Kinetic Theory Of Gases Question 49
Question: The molecules of a given mass of a gas have r.m.s. velocity of $ 200m{{s}^{-1}} $ at $ 27{}^\circ C $ and $ 1.0\times 10^{5}N{{m}^{-2}} $ pressure. When the temperature and pressure of the gas are respectively, $ 127{}^\circ C $ and $ 0.05\times 10^{5}N{{m}^{-2}}, $ the r.m.s. velocity of its molecules
Options:
A) $ 100\sqrt{2} $
B) $ \frac{400}{\sqrt{3}} $
C) $ \frac{100\sqrt{2}}{3} $
D) $ \frac{100}{3} $
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Answer:
Correct Answer: B
Solution:
[b] Here $ v _{1}=200m/s; $ temperature $ T _{1}=27{}^\circ C=27+273=300k $ temperature $ T _{2}=127{}^\circ C=127+273=400k, $ V=? R.M.S. Velocity, $ V\propto \sqrt{T} $
$ \Rightarrow \frac{v}{200}=\sqrt{\frac{400}{300}}\Rightarrow v=\frac{400}{\sqrt{3}}m/s $
BETA
