Kinetic Theory Of Gases Question 161
Question: The molecules of a given mass of gas have a $ rms $ velocity of 200 m/s at $ 27^{o}C $ and $ 1.0\times 10^{5},N/m^{2} $ pressure. When the temperature is $ 127{}^\circ C $ and pressure is $ 0.5\times 10^{5},N/m^{2}, $ the $ rms $ velocity in m/s will be
Options:
A) $ \frac{100\sqrt{2}}{3} $
B) $ 100\sqrt{2} $
C) $ \frac{400}{\sqrt{3}} $
D) None of these
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Answer:
Correct Answer: C
Solution:
[c] Change in pressure will not affect the $ rms $ velocity of molecules. So we will calculate only the effect of temperature. As $ v _{rms}\propto \sqrt{T} $
$ \
Therefore $ $ \frac{{v _{300^{\circ}}}}{{v _{400^{\circ}}}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}\Rightarrow ,\frac{200}{{v _{400^{\circ}}}}=\sqrt{\frac{3}{4}} $
$ \Rightarrow $ $ {v _{400^{0}}}=\frac{200\times 2}{\sqrt{3}}=\frac{400}{\sqrt{3}},m/s $
BETA
