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(C) The velocity of sound in an ideal gas is given by $V = \sqrt{\frac{\gamma RT}{M}}$.Since $\gamma$, $R$, and $M$ are constant, $V \propto \sqrt{T}$

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$819$

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(C) The velocity of sound in an ideal gas is given by $V = \sqrt{\frac{\gamma RT}{M}}$.Since $\gamma$, $R$, and $M$ are constant, $V \propto \sqrt{T}$, where $T$ is the absolute temperature in Kelvin.Given that the velocity doubles, if $V_1 = V_0$ at $T_1 = 0^{\circ} C = 273 \ K$, then $V_2 = 2V_0$ at $T_2 = (\alpha + 273) \ K$.Using the ratio: $\frac{V_1}{V_2} = \sqrt{\frac{T_1}{T_2}}$.Substituting the values: $\frac{V_0}{2V_0} = \sqrt{\frac{273}{T_2}}$.Squaring both sides: $\frac{1}{4} = \frac{273}{T_2}$.Therefore, $T_2 = 4 	imes 273 = 1092 \ K$.Since $T_2 = \alpha + 273$, we have $\alpha = 1092 - 273 = 819^{\circ} C$.

The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} C$ to $\alpha^{\circ} C$. The value of $\alpha$ is . . . . . . .

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