COMEDK · Physics · 14. Kinetic Theory of Gases
The molecules of a given mass of a gas have root mean square speed of \(120 \mathrm{~m} / \mathrm{s}\) at \(88^{\circ} \mathrm{C}\) and 1 atmospheric pressure. The root mean square speed of the molecules at \(127^{\circ} \mathrm{C}\) and 2 atmospheric pressure is
- A 1.443 m/s
- B 126.3 m/s
- C 88.12 m/s
- D 105.2 m/s
Answer & Solution
Correct Answer
(B) 126.3 m/s
Step-by-step Solution
Detailed explanation
The root mean square speed \(v_{rms}\) of gas molecules is given by the formula \(v_{rms} = \sqrt{\dfrac{3RT}{M}}\). From this formula, it is evident that \(v_{rms}\) depends only on the temperature \(T\) and the molar mass \(M\) of the gas. It is independent of the pressure…
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