CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • 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)  \[{{75}^{o}}C\]                                

    B)  \[{{67}^{o}}C\]

    C)  \[{{25}^{o}}C\]                                

    D)  \[{{33}^{o}}C\]

    Correct Answer: A

    Solution :

    Temperature of interface                 \[\theta =\frac{{{K}_{1}}{{\theta }_{1}}{{l}_{2}}+{{K}_{2}}{{\theta }_{2}}{{l}_{1}}}{{{K}_{1}}{{l}_{2}}+{{K}_{2}}{{l}_{1}}}\] It is given that \[{{K}_{Cu}}=9{{K}_{s}}\]. So, if \[{{K}_{s}}={{K}_{1}}=K\], then \[{{K}_{Cu}}={{K}_{2}}=9K\] \[\Rightarrow \]               \[\theta =\frac{9K\times 100\times 6+K\times 0\times 18}{9K\times 6+K\times 18}\]                 \[=\frac{5400\,K}{72\,K}={{75}^{o}}C\]


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