Kinetic Theory Of Gases Question 111
Question: A cubical box with porous walls containing an equal number of $ O _{2} $ and $ H _{2} $ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of $ v _{rms} $ of $ O _{2} $ molecules to that of the $ v _{rms} $ of $ H _{2} $ molecules, found in the chamber outside the box after a short interval is
Options:
A) $ \frac{1}{2\sqrt{2}} $
B) $ \frac{1}{4} $
C) $ \frac{1}{\sqrt{2}} $
D) $ \sqrt{2} $
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Answer:
Correct Answer: B
Solution:
Temperature remains constant so $ v _{rms}\propto \frac{1}{\sqrt{M}} $
Therefore $ \frac{{v _{O _{2}}}}{{v _{H _{2}}}}=\sqrt{\frac{{M _{H _{2}}}}{{M _{O _{2}}}}}=\sqrt{\frac{1}{16}}=\frac{1}{4} $
BETA
