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Mechanical Properties Of Fluids

Question
CBSEENPH11018732

Derive the relation between velocity of sound V in gas and rms velocity v of gas 

Solution
According to kinetic theory of gases, 
                       straight P equals 1 third ρv squared 
∴                       straight v equals square root of fraction numerator 3 straight P over denominator straight rho end fraction end root           ...(1) 
Also the velocity of sound in gas is given by, 
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#6 {main}</pre>           ...(2)
From (1) and (2), 
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#6 {main}</pre> 
This expression gives us the relationship between the velocity of sound in gas and rms velocity of gas.