J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The molecules in an ideal gas at \[{{27}^{o}}C\]have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?                                     

    A)  \[{{54}^{o}}C\]             

    B)  \[{{327}^{o}}C\]                 

    C)  \[{{1200}^{o}}C\]          

    D)  \[{{927}^{o}}C\]                

    Correct Answer: D

    Solution :

    Mean velocity of gas molecules \[v=\sqrt{\frac{8RT}{\pi T}}\] \[v\propto \sqrt{T}\] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{300}{{{T}_{2}}}}\] \[\frac{{{v}_{1}}}{2{{v}_{1}}}=\sqrt{\frac{300}{{{T}_{2}}}}\] \[\frac{1}{4}=\frac{300}{{{T}_{2}}}\] \[{{T}_{2}}=1200\,K=1200-273\] \[={{927}^{o}}C\]


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