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

  • question_answer
    If two rods A and B of equal length L, and different areas of cross-section \[{{\operatorname{A}}_{1}}\]and\[{{A}_{2}}\]have one end each at temperature\[{{\operatorname{T}}_{1}}\]and \[{{T}_{2}}\], have equal rates of flow of heat, then

    A) \[{{A}_{1}}={{A}_{2}}\]

    B)  \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{K}_{1}}}{{{K}_{2}}}\]

    C) \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{K}_{2}}}{{{K}_{1}}}\]

    D) \[{{K}_{1}}={{K}_{2}}\]

    Correct Answer: C

    Solution :

    [c] \[\frac{\Delta {{Q}_{1}}}{\Delta t}=\frac{\Delta {{Q}_{2}}}{\Delta t}\] \[\Rightarrow {{K}_{1}}{{A}_{1}}\frac{{{T}_{1}}-{{T}_{2}}}{{{L}_{1}}}={{K}_{2}}{{A}_{2}}\frac{{{T}_{1}}-{{T}_{2}}}{{{L}_{2}}}\] \[\left( {{L}_{1}}={{L}_{2}} \right)\therefore \frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{K}_{2}}}{{{K}_{1}}}\]


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