A) \[\text{519}{{\,}^{\text{o}}}\text{C}\]
B) \[\text{619}{{\,}^{\text{o}}}\text{C}\]
C) \[\text{719}{{\,}^{\text{o}}}\text{C}\]
D) \[\text{819}{{\,}^{\text{o}}}\text{C}\]
Correct Answer: D
Solution :
We have \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}};\]at \[T={{T}_{0}}\](NTP) \[{{v}_{rms}}=\sqrt{\frac{3R{{T}_{0}}}{M}}\] But at temperature \[T,{{v}_{rms}}=2\times \sqrt{\frac{3R{{T}_{0}}}{M}}\] \[\Rightarrow \] \[\sqrt{\frac{3RT}{M}}=2\sqrt{\frac{3R{{T}_{0}}}{M}}\Rightarrow \sqrt{T}=\sqrt{4{{T}_{0}}}\] or \[T=4{{T}_{0}}\] \[T=4\times 273\,K=1092\,K\] \[\therefore \] \[T=819{{\,}^{o}}C\]
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