Question

Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2 v$.
In the light of the above statements, choose the correct answer from the options given below :

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

Answer: (D)

$ {\left[ P _{ avg }=0\right]} $ (due to random motion)
$ v _{ rms }=\sqrt{\frac{3 RT }{ M }} $
$ T _\text{ new }=2 T$
$ M _{\text {new }}=\frac{ M }{2} $
$ \frac{ v _{\text {new }}}{ v }=\frac{\sqrt{\frac{2 T }{ M / 2}}}{\sqrt{\frac{ T }{ M }}}$