JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission of Heat (3-5-21)

  • question_answer
    Two rods A and B are of equal lengths. Their ends are kept between the same temperature and their area of cross-sections are \[{{A}_{1}}\]and \[{{A}_{2}}\]and thermal conductivities \[{{K}_{1}}\] and \[{{K}_{2}}\]. The rate of heat transmission in the two rods will be equal, if

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

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

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

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

    Correct Answer: B

    Solution :

    \[{{\left( \frac{Q}{t} \right)}_{1}}=\frac{{{K}_{1}}{{A}_{1}}({{\theta }_{1}}-{{\theta }_{2}})}{l}\] and \[{{\left( \frac{Q}{t} \right)}_{2}}=\frac{{{K}_{2}}{{A}_{2}}({{\theta }_{1}}-{{\theta }_{2}})}{l}\] given \[{{\left( \frac{Q}{t} \right)}_{1}}={{\left( \frac{Q}{t} \right)}_{2}}\]\[\Rightarrow \] \[{{K}_{1}}{{A}_{1}}={{K}_{2}}{{A}_{2}}\]

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