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

  • question_answer
    A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length I- each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at \[100{}^\circ C\]band that of steel at \[9{}^\circ C\]then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)                 

    A) \[99{}^\circ C\]            

    B)        \[59{}^\circ C\]

    C) \[19{}^\circ C\]                        

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

    Correct Answer: A

    Solution :

    [a] From formula temperature of junction; \[\theta =\frac{{{k}_{copper}}{{\theta }_{copper}}{{l}_{steel}}\text{+}{{\text{K}}_{steel}}{{\theta }_{steel}}{{l}_{copper}}}{{{K}_{copper}}{{l}_{steel}}+{{k}_{steel}}{{l}_{copper}}}\] \[=\frac{9k\times 100\times \frac{L}{2}+k\times 0\times \frac{L}{2}}{9k\times \frac{L}{2}+k\times \frac{L}{2}}=\frac{\frac{900}{2}kL}{\frac{10kL}{2}}={{90}^{\operatorname{o}}}C\]


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