Kinetic Theory Of Gases Question 138
Question: A gas mixture consists of molecules of type 1, 2 and 3, with molar masses $ m _{1}>m _{2}>m _{3}. $ $ V _{rms} $ and $ \overline{K} $ are the r.m.s. speed and average kinetic energy of the gases. Which of the following is true
Options:
A) $ {{( V _{rms} )} _{1}}<{{( V _{rms} )} _{2}}<{{( V _{rms} )} _{3}} $ and $ {{(\overline{K})} _{1}}={{(\overline{K})} _{2}}=({{\overline{K}} _{3}}) $
B) $ {{( V _{rms} )} _{1}}={{( V _{rms} )} _{2}}={{( V _{rms} )} _{3}} $ and $ {{(\overline{K})} _{1}}={{(\overline{K})} _{2}}>{{(\overline{K})} _{3}} $
C) $ {{( V _{rms} )} _{1}}>{{( V _{rms} )} _{2}}>{{( V _{rms} )} _{3}} $ and $ {{(\overline{K})} _{1}}<{{(\overline{K})} _{2}}>({{\overline{K}} _{3}}) $
D) $ {{( V _{rms} )} _{1}}>{{( V _{rms} )} _{2}}>{{( V _{rms} )} _{3}} $ and $ {{(\overline{K})} _{1}}<{{(\overline{K})} _{2}}<{{(\overline{K})} _{3}} $
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Answer:
Correct Answer: A
Solution:
[a] $ v _{rms}\frac{1}{\sqrt{M}}$
$\Rightarrow$
$(v _{rms})_1$ <
$(v _{rms})_2$<
$(v _{rms})_3 $
also in mixture temperature of each gas will be same, hence kinetic energy also remains same.
BETA
