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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    A body with an initial temperature \[{{\theta }_{i}}\] is allowed to cool in a surrounding which is at a constant temperature of \[{{\theta }_{0}}({{\theta }_{0}}<{{\theta }_{i}})\]. Assume that Newton's law of cooling is obeyed. Let k = constant. The temperature of the body after time t is best expressed by (where B is integrating constant)

    A) \[({{\theta }_{i}}-{{\theta }_{0}}){{e}^{-kt}}\]        

    B) \[({{\theta }_{i}}-{{\theta }_{0}})\,\,In\,\,(kt)\]

    C) \[{{\theta }_{0}}+{{e}^{-kt/C}}\]      

    D) \[{{\theta }_{i}}{{e}^{-kt}}-{{\theta }_{0}}\]

    Correct Answer: C

    Solution :

      [c] \[-\frac{\theta t}{dt}=K(\theta -{{\theta }_{0}})\] \[\frac{dt}{\theta -{{\theta }_{0}}}=-Kdt\] \[\log \,\,(\theta -{{\theta }_{0}})=-Kt+C\] \[\theta -{{\theta }_{0}}={{e}^{-Kt/C}}\] \[\theta ={{\theta }_{0}}={{e}^{-Kt/C}}\]  


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