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

  • question_answer
    A sphere of density p, specific heat capacity c and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to

    A) \[\frac{c}{{{r}^{3}}\rho }\]

    B) \[\frac{1}{{{r}^{3}}\rho c}\]

    C) \[3{{r}^{3}}\rho c\]

    D) \[\frac{1}{r\rho c}\]

    Correct Answer: D

    Solution :

    [d] \[\left[ \frac{-dT}{dr} \right]=\frac{A}{mc}\left[ T-{{T}_{0}} \right]=\frac{4\pi {{r}^{2}}}{\rho \times \frac{4}{3}\pi {{r}^{3}}c}\left[ T-{{T}_{0}} \right]\] \[\therefore \left[ \frac{-dT}{dr} \right]\propto \frac{1}{\rho rc}\]


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