A) 1.4 times
B) 4 times
C) 2 times
D) \[\frac{1}{4}\]times
Correct Answer: B
Solution :
Average speed is the arithmetic mean of the speeds of molecules in a gas at a given temperature, ie, \[{{v}_{av}}=({{v}_{1}}+{{v}_{2}}+{{v}_{3}}.......)/N\] and according to kinetic theory of gases \[{{v}_{av}}=\sqrt{\frac{8RT}{M\pi }}\] ?..(i) \[{{v}_{rms}}=\sqrt{(v_{1}^{2}+v_{2}^{2}+v_{3}^{2}....)}/N\] and according to kinetic theory of gases \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] From Eqs. (i) and (ii), we get \[{{v}_{rms}}=\sqrt{\left( \frac{8}{3\pi } \right){{v}_{rms}}}\] \[=0.92{{v}_{rms}}\] Therefore, \[\frac{{{v}_{av}}}{{{v}_{rms}}}=\]constant Hence, root mean square velocity is also become 4 times.
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