Calculating Speed of Sound in Helium Gas at 293k

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SUMMARY

The speed of sound in helium gas at 293K can be calculated to match the speed of sound in fresh water, which is 1482 m/s. The relevant properties of helium include its monatomic nature, with a specific heat ratio (γ) of 1.67 and an atomic mass of 4.003 u. The discussion highlights the importance of unit conversion, particularly for atomic mass, to derive the correct temperature at which the speed of sound in helium equals that of water. The correct temperature options provided include 442K, 377K, 525K, 313K, and 633K.

PREREQUISITES
  • Understanding of monatomic ideal gas properties
  • Familiarity with the speed of sound equations
  • Knowledge of unit conversions, particularly for atomic mass
  • Basic grasp of Boltzmann's Constant and its units
NEXT STEPS
  • Research the equation for the speed of sound in gases
  • Learn about unit conversions for atomic mass (amu to kg)
  • Study the application of Boltzmann's Constant in thermodynamics
  • Explore the properties of monatomic gases and their specific heat ratios
USEFUL FOR

Students in physics or engineering, particularly those studying thermodynamics and gas properties, as well as educators looking for practical examples of unit conversion and speed of sound calculations.

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Homework Statement


The speed of sound in fresh water at 293k is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293k? Helium is considered a monatomic ideal gas (y = 1.67 and atomic mass = 4.003u).
A)442K
B)377K
C)525K
D)313K
E)633K


Homework Equations




chart?cht=tx&chl=Vgas%20%3D%20%5Csqrt%20%7B%5Cfrac%20%7BykT%7D%7Bm%7D%7D&chs=&chf=&chco=.png


The Attempt at a Solution



Changed equation to --->


chart?cht=tx&chl=%5Cfrac%20%7BVgas%5E2%20m%7D%7Byk%7D%20%3D%20T&chs=&chf=&chco=.png


%7B1482%5E2%20(4.003)%7D%7B(1.67)(1.38%20%5Ctimes%2010%5E%7B-23%7D)%7D%20%3D%20T&chs=&chf=&chco=.png


Getting really large numbers...
 
Last edited:
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Check your units. You forgot to do a conversion somewhere.
 
Mike Pemulis said:
Check your units. You forgot to do a conversion somewhere.

I'm guessing it is the atomic mass that needs to conversion...but I can't seem to find it in my lecture notes... is there an equation for it?
 
Good guess. You can look up the definition of an amu on Wikipedia, or Google will just do unit conversions for you. (Type "2 inches in centimeters" and it spits out "5.08 cm." Very handy).

Of course, you still need to know what units to convert amu's into. To figure that out, you can write out all the units on the left-hand side of your last equation, and see what units the atomic mass has to be into get a result in Kelvin. Wikipedia or Google can supply the unit for Boltzmann's Constant if you don't know it.
 
AH I got it, man my professor made this pretty sticky haha. Thanks for the help.

%20%5Ctimes%2010%5E%7B-3%7D%20%3D%206.647%20%5Ctimes%2010%5E%7B-27%7D%20kg%2Fmol&chs=&chf=&chco=.png




B-27%7D)%7D%7B(1.67)(1.38%20%5Ctimes%2010%5E%7B-23%7D)%7D%20%3D%20T%20%3D%20633K&chs=&chf=&chco=.png
 
No problem. :smile:
 

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