The ratio of the speed of sound in nitrogen g | vedclass

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(C) The speed 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 unive

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$\sqrt{3}/5$

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(C) The speed 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 temperature,and $M$ is the molar mass of the gas.Since the temperature $T$ is the same for both gases,the ratio of the speeds is given by $\frac{v_{N_2}}{v_{He}} = \sqrt{\frac{\gamma_{N_2}}{\gamma_{He}} 	imes \frac{M_{He}}{M_{N_2}}}$.For nitrogen $(N_2)$,which is a diatomic gas,$\gamma_{N_2} = 1.4 = 7/5$ and the molar mass $M_{N_2} = 28 \ g/mol$.For helium $(He)$,which is a monatomic gas,$\gamma_{He} = 1.67 = 5/3$ and the molar mass $M_{He} = 4 \ g/mol$.Substituting these values: $\frac{v_{N_2}}{v_{He}} = \sqrt{\frac{7/5}{5/3} 	imes \frac{4}{28}} = \sqrt{\frac{7}{5} 	imes \frac{3}{5} 	imes \frac{1}{7}} = \sqrt{\frac{3}{25}} = \frac{\sqrt{3}}{5}$.

The ratio of the speed of sound in nitrogen gas to that in helium gas,at $300 K$ is

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