At What Temperature The Speed Of Sound In Oxygen Will Be Same As That In Nitrogen At 14oC? The Molecular Weights Of Oxygen And Nitrogen Are 32 And 28 Respectively.

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Question

At what temperature the speed of sound in oxygen will be same as that in nitrogen at 14oC? The molecular weights of oxygen and nitrogen are 32 and 28 respectively.

Solution

Correct option is

 

If the molecular weight of a gas be M and its absolute temperature be T, then the speed of sound in that gas is given by  

                            

Where R is the universal gas constant.

Suppose the speed of sound in oxygen at temperature t is the same as in nitrogen at 14oC. Then 

       

and    speed of sound in nitrogen at 14oC   

                                                                       

These two speeds must be equal. Also, the value of γ is same for both gases. Therefore,

                   

       

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