A) \[273\div 16\text{ }K\]
B) \[~273\times 8\,K\]
C) \[273\div 32K\]
D) \[273\times 4\,K\]
Correct Answer: A
Solution :
Key Idea: \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] For \[{{O}_{2}}\] \[T=273K,\,M=32\] \[\therefore \] \[{{v}_{rms}}({{O}_{2}})=\sqrt{\frac{3R\times 273}{32}}\] ?(i) For \[{{H}_{2}}\]\[T=?\,M=2\] \[{{v}_{rms}}\,{{H}_{2}}=\sqrt{\frac{3R\times T}{2}}\] Given \[{{v}_{rms}}{{O}_{2}}={{v}_{rms}}\,{{H}_{2}}\] \[\therefore \] \[\sqrt{\frac{3R\times 273}{32}}=\sqrt{\frac{3R\times T}{2}}\] or \[\frac{273}{32}=\frac{T}{2}\] \[\therefore \] \[T=\frac{273\times 2}{32}=\frac{273}{16}K\]
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