A) \[10.35\times {{10}^{-21}}J\]
B) \[52.2\times {{10}^{-21}}J\]
C) \[5.22\times {{10}^{-21}}J\]
D) \[11.35\times {{10}^{-21}}J\]
Correct Answer: A
Solution :
We know that the K.E of one mole of a gas molecules at a temperature T is given by \[K=\frac{3}{2}KT\] Now, \[{{T}_{1}}={{27}^{0}}C\,=300\,K\] \[{{K}_{1}}=6.21\times {{10}^{-21}}J\] \[{{T}_{2}}={{227}^{o}}C=500K\] \[{{K}_{2}}=?\] We have. \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}}\] \[\Rightarrow \] \[{{K}_{2}}=\frac{{{T}_{1}}}{{{T}_{2}}}\times {{K}_{1}}=\frac{500}{300}\times 6.21\times {{10}^{-21}}\] \[=10.35\times {{10}^{-21}}J\]
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