JEE Main & Advanced Physics Transmission of Heat Question Bank Conduction

  • question_answer
    The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio 1 : 2 are maintained  at the same temperature difference. If the rate of flow of heat in the larger rod is 4 \[4\ cal/\sec \], that in the shorter rod in \[cal/\sec \] will be [EAMCET 1986]

    A)            1    

    B)            2

    C)            8    

    D)            16

    Correct Answer: A

    Solution :

                       \[\frac{dQ}{dt}=\frac{K(\pi {{r}^{2}})d\theta }{dl}\]Þ \[\frac{{{\left( \frac{dQ}{dt} \right)}_{s}}}{{{\left( \frac{dQ}{dt} \right)}_{l}}}=\frac{{{K}_{s}}\times r_{s}^{2}\times {{l}_{l}}}{{{K}_{l}}\times r_{l}^{2}\times {{l}_{s}}}\]                   = \[\frac{1}{2}\times \frac{1}{4}\times \frac{2}{1}\]            Þ  \[{{\left( \frac{dQ}{dt} \right)}_{s}}=\frac{{{\left( \frac{dQ}{dt} \right)}_{l}}}{4}=\frac{4}{4}=1\]              


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