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Ratio of rms, average and most probable speeds

This type of question, asked 4 times: 2021 Paper 10, 25 Jun 2022, 29 Jan 2023, 13 Apr 2023. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 10

    19
    Consider a sample of oxygen behaving like an ideal gas. At 300 K300\text{ }K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be: (Molecular weight of oxygen is 32 g/mol32\text{ }g/mol; R=8.3 J K−1 mol−1R = 8.3\text{ }J{\text{ }K}^{- 1}{\text{ }mol}^{- 1} )

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  2. Question 2

    25 Jun 2022

    7
    The relation between root mean square speed (vrms)\left( v_{rms} \right) and most probable speed (vp)\left( v_{p} \right) for the molar mass MM of oxygen gas molecule at the temperature of 300 K300\text{ }K will be :-

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  3. Question 3

    29 Jan 2023

    109
    At 300 K300\text{ }K the rms speed of oxygen molecules is α+5α\sqrt{\frac{\alpha + 5}{\alpha}} times to that of its average speed in the gas. Then, the value of α\alpha will be (use π=227\pi = \frac{22}{7})

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  4. Question 4

    13 Apr 2023

    13
    The rms speed of oxygen molecule in a vessel at particular temperature is (1+5x)12v\left( 1 +\frac{5}{x} \right)^{\frac{1}{2}}v, where vv is the average speed of the molecule. The value of xx will be:(Take π=227\pi =\frac{22}{7} )

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