GREPhysics.NET: GR8677 #88

GR8677 #88

Problem

GREPhysics.NET Official Solution

Alternate Solutions

Statistical Mechanics $\Rightarrow$ }Pressure

Recall the following results for low temperatures,

$P_{boson} \propto T^{5/2} \; \; \; P_{fermion}\propto T_F \approx big \;\;\; P_{classical} \propto T, <br />$

where one realizes that the Fermi temperature, $T_F$ tends to be on the order of thousands for most material, and that the low temperature regime temperatures are definitely far less than the Fermi temperature; one thus has $P_F>P_B,P_C$ . Moreover, classical effects occur at around $T=300K$ , while the problem specifies the temperature domain for bosons to be far lower than that, thus one deduces that $P_B < P_C$ . Therefore, $P_F>P_C>P_B$ .

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Comments

Bolek
2010-04-09 15:08:48

Just would like to add a captivating factoid. The pressure due to the Pauli exclusion principle for electrons in a metal is so high that you can always treat metals as if they were at 0K!!! Or conversely, the electrons in a metal at 0K behave almost exactly as they do at 300K.

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neutrinosrule
2008-09-14 12:40:48

Bosons can occupy the same energy state as each other, where fermions have to obey the pauli-exclusion principle. Therefore, at cold enough temperatures, bosons would all be in the lowest energy state and it makes sense that they would have the lowest pressure, while fermions would be all over the place and have a higher pressure. If quantum effects were ignored, it makes sense that that pressure would be in between since fermions and bosons seem to be at two extremes.

jmason86
2009-08-13 20:41:20

exactly how I did it too.

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