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

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)`.

Text Solution

Verified by Experts

`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 to that in helium gas at the same temperature is

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

  • The adiabatic elasticity of hydrogen gas (gamma=1.4) at NTP

    A
    `1xx10^5(N)/(m^2)`
    B
    `1xx10^8(N)/(m^2)`
    C
    `1.4(N)/(m^2)`
    D
    `1.4xx10^5(N)/(m^2)`

  • The ratio of the velocity of sound in oxygen to that in hydrogen at same temperature and pressure is approximately :

    A
    `16:1`
    B
    `1:16`
    C
    `4:1`
    D
    `1:4`