A) \[100{}^\circ C\]
B) \[273{}^\circ C\]
C) \[173\text{ }K\]
D) \[0{}^\circ C\]
Correct Answer: D
Solution :
\[\frac{{{v}_{He}}}{v{{H}_{2}}}=\frac{\sqrt{\frac{3R{{T}_{He}}}{{{M}_{He}}}}}{\sqrt{\frac{3RT{{H}_{2}}}{M{{H}_{2}}}}}=\sqrt{\frac{{{M}_{H2}}}{{{M}_{He}}}.\frac{{{T}_{He}}}{{{T}_{H2}}}}\] \[\frac{{{v}_{He}}}{{{v}_{H2}}}\sqrt{\frac{2}{4}\times \frac{{{T}_{He}}}{273}}\] \[\frac{5}{7}=\sqrt{\frac{{{T}_{He}}}{2\times 273}}\] \[\Rightarrow \] \[{{T}_{He}}=\frac{25\times 273\times 2}{49}\] \[\approx \text{278K=}{{\text{5}}^{\text{0}}}\text{C}\cong {{\text{0}}^{\text{0}}}\text{C}\]
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