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JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission Of Heat

  • question_answer
    One day in a room a heater connected to supply maintained temperature \[20{}^\circ C\] when outside temperature was \[-20{}^\circ C\]. Another day with the same heater, in the same room, temperature was \[10{}^\circ C\] when outside temperature was \[-40{}^\circ C\]. If temperature of heater is same both the days. Find this value. (use \[\frac{dT}{dt}=k(T-{{T}_{0}})\] and k is same for both days).

    A) \[120{}^\circ C\]

    B) \[30{}^\circ C\]

    C) \[40{}^\circ C\]

    D) \[60{}^\circ C\]

    Correct Answer: D

    Solution :

    [d] \[mS\left( \frac{dT}{dt} \right)\,=\,ka\,A\,({{\theta }_{in}}-{{\theta }_{out}})\]
    at heater at the wall
    \[k\,(\theta -20)=k'\,A\,(20+20)\]
    \[k\,(\theta -10)=k'\,A\,(10+40)\]
    \[\frac{\theta -20}{\theta -10}=\frac{40}{50}\]
    \[5\theta -100=4\theta -4\theta \]
    \[\theta =60{}^\circ C\]


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