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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 8

  • question_answer
    A thermally insulated piece of metal is heated under atmospheric pressure by the source providing constant power P, due to this its absolute temperature depends on time as  \[T\left( t \right)={{T}_{0}}{{\left[ 1+K\left( t-{{t}_{0}} \right) \right]}^{1/4}}\]. Here K, \[{{T}_{0}}\] and \[{{t}_{0}}\] are constants. Then the heat capacity \[{{C}_{p}}(T)\] can be given by

    A) \[\frac{4P}{K{{T}_{0}}}\]        

    B) \[\frac{4P{{T}^{3}}}{KT_{0}^{4}}\]

    C) \[\frac{2P{{T}^{3}}}{KT_{0}^{4}}\] 

    D)  \[\frac{2P}{K{{T}_{0}}}\]

    Correct Answer: B

    Solution :

    [b] \[dQ=Pdt\] \[{{C}_{p}}=\frac{P}{\left( \frac{dT}{dt} \right)}=\frac{P}{\frac{d}{dt}\left[ {{T}_{0}}\{1+K{{(t-{{t}_{0}}\}}^{1/4}} \right]}=\frac{4P{{T}^{3}}}{KT_{0}^{4}}\]


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