Calculating Speed of Sound in Helium Gas at 293k

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Homework Help Overview

The discussion revolves around calculating the temperature at which the speed of sound in helium gas equals that of fresh water at 293K. The problem involves understanding the properties of helium as a monatomic ideal gas and requires knowledge of relevant equations and unit conversions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for unit conversions, particularly regarding atomic mass, and question the appropriate units to use in the calculations. There is an exploration of how to manipulate the equations to find the desired temperature.

Discussion Status

Some participants have provided guidance on checking units and suggested looking up definitions and conversions. There is an acknowledgment of the complexity of the problem, and while some progress has been made, no consensus or resolution has been reached.

Contextual Notes

Participants note the challenge posed by the problem and the potential need for additional resources or references to clarify unit conversions and relevant constants.

huykma
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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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