JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Heat & Thermodynamics

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Consider a sample of oxygen behaving like an ideal gas. At 300 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 / mol

;

R = 8.3 JK^{- 1} mol^{- 1}

)

(A) $\frac{8 π}{3}$
(B) $\frac{8}{3}$
(C) $\frac{3}{3}$
(D) $\frac{3 π}{8}$ ✓ Correct

Answer: (D)

Solution

For a gas at temperature

T

and molar mass

M

v_{rms} = \frac{3 R T}{M}, v_{av} = \frac{8 R T}{π M}

Both carry the same dependence on

T

and

M

, so these cancel in the ratio:

\frac{v _{rms}}{v _{av}} = \frac{3 R T}{M} \cdot \frac{π M}{8 R T} = \frac{3 π}{8}

The ratio is

\frac{3 π}{8}

, the same for every gas at every temperature, so the data on oxygen are not needed.

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option

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