JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    A hot body placed in air is cooled according to Newton's law of cooling, the rate of decrease of temperature being k times the temperature difference from the surroundings. Starting from \[t=0,\]find the time in which the body will lose half the maximum heat it can lose.

    A) \[\frac{1}{k}\]                    

    B) \[\frac{In\,\,2}{k}\]      

    C) \[\frac{1}{2k}\]                 

    D) None of these

    Correct Answer: B

    Solution :

    [b] Max. heat loss for temperature change \[={{T}_{b}}-{{T}_{s}}\] \[\frac{dT}{dt}=-k(T-{{T}_{s}})\] \[\int{\frac{dT}{T-{{T}_{s}}}}=-\int{k\,\,dt}\] In   \[[T-{{T}_{s}}]_{i}^{{{T}_{s}}}=-kt\] In   \[[\frac{{{T}_{f}}-{{T}_{s}}}{{{T}_{i}}-{{T}_{s}}}]=-kt\] \[-In\,\,2=-kt\] \[t=\frac{In\,2}{k}\]       

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