The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at 57 is (molecular masses of oxygen and helium are 32 and 4 respectively.) (a) 1320 K (b) 2240 K (c) 2640 K (d) 3230 K

Answer: (c). Equal vrms means equal T/M. THe = 57 + 273 = 330 K TO/32 = 330/4 ⇒ TO = 2640 K So the answer is (c) 2640 K.

The temperature at which oxygen molecules will have same r.m.s. speed… | MHT CET 2025 (26 Apr, Shift 1)

Q18MHT CET 2025 · 26 APR · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at $57^\circ\text{C}$ is (molecular masses of oxygen and helium are 32 and 4 respectively.)

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Answer: (c)

Equal $v_{rms}$ means equal $\frac{T}{M}$ .
$T_{He} = 57 + 273 = 330\text{ K}$
$\frac{T_O}{32} = \frac{330}{4} \Rightarrow T_O = 2640\text{ K}$
So the answer is (c) 2640 K.

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