Find Out The Ratio Of The Velocity Of Sound In Helium And In Nitrogen Gases At 300 K Temperature. Molecular Weights Of Helium And Nitrogen Are 4 And 28 Respectively.

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Question

Find out the ratio of the velocity of sound in helium and in nitrogen gases at 300 K temperature. Molecular weights of helium and nitrogen are 4 and 28 respectively.

Solution

Correct option is

2.9

 

The speed of sound in a gas is, 

Where T is absolute temperature of the gas and M is molecular weight of the gas. The speed of sound in helium is 

                           

And that in nitrogen is  

                        

                     

We know that for a mono-atomic gas (as He) the value of γ is 5/3, and for a diatomic gas (as N) is 7/5.

Given: MN = 28 and MHe = 4.  

                    

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