Q139 / 160 · AP EAMCET 2018 (24 Apr Shift 1) · Physics
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
- A1 : 2
- Correct answerB$\sqrt{5}: \sqrt{12}$
- C3 : 4
- D$\sqrt{13}: \sqrt{17}$
Solution
Speed of sound in gas
For monoatonic gas, $r=\frac{5}{3}$ Also, $T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}$, $$ \begin{aligned} & \therefore \quad \text { Ratio, } \frac{v}{c}=\sqrt{\frac{\gamma \cdot \mathrm{T}_1}{3 \cdot T_2}}=\sqrt{\frac{5 / 3 \times 300}{3 \times 400}} \\ & \quad \frac{v}{c}=\frac{\sqrt{5}}{\sqrt{12}} \end{aligned} $$
For monoatonic gas, $r=\frac{5}{3}$ Also, $T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}$, $$ \begin{aligned} & \therefore \quad \text { Ratio, } \frac{v}{c}=\sqrt{\frac{\gamma \cdot \mathrm{T}_1}{3 \cdot T_2}}=\sqrt{\frac{5 / 3 \times 300}{3 \times 400}} \\ & \quad \frac{v}{c}=\frac{\sqrt{5}}{\sqrt{12}} \end{aligned} $$
Hence, the correct answer is option: 'B'.