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The ratio of the velocity of sound in hy...

The ratio of the velocity of sound in hydrogen `( gamma = 7/5)` to that in helium `( gamma = 5/3)` at the same temperature is

Text Solution

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`v_("sound") = sqrt((gamma RT)/(M))`
`(v_(H_(2)))/(v_(He)) = sqrt((gamma_(H_(2))//M_(H_(2))))/(sqrt(gamma _(He)//M_(He))) = sqrt((7//5)//2)/(sqrt((5//3)//4)) =sqrt((42)/(25))`.
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Knowledge Check

  • The ratio of the velocity of sound in Hydrogen gas (gamma=7/5) to that in Helium gas (gamma=5/3) at the same temperature is sqrt(21/3) .

    A
    `sqrt(5/42)`
    B
    `sqrt(5/21)`
    C
    `sqrt(42)/5`
    D
    `sqrt(21)/5`

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