The ratio of the speed of sound in a monatomic gas at $27^{\circ} \mathrm{C}$ and rms speed of the molecules…

The ratio of the speed of sound in a monatomic gas at $27^{\circ} \mathrm{C}$ and rms speed of the molecules of the same gas at a temperature of $127^{\circ} \mathrm{C}$ is
  1. 1 : 2
  2. $\sqrt{5}: \sqrt{12}$
  3. 3 : 4
  4. $\sqrt{13}: \sqrt{17}$

Solution

Speed of sound in gas
For monoatonic gas, $r=\frac{5}{3}$ Also, $T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}$, $ \begin{aligned} & \therefore \quad \text { Ratio, } \frac{v}{c}=\sqrt{\frac{\gamma \cdot \mathrm{T}_1}{3 \cdot T_2}}=\sqrt{\frac{5 / 3 \times 300}{3 \times 400}} \\ & \quad \frac{v}{c}=\frac{\sqrt{5}}{\sqrt{12}} \end{aligned} $

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

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