AP EAMCET · PHYSICS · Kinetic Theory of Gases
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
- A 1 : 2
- B \(\sqrt{5}: \sqrt{12}\)
- C 3 : 4
- D \(\sqrt{13}: \sqrt{17}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{5}: \sqrt{12}\)
Step-by-step Solution
Detailed explanation
Speed of sound in gas \(v=\sqrt{\frac{\gamma R T_1}{M}}\) ...(i) rms speed of molecules, \(c=\sqrt{\frac{3 R T_2}{M}}\) ...(ii) For monoatonic gas, \(r=\frac{5}{3}\) Also, \(T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}\),…
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