RAJASTHAN PMT Rajasthan - PMT Solved Paper-2010

  • question_answer
    The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

    A) \[75{}^\circ C\]                                 

    B) \[67{}^\circ C\]

    C)  \[33{}^\circ C\]                

    D)         \[25{}^\circ C\]

    Correct Answer: A

    Solution :

    Temperature of interface                 \[\theta =\frac{{{K}_{1}}{{\theta }_{1}}{{l}_{2}}+{{K}_{2}}{{\theta }_{2}}{{l}_{2}}}{{{K}_{2}}{{l}_{1}}+{{K}_{1}}{{l}_{2}}}\] According to                 \[{{K}_{cu}}=9\,\,{{K}_{s}}\] Let          \[{{K}_{s}}={{K}_{2}}=K\] \[\therefore \]  \[{{K}_{cu}}=9K\]                 \[\theta =\frac{9K\times 100\times 6+K\times 0\times 18}{9K\times 6+K\times 18}\]                 \[\theta =\frac{5400K}{72K}={{75}^{o}}C\]


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