be pair-produced. There's very little difference between composite and fundamental particles in particle physics. It has been proposed many times that the Standard Model fundamental particles are actually composite, and it was even proposed that there's no such thing as a fundamental particle (bootstrap model). -- BenRG (talk) 01:52, 27 October 2011 (UTC)

So it's turtles all the way down then? --Jayron32 01:56, 27 October 2011 (UTC)

Apparently yes. Turtles on top of turtles, even unto the Nth generation. I wonder if that is occasion for encouragement or despair. Wanderer57 (talk) 05:11, 27 October 2011 (UTC)

Maybe I should have made it clearer that the bootstrap model was a failure, and the successful Standard Model does have elementary particles. You can never be absolutely sure that they're not composite, because it's hard to tell the difference (the fact that electrons can be pair-produced doesn't help, for example). But the increasingly precise experimental confirmations of the Standard Model do make it increasingly implausible that they're composite. -- BenRG (talk) 20:27, 27 October 2011 (UTC)

There are certain rules that must be followed when considering whether a group of particles can transform in a different group. Those rules include conservation of energy, conservation of momentum, angular momentum, conservation of electric charge, and so forth and so on (There are too many for me to list them all here). Because of all that, a single photon by itself cannot transform into anything else. There just isn't any way to avoid breaking all the rules, so it doesn't happen. But if the photon collides with something else, allowing it to shed some excess energy, then pair production as described by Jayron in the previous post can happen. Dauto (talk) 20:03, 26 October 2011 (UTC)

Dry ice snow

According to our article on Vostok Station, the coldest naturally occuring temperature recorded on earth is -89.2°C. This is colder than the freezing point of carbon dioxide. Has dry ice snow ever actually been observed? SpinningSpark 21:32, 26 October 2011 (UTC)

This has been asked before -- the answer is no; here is a thorough explanation of why (basically, because the freezing point is pressure-dependent). Looie496 (talk) 21:44, 26 October 2011 (UTC)

I asked myself the same question a few years back. I came to the conclusion that CO2 snow was unlikely -as it requires colder temperatures to form. I thought it possible, that liquid CO2 might form on the floors of basement/cellars were it would natural collect (colder temperatures would make it sink to these places). However, I never found any accounts that this had been observed, only that people reported 'coughing' due to the high levels of CO2 when descending down into them.--Aspro (talk) 21:55, 26 October 2011 (UTC)

CO2 doesn't become liquid at sea-level pressure. You need at least five times more pressure to produce liquid CO2. That's why dry ice is dry. Dauto (talk) 22:05, 26 October 2011 (UTC)

(EC)Just because the temperature is below the freezing point doesn't mean the CO2 will freeze. A more familiar situation might help you understand. Right now where you are the air temperature is below the 100 Celsius boiling point of water but that doesn't mean that the water vapor in the air will start condensing. In fact, the opposite is more likely to happen and if you spill some water on the table it will evaporate over time. That happens because the air is not saturate with water vapor - that is the water vapor partial pressure is below the saturation partial pressure. The CO2 partial pressure in our atmosphere is just to small to get even close to saturation (even at Vostock). Dauto (talk) 22:02, 26 October 2011 (UTC)

Is that quite the same thing? I mean, clouds form and rain happens (just rarely indoors).  Card Zero  (talk) 17:01, 27 October 2011 (UTC)

Clouds form when relative humidity reaches 100% - that is when the air is saturated. Dauto (talk) 23:22, 27 October 2011 (UTC)