A) half
B) twice
C) four times
D) one- fourth
Correct Answer: A
Solution :
Root mean square velocity \[({{v}_{rms}})\] of an ideal gas at temperature T is \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] Given, \[{{T}_{1}}={{27}^{o}}C=273+27=300\,K\], \[{{T}_{2}}={{927}^{o}}C\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{300}{1200}}=\frac{1}{2}\] Hence, root mean square velocity will become double.
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