A) \[\frac{150}{\sqrt{3}}m/s\]
B) \[\frac{125}{\sqrt{3}}m/s\]
C) \[\frac{200}{\sqrt{3}}m/s\]
D) \[100\sqrt{3}m/s\]
Correct Answer: C
Solution :
[c] We know that for a given mass of a gas \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] Where R is gas constant, T is temperature in kelvin and M is molar mass of the gas. Clearly for a given gas, \[{{v}_{rms}}\propto \sqrt{T}\], as R, M are constants. Hence, \[\frac{{{({{v}_{rms}})}_{1}}}{{{({{v}_{rms}})}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}...(i)\] Given, \[{{({{v}_{rms}})}_{1}}=100m/s\] \[{{T}_{1}}=27{}^\circ C=27+273=300K\] \[{{T}_{2}}=127{}^\circ C=127+273=400K\] \[\therefore \]Form Eq. (i) \[\frac{100}{{{({{v}_{rms}})}_{2}}}=\sqrt{\frac{300}{400}}=\frac{\sqrt{3}}{2}\] \[\Rightarrow {{({{v}_{rms}})}_{2}}=\frac{2\times 100}{\sqrt{3}}=\frac{200}{\sqrt{3}}m/s\]
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