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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is thrice that of C and half of that of A. The effective thermal conductivity of the system will be (\[{{K}_{A}}\]a is the thermal conductivity of rod A)

    A)  \[\frac{1}{3}{{K}_{A}}\]                               

    B)  \[3{{K}_{A}}\]

    C)  \[2{{K}_{A}}\]                  

    D)  \[\frac{2}{3}{{K}_{A}}\]

    Correct Answer: A

    Solution :

    A B C
    Given,   \[{{K}_{B}}={{K}_{A}}/2\] and        \[{{K}_{B}}=3{{K}_{c}}\] \[\therefore \]  \[{{K}_{C}}={{K}_{A}}/6\] Rods are in series form so                 \[\frac{L}{K}=\frac{{{l}_{1}}}{{{K}_{A}}}+\frac{{{l}_{2}}}{{{K}_{B}}}+\frac{{{l}_{3}}}{{{K}_{C}}}\]                                                 \[(\because \,l={{l}_{1}}={{l}_{2}}={{l}_{3}})\]                 \[\frac{3l}{K}=\frac{l}{{{K}_{A}}}+\frac{l}{{{K}_{A}}/2}+\frac{l}{{{K}_{A}}/6}\] or            \[\frac{3l}{K}=\frac{9l}{{{K}_{A}}}\] or            \[K=\frac{{{K}_{A}}}{3}\]


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