Low Temp Physics: Why He (3) Needs Higher Pressure to Solidify

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SUMMARY

At absolute zero, Helium-3 (He-3) exhibits a larger molar volume and requires higher pressure to solidify compared to Helium-4 (He-4) due to the Pauli exclusion principle. This principle affects fermions like He-3, making them less confined than bosons such as He-4, resulting in a larger molar volume. The relationship between pressure and volume, as described by the ideal gas law (Pv = nRT), indicates that an increase in volume does not necessarily lead to a decrease in pressure when considering the unique quantum properties of He-3, including pairing processes that involve bosonic behavior.

PREREQUISITES
  • Understanding of the Pauli exclusion principle
  • Familiarity with the properties of fermions and bosons
  • Basic knowledge of thermodynamics and the ideal gas law
  • Concept of quantum statistics and its implications on atomic behavior
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  • Research the implications of the Pauli exclusion principle on fermionic behavior
  • Study the differences in quantum statistics between fermions and bosons
  • Explore the phase transitions of Helium-3 and Helium-4 at low temperatures
  • Learn about the pairing mechanisms in quantum fluids
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Physicists, students studying low-temperature physics, and researchers interested in quantum mechanics and the properties of helium isotopes.

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Homework Statement


Why at absolute zero does He (three) have a larger molar volume and require a higher pressure to solidify than He(four)?



The Attempt at a Solution



I feel the answer lies in the Pauli exclusion principle, at low temps the ferions are nopt as easily confined as the bosons so they will have a larger molar volume, but i can't explain why this would then require a higher pressure to solidify:

Pv = nRT

where if v is increased surely P must decrease?
 
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I think I saw some pairing process for He3 - so you have to consider "molecules" (those are bosons again) instead of atoms.
 

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