The temperature at which the speed of sound i | 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 gas c

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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 gas constant,$T$ is the absolute temperature in Kelvin,and $M$ is the molar mass of the gas.From this relation,we can see that $v \propto \sqrt{T}$.Let $v_1$ be the speed of sound at temperature $T_1$ and $v_2$ be the speed at $T_2$.Given $T_1 = 27^\circ C = 27 + 273 = 300 \ K$.We want the speed to be doubled,so $v_2 = 2v_1$.Using the proportionality $v_2/v_1 = \sqrt{T_2/T_1}$,we get $2 = \sqrt{T_2/300}$.Squaring both sides,$4 = T_2/300$,which gives $T_2 = 1200 \ K$.Converting back to Celsius,$T_2 = 1200 - 273 = 927^\circ C$.

The temperature at which the speed of sound in air becomes double of its value at $27^\circ C$ is ... $^\circ C$

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