The ratio of the velocity of sound in hydroge | vedclass

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(B) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$,where $\gamma$ is the adiabatic index,$R$ is the un

Vedclass · Accepted Answer

$4:1$

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(B) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$,where $\gamma$ is the adiabatic index,$R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.For a given temperature and assuming both gases are diatomic ($\gamma$ is the same),the velocity is inversely proportional to the square root of the molar mass: $v \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the velocity of sound in hydrogen $(H_2)$ to oxygen $(O_2)$ is:$\frac{v_{H_2}}{v_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}}$The molar mass of oxygen $(O_2)$ is $32 \ g/mol$ and the molar mass of hydrogen $(H_2)$ is $2 \ g/mol$.$\frac{v_{H_2}}{v_{O_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$.Thus,the ratio is $4:1$.

The ratio of the velocity of sound in hydrogen gas to that in oxygen gas at a given temperature is:

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