A) \[819{}^\circ C\]
B) \[719{}^\circ C\]
C) \[909{}^\circ C\]
D) none of these
Correct Answer: A
Solution :
Root mean square velocity is \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] where R is gas constant, T the absolute temperature and M the molecular weight. \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] Given, \[{{v}_{1}}:{{v}_{2}}=1:2,\] \[{{T}_{1}}=273\,K\] \[\therefore \] \[\frac{1}{2}=\sqrt{\frac{273}{{{T}_{2}}}}\] \[\Rightarrow \] \[{{T}_{2}}=4\times 273=1092K\] In centigrade \[{{T}_{2}}={{(1092-273)}^{o}}C={{819}^{o}}C\]
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