At what temperature is the velocity of sound | vedclass

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Question

(B) The velocity of sound in a gas is directly proportional to the square root of its absolute temperature: $v \propto \sqrt{T}$.Given that the veloci

Vedclass · Accepted Answer

$819^{\circ}C$

Vedclass · Answer

(B) The velocity of sound in a gas is directly proportional to the square root of its absolute temperature: $v \propto \sqrt{T}$.Given that the velocity at temperature $T_2$ is double the velocity at $T_1 = 0^{\circ}C = 273 \ K$,we have:$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$Substituting the given values:$2 = \sqrt{\frac{T_2}{273}}$Squaring both sides:$4 = \frac{T_2}{273}$$T_2 = 4 	imes 273 = 1092 \ K$To convert this to Celsius:$T(^{\circ}C) = 1092 - 273 = 819^{\circ}C$.Therefore,the correct option is $B$.

At what temperature is the velocity of sound double that of its velocity at $0^{\circ}C$?

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