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Physics · PYQ NEET UG 2016(1)
हिन्दीThe molecules of a given mass of a gas have r.m.s velocity of \( 200\text{ ms}^{-1} \) at \( 27^\circ\text{C} \) and \( 1.0 \times 10^5\text{ Nm}^{-2} \) pressure. When the temperature and pressure of the gas are respectively, \( 127^\circ\text{C} \) and \( 0.05 \times 10^5\text{ Nm}^{-2} \), the r.m.s. velocity of its molecules in \( \text{ms}^{-1} \) is
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Correct answer · Option D
\( \frac{400}{\sqrt{3}} \)
Explanation
The r.m.s. velocity depends only on temperature as \( v_{rms} = \sqrt{\frac{3RT}{M}} \). Thus \( \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{400}{300}} = \frac{2}{\sqrt{3}} \), so \( v_2 = 200 \times \frac{2}{\sqrt{3}} = \frac{400}{\sqrt{3}}\text{ ms}^{-1} \).
