At which temperature will the speed of sound | vedclass

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(D) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$.Since the speed of sound is the same for both gases,we

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$-249.7$

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(D) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$.Since the speed of sound is the same for both gases,we have $v_{H_2} = v_{O_2}$.Assuming $\gamma$ is constant for both gases,we get $\frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$,which implies $T_{H_2} = T_{O_2} 	imes \frac{M_{H_2}}{M_{O_2}}$.Given $T_{O_2} = 100 + 273 = 373 \, K$,$M_{H_2} = 2 \, g/mol$,and $M_{O_2} = 32 \, g/mol$.Substituting the values: $T_{H_2} = 373 	imes \frac{2}{32} = 373 	imes \frac{1}{16} = 23.3125 \, K$.Converting to Celsius: $T(^{\circ}C) = 23.3125 - 273 = -249.6875 \, ^{\circ}C \approx -249.7 \, ^{\circ}C$.

At which temperature will the speed of sound in hydrogen be the same as the speed of sound in oxygen at $100\,^{\circ}C$?

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