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27 Nov 2019

Compute the fraction of helium atoms in the superfluid state at (a) T=Tc/2 and (b) T=Tc/4?

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

The isotherms for the VdW fluid (as calculated directly from theVdW equation of state, without performing the Maxwellconstruction)increase monotonically for T > Tc as V isdecreased. For T < Tc , they pass through a maximum and then aminimum before steeply increasing as V is decreased.

What does this tell you about the first and second derivativesof P with respect to V, when the pressure, temperature, and volumeall attain their critical values?

What is the thermal conductivity of the superfluid component ofHelium II. Wikipedia claims that it is infinite, but I don'tbelieve that. I base my believes mostley on experiments regardingsuperleask (I haven't done any of those myself, but I've read aboutthe work of others) In these experiments two bodies of Helium IIare connected through a very narrow path, the path is so narrow itonly allows the super component of Helium II to pass. When one ofthe two bodies is heated you'll see that there will be atemperature difference and a pressure difference.
From what I understood super components of Helium II from the coldbath shall travel to the warmer bath so that both baths have thesame concentration of super components. This combined withwikipedia's claim that the conductivity of the super components areinfinite possses a problem for me. For if the conductivity isinfinite how can there be a temperature difference? But regardlessof this problem (I can think a way around this). Thesupercomponents would need to travel at the speed of light to makesure that both baths have the same concentration of supercomponents.

Hope someone can help me with this.

An atom with an electron in a very high n state is said to be in a“Rydberg state.” In Chap. 3 we learned that the radius of anelectron in state n is rn = n^ x h^2/4p^2 x me^2 = n^2 x r(B) wherethe Bohr radius r(B) = 0.0525nm. The (classical) cross section inthis model is s = prn^2, and for large n this gets so large that itmakes no sense to think about a bound electron. Let’s do a veryrough calculation to see where this model breaks down.

• Assume you have a gas cloud with T = 104K and density n(H) = 1atom/cm^3. (Watch out: in this problem we have the energy level nand the density nH .) What is the rms speed of an H atom in thisgas, in cm/s?
• Assuming each atom has the cross section given above, what is themean free path for collisions (the formula in terms of rB andn)?
• If all the atoms move at vrms what is the mean time betweencollisions, tc (in terms of rB and n)?
• For large n, the decay time, td, to go from state n to state n -1 is roughly n2 times 50 ns. For n = 100, nH = 1 and T = 104,calculate tc and td. Which is larger? Does it make sense to talkabout a bound state for n = 100?
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• Those calculations were for the diffuse gas between the stars.Now assume we are in a stellar atmosphere, and nH = 1024 atoms/cm3.For what n does tc = td? Does this mean collisions or decays happenmore often? Given this, why is the gas not completely ionized?

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