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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Self Evaluation Test - Thermal Properties of Matter

  • question_answer
    Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are \[{{\operatorname{K}}_{1}} and {{K}_{2}}\]. The thermal conductivity of the composite rod will be :

    A) \[\frac{3({{K}_{1}}+{{K}_{2}})}{2}\]  

    B)        \[{{K}_{1}}+{{K}_{2}}\]

    C) \[2\left( {{K}_{1}}+{{K}_{2}} \right)\]              

    D) \[\frac{{{K}_{1}}+{{K}_{2}}}{2}\]

    Correct Answer: D

    Solution :

    [d] Heat current \[\operatorname{H}= {{H}_{1}}+{{H}_{2}}\] \[=\frac{{{K}_{1}}A\left( {{T}_{1}}-{{T}_{2}} \right)}{d}+\frac{{{K}_{2}}A\left( {{T}_{1}}-{{T}_{2}} \right)}{d}\] \[=\frac{{{K}_{EQ}}2A\left( {{T}_{1}}-{{T}_{2}} \right)}{d}+\frac{A\left( {{T}_{1}}-{{T}_{2}} \right)}{d}\left[ {{K}_{1}}+{{K}_{2}} \right]\] Hence equivalent thermal conductivities for two rods of equal area is given by \[{{K}_{EQ}}=\frac{{{k}_{1}}+{{k}_{2}}}{2}\]


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