[math-fun] Physics question
Suppose there was a closed glass cylinder, with a thin planar membrane separating the cylinder into two chambers. The chambers contain colored water of two different colors, having the same density and no chemical reaction with one another. The water in one chamber is warmer than the water in the other chamber, but we do not know what color water is warmer. The cylinder is put into a zero-gravity environment, allowed to come to rest, and the membrane is removed, allowing the water allowed to mix. Can we tell by the flow patterns of the mixing water which color is warmer and which cooler?
David, 'same density' and 'zero gravity' conditions both imply there will be no bulk motions or currents occurring. Thermal conductivity being a few orders of magnitude larger than molecular diffusion, we should expect to see only temperature redistribution over an Erf[x/Sqrt[S.t]] gradient. But this assumes other properties (expansion coefficient, contact angle water-glass, temperature derivatives of ..) to be *also* equal at both temperatures. Wouter. ----- Original Message ----- From: "David Wilson" <davidwwilson@comcast.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, July 16, 2006 6:30 AM Subject: [math-fun] Physics question Suppose there was a closed glass cylinder, with a thin planar membrane separating the cylinder into two chambers. The chambers contain colored water of two different colors, having the same density and no chemical reaction with one another. The water in one chamber is warmer than the water in the other chamber, but we do not know what color water is warmer. The cylinder is put into a zero-gravity environment, allowed to come to rest, and the membrane is removed, allowing the water allowed to mix. Can we tell by the flow patterns of the mixing water which color is warmer and which cooler? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun __________ NOD32 1.1663 (20060716) Informatie __________ Dit bericht is gecontroleerd door het NOD32 Antivirus Systeem. http://www.nod32.nl
Seems to me that if the membrane is removed without introducing currents into the water, then the only thing going on would be the mixing by diffusion. The warmer water would have particles that have higher kinetic energies (on average) than the cooler water, so they would more energetically move into the other space. So, see if there is more blue water in the former red space or red water in the former blue space. The color with more water in the other space (for some short time after the membrane removal) was the warmer color. Kerry -- lkmitch@gmail.com www.fractalus.com/kerry
Kerry Mitchell wrote:
...So, see if there is more blue water in the former red space or red water in the former blue space.
But of course these must be equal, by conservation of volume. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
You know, I should give my motives when I ask questions. This all follows from a theological discussion I am having in other realms, where our side claims that evil is different in nature from good, while the opponent says that evil is want of good that is experienced differently, just as cold is experienced differently from heat. This got me wondering. Prior to the 1700's would heat and cold have been viewed as opposing qualities (for lack of a more accurate word), or would cold have been seen as lack of heat? Would there have been a qualitative way to see this? That's what made me wonder if there was any qualitative way heat and cold could be distinguished, like the way heat diffuses into cold.
There seems to be another analog to this system: semiconductors. The electrons act a little like a gas & bounce around, while the places they leave are called "holes". However, they aren't identical: electrons have higher mobility than holes, which is why NPN transistors are faster than PNP transistors. http://en.wikipedia.org/wiki/Transistor At 06:28 AM 7/16/2006, David Wilson wrote:
You know, I should give my motives when I ask questions.
This all follows from a theological discussion I am having in other realms, where our side claims that evil is different in nature from good, while the opponent says that evil is want of good that is experienced differently, just as cold is experienced differently from heat. This got me wondering. Prior to the 1700's would heat and cold have been viewed as opposing qualities (for lack of a more accurate word), or would cold have been seen as lack of heat? Would there have been a qualitative way to see this? That's what made me wonder if there was any qualitative way heat and cold could be distinguished, like the way heat diffuses into cold.
participants (5)
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David Wilson -
Henry Baker -
Kerry Mitchell -
Michael Kleber -
wouter meeussen