STANDARD Physics Root Mean Square Velocity MCQ Question
The molecules of a given mass of a gas have rms velocity of 200 ms⁻¹ at 27°C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 10⁵ N m⁻², the rms velocity of its molecules in ms⁻¹ is:
100√2/3
100/3
100√2
400/√3
Correct Answer
Detailed Explanation
The rms velocity is given by v_rms = √(3kT/m). The velocity is proportional to the square root of temperature. Therefore, the new velocity is calculated using the ratio of temperatures: v_127 = v_27 × √((127 + 273)/(27 + 273)) = 400/√3 ms⁻¹.
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