TS EAMCET · Physics · Kinetic Theory of Gases
If the rms speed of the molecules of a gas at a temperature of \(77^{\circ} \mathrm{C}\) is \(50 \mathrm{~ms}^{-1}\), then the rms speed of the same gas molecules at a temperature of \(150.5^{\circ} \mathrm{C}\) is
- A \(65 \mathrm{~ms}^{-1}\)
- B \(35 \mathrm{~ms}^{-1}\)
- C \(55 \mathrm{~ms}^{-1}\)
- D \(45 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(C) \(55 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
\(T_1 = 77 + 273 = 350 \mathrm{~K}\) \(T_2 = 150.5 + 273 = 423.5 \mathrm{~K}\) \(v_2 = v_1 \sqrt{\frac{T_2}{T_1}}\) \(v_2 = 50 \sqrt{\frac{423.5}{350}}\) \(v_2 = 50 \sqrt{1.21}\) \(v_2 = 50 \times 1.1 = 55 \mathrm{~ms}^{-1}\)
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