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At what temperature will the speed of sound be nearly 1.5 times its value at N.T.P.?
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1433 Upvotes
Verified Answer
The correct answer is:
$341^{\circ} \mathrm{C}$
Speed of sound depends on $T$ temperature, $M$ molar mass and $\gamma$ gas exponent:
$\begin{aligned}
& v=\sqrt{\frac{\gamma R T}{M}} \\
& \Rightarrow \frac{v^{\prime}}{v}=\sqrt{\frac{T^{\prime}}{T}}=1.5 \\
& \Rightarrow \sqrt{T^{\prime}}=1.5 \sqrt{(273)} \\
& T^{\prime}=2.25 \times 273 \mathrm{~K}=614 \mathrm{~K}
\end{aligned}$
On writing in degree Celsius:
$T^{\prime}=341^{\circ} \mathrm{C}$
$\begin{aligned}
& v=\sqrt{\frac{\gamma R T}{M}} \\
& \Rightarrow \frac{v^{\prime}}{v}=\sqrt{\frac{T^{\prime}}{T}}=1.5 \\
& \Rightarrow \sqrt{T^{\prime}}=1.5 \sqrt{(273)} \\
& T^{\prime}=2.25 \times 273 \mathrm{~K}=614 \mathrm{~K}
\end{aligned}$
On writing in degree Celsius:
$T^{\prime}=341^{\circ} \mathrm{C}$
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