Calculate RMS Velocity of Air at 72 cm-Hg, 344.7013 m/s, 22.6 C

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SUMMARY

The discussion focuses on calculating the root mean square (RMS) velocity (Vrms) of air given specific parameters: air pressure at 72 cm-Hg, sound velocity at 344.7013 m/s, and temperature at 22.6°C. The equation used is velocity = Vrms * sqrt[(1.40 * n * Na * m) / (3 * density * Vol)]. The user expresses confusion regarding the assignment of values and the interpretation of "velocity" in the equation, suggesting a need for clarification on the relationship between Vrms and temperature.

PREREQUISITES
  • Understanding of the ideal gas law and its components
  • Familiarity with the concept of root mean square velocity (Vrms)
  • Knowledge of Avogadro's number (Na = 6.02 x 10^23)
  • Basic principles of thermodynamics related to gas behavior
NEXT STEPS
  • Review the derivation of the RMS velocity formula for gases
  • Study the relationship between temperature and molecular speed in gases
  • Explore the ideal gas law and its application in calculating density and volume
  • Investigate additional equations involving Vrms and temperature from thermodynamics textbooks
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone involved in gas dynamics calculations will benefit from this discussion.

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Homework Statement


If the air pressure is 72 cm-Hg (as measured with a barometer), the velocity of sound is 344.7013 m/s and the temperature is 22.6 C calculate the Vrms.


Homework Equations



velocity = Vrms*sqrt[(1.40*n*Na*m)/(3*density*Vol)]

The Attempt at a Solution



I am under the impression that the Nam cancels out the density*volume, but I'm not getting the right answer. I'm really having trouble assigning values for all the parts of the equation.

Thanks in advance.
 
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If the quantities are what I think they are***, then n*Na*m would cancel density*volume. This will leave an equation with two quantities, "velocity" and "Vrms". I know what Vrms is, but have know idea what "velocity" refers to in this equation.

Hint: can you find a different equation in your textbook, one that involves both Vrms and Temperature?

*** p.s. correct me if I'm wrong, but I believe that:
n is the number of moles of air molecules
Na is Avagadro's number, 6.02 x 10^23
m is the mass of a single molecule.
 

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