Question about heat transfer

A Brown
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I believe that this argument

Message 25083 in response to message 25082

I believe that this argument is flawed. Let's try to solve this. Each cross-section of the thermally insulated tank has a unique value of pressure in the equation PV = nRT. and each volume will be the same (let's say V = Ah/100, where h is the height of the tank and A is the area of the two-dimensional cross-section, for mathematical purposes).
Since R is a constant, dependant on the substance we are using, and n is a universal constant, we may show easily that in order to maintain equilibrium, as pressure increases, the temperature of the liquid in that cross-section must also increase.
If my Chemistry is correct and not lacking any collegiate knowledge, then this would indicate a higher-temperature spot near the bottom and a lower temperature spot near the top, but all molecules most likely would not enter a convection current, due to the fact that eventually, all molecules will fall into place in this arrangement. This, I believe, is correct, as long as our liquid is uncompressible.

Odysseus
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RE: I believe that this

Message 25084 in response to message 25083

Quote:
I believe that this argument is flawed. Let's try to solve this. Each cross-section of the thermally insulated tank has a unique value of pressure in the equation PV = nRT. and each volume will be the same (let's say V = Ah/100, where h is the height of the tank and A is the area of the two-dimensional cross-section, for mathematical purposes).
Since R is a constant, dependant on the substance we are using, and n is a universal constant, we may show easily that in order to maintain equilibrium, as pressure increases, the temperature of the liquid in that cross-section must also increase. ...

Rydberg's constant R is not dependent on the substance, but is universal. Remember that the PV = nRT formula is for ideal gases, visualized as comprising geometric-point particles that don't interact except in collisions. Moreover n is not a constant in general; here it represents the number of molecules in the system divided by Avogadro's number.

You can't apply the gas laws to liquids, anyway. The incompressibility you mentioned in the bit I snipped should provide a clue as to why not.

Chipper Q
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ADDMP, with regard to

ADDMP, with regard to mechanisms, I don't see why the helium atom should experience so ideal a collision with the bottom plate; I'd expect it to penetrate a certain depth into the plate before encountering an atom in the lattice with which to collide, and thereafter ricochet in any of numerous possible directions, maybe back into the tank, but more likely down (being in a gravitational field) until finally it will leak out of the tank, passing entirely through the bottom plate...

A Brown
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RE: Rydberg's constant R

Message 25086 in response to message 25084

Quote:


Rydberg's constant R is not dependent on the substance, but is universal. Remember that the PV = nRT formula is for ideal gases, visualized as comprising geometric-point particles that don't interact except in collisions. Moreover n is not a constant in general; here it represents the number of molecules in the system divided by Avogadro's number.

You can't apply the gas laws to liquids, anyway. The incompressibility you mentioned in the bit I snipped should provide a clue as to why not.


Yeah, kinda forgot about that "Gas law" part... Damn.

Mike Hewson
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RE: until finally it will

Message 25087 in response to message 25085

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until finally it will leak out of the tank, passing entirely through the bottom plate...


Yeah it would too!
This reminds me that the LIGO's have broken records for the largest volume of the highest vacuum on Earth. You have two arms 4km long, tube shaped, of a metre or two diameter, all pumped down really low. At that level outgassing of stuff from within the lattice of the metallic wall is significant and probably took ages to achieve the low pressure. I don't know what the time scale is but smaller molecules and atoms would gradually seep right in/through from the atmosphere!

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

Ben Owen
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RE: RE: until finally it

Message 25088 in response to message 25087

Quote:
Quote:
until finally it will leak out of the tank, passing entirely through the bottom plate...

Yeah it would too!
This reminds me that the LIGO's have broken records for the largest volume of the highest vacuum on Earth. You have two arms 4km long, tube shaped, of a metre or two diameter, all pumped down really low. At that level outgassing of stuff from within the lattice of the metallic wall is significant and probably took ages to achieve the low pressure. I don't know what the time scale is but smaller molecules and atoms would gradually seep right in/through from the atmosphere!

We just had a PhD defense where a student put it "LIGO is the biggest hole in the Earth's atmosphere." It's true. And yes, the outgassing from the walls is a problem. It was ages ago, but I dimly recall when they were making the beam tubes they had to use some kind of special welds. Each arm is basically a long spiral of metal with long welds, a major engineering accomplishment by itself.

Before turning on the first time they "baked out" the tubes so that the stuff in the metal would mostly gas out. GEO is an R&D instrument so they change things a lot and I believe have done this multiple times. They do it simply by running a nice electrical current through the thing. Yes there is insulation, but GEO sits in between two turnip fields so there were a few dead mice as a result. They see insulation as nesting material.

I think the timescale for stuff to seep through outright is much longer than the life of the experiment, though.

Ben

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