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JEE Main & Advanced AIEEE Solved Paper-2011

  • question_answer
    Three perfect gases at absolute temperatures \[{{T}_{1}},{{T}_{2}}\] and \[{{T}_{3}}\] are mixed. The masses of molecules are \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] and the number of molecules are \[{{n}_{1}},{{n}_{2}}\] and \[{{n}_{3}}\] respectively. Assuming no loss of energy, the final temperature of the mixture is   AIEEE  Solved  Paper-2011

    A)  \[\frac{n_{1}^{2}T_{1}^{2}+n_{2}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]  

    B)  \[\frac{{{T}_{1}}+{{T}_{2}}+{{T}_{3}}}{3}\]

    C)  \[\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}\]

    D)  \[\frac{{{n}_{1}}T_{1}^{2}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]

    Correct Answer: C

    Solution :

    \[U=\frac{\frac{{{n}_{1}}}{N}{{T}_{1}}+\frac{{{n}_{2}}}{N}{{T}_{2}}+\frac{{{n}_{3}}}{N}{{T}_{3}}}{\frac{{{n}_{1}}}{N}+\frac{{{n}_{2}}}{N}+\frac{{{n}_{3}}}{N}}\] \[=\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}\]


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