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Find the speed of sound in `H_(2)` at temperature `T`, if the speed of sound in `O_(2)` is `450 m//s` at this temperature, |
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Answer» Correct Answer - `1800 m//s` `v = sqrt((gammaRT)/(M))` since termperature, `T` is constant, `(v_(H_(2)))/(v_(H_(1))) = sqrt((M_(O_(2)))/(M_(O_(2)))) = sqrt((32)/(2)) = 4` `v(H_(2)) = 4 xx 450 = 1800 m//s` Aliter : The speed of sound in a gas is given by `u = sqrt((gammaP)/(rho))`. At `STP, 22.4` liters of oxygen has a mass of `32 g` whereas the same volume of hydrogen has a mass of `2 g`. Thus, the density of oxygen is `16` times the density of hydrogen at the same temperature and pressure. As `gamma` is same for both the gases, `v_(("hydrogen"))/(v_(("oxygen"))) = sqrt((rho_(("oxygen")))/(rho_(("hydrogen"))))` or, `v_(("hydrogen") = 4v_(("oxygen"))` `= 4 xx 450 m//s = 1800 m//s` |
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