Heat and Thermodynamics 4 Question 38
40. The root mean square (rms) speed of oxygen molecules $\left(O _2\right)$ at a certain temperature $T$ (degree absolute) is $V$. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged.
(1987, 2M)
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Solution:
- $v _{rms}=\sqrt{\frac{3 R T}{M}} \quad$ or $\quad v _{rms} \propto \sqrt{\frac{T}{M}}$
When oxygen gas dissociates into atomic oxygen its atomic mass $M$ will remain half. Temperature is doubled. So, from Eq. (i) $v _{\text {rms }}$ will become two times.
