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

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 :

TestHub · Accepted Answer

Momentum is a vector quantity and average momentum of molecules of a sample is zero due to random motion.
$P_{avg} = 0$
RMS speed of a molecule is given by
$v_{rms} = \sqrt{\frac{3 R T}{M}}$
Now the temperature is doubled $T_{new} = 2 T$ and due to dissociation $M_{new} = \frac{M}{2}$ .
$\Rightarrow \frac{v_{new}}{v} = \frac{\sqrt{\frac{2 T}{\frac{M}{2}}}}{\sqrt{\frac{T}{M}}}$
$\Rightarrow v_{new} = 2 v$

Physics - Heat & Thermo Question with Solution | TestHub

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