At what temperature will the speed of sound b | vedclass

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(C) The speed of sound $v$ in a gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$.Since $\gamma$,$R$,and $M$ are constants for a given gas

Vedclass · Accepted Answer

$341$

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(C) The speed of sound $v$ in a gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$.Since $\gamma$,$R$,and $M$ are constants for a given gas,the speed of sound is directly proportional to the square root of the absolute temperature: $v \propto \sqrt{T}$.Let $v$ be the speed at $N.T.P.$ $(T = 273 \ K)$ and $v'$ be the speed at temperature $T'$.Given that $v' = 1.5 v$,we have:$\frac{v'}{v} = \sqrt{\frac{T'}{T}} = 1.5$.Squaring both sides:$\frac{T'}{T} = (1.5)^2 = 2.25$.$T' = 2.25 	imes 273 \ K = 614.25 \ K$.To convert this temperature to degree Celsius:$T(^{\circ} C) = T(K) - 273 = 614.25 - 273 = 341.25^{\circ} C$.Thus,the temperature is approximately $341^{\circ} C$.

At what temperature will the speed of sound be nearly $1.5$ times its value at $N.T.P.$ (in $^{\circ} C$)?

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