Speed of sound in sodium at absolute zero?

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SUMMARY

The speed of sound in metallic sodium at absolute zero (T = 0 K) is calculated to be 14.5 meters per second using Fermi-Dirac statistics. This result is significantly slower than expected when compared to the speed of sound in gases, which is influenced by molecular speed. At absolute zero, all materials are in a solid state, and the speed of sound is affected by the vibrational states of the solid's molecules, which decrease as temperature approaches zero. This counter-intuitive result highlights the unique properties of sound propagation in solids versus gases.

PREREQUISITES
  • Understanding of Fermi-Dirac statistics
  • Knowledge of sound propagation in solids
  • Familiarity with the concept of absolute zero (0 K)
  • Basic principles of thermodynamics
NEXT STEPS
  • Research the properties of sound in solids versus gases
  • Study the implications of Fermi-Dirac statistics on material properties
  • Explore the effects of temperature on sound speed in various materials
  • Investigate the behavior of materials at absolute zero
USEFUL FOR

Physicists, materials scientists, and students studying thermodynamics and solid-state physics will benefit from this discussion.

quarky2001
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I don't need help with a numerical solution here - mostly a concept check.

I've been asked to calculate the speed of sound in metallic sodium at T = 0 K using Fermi-Dirac statistics.

After doing so, I get a speed of 14.5 meters per second, which is, well, really slow.

I would have expected sound to travel much more quickly than in air at that temperature. Is my answer likely to be right? If so, could someone explain why the result is so counter-intuitive?
 
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From what I have read, the speed of sound is roughly proportional to the speed of the molecules if it is a gas. I think it is intuitive to assume that the speed of sound is dependent in a similar fashion to the vibarational states of the molecules in a solid, and thus increase with increasing temperature.

For the air comment, remember that at T=0K, air cannot exist. Everything is a solid at T=0, right?
 
Last edited:
Ah, I suppose that makes sense. Thanks.
 

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