A) \[516\,\,m/s\]
B) \[450\,\,m/s\]
C) \[310\,\,m/s\]
D) \[746\,\,m/s\]
Correct Answer: A
Solution :
The root mean square velocity of the gas is given by \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] Where \[R\] is gas constant, \[T\] is absolute temperature and \[M\] is the molecular weight of the gas. \[{{T}_{1}}=27{{\,}^{\circ }}C=273+27=300\,K\] \[{{T}_{2}}=227{{\,}^{\circ }}C=273+227=500\,K\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{300}{500}=\sqrt{\frac{3}{5}}}\] Given, \[{{v}_{1}}=400\,m/s,\,{{v}_{2}}={{v}_{s}}\] \[\therefore \] \[{{v}_{s}}=\sqrt{\frac{5}{3}}\times 400\] \[=1.29\times 400\] \[=516.39\,m/s\approx 516\,m/s\] Note: If the absolute temperature of the gas becomes zero, then the motion of molecules will cease.
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