JEE Main & Advanced Physics Thermodynamical Processes Question Bank Topic Test - Thermodynamical Processes

  • question_answer
    The molar heat capacity of a certain substance varies with temperature according to the given equation, \[C=27.2+(4\times {{10}^{-3}})T.\] The heat necessary to change the temperature of 2 mol. of the substance from 300K to 700K is

    A) \[3.46\times {{10}^{4}}J\]

    B) \[2.33\times {{10}^{3}}J\]

    C) \[12\times {{10}^{5}}\]

    D) \[2.33\times {{10}^{4}}J\]

    Correct Answer: D

    Solution :

    [d] Initial temperature, \[{{T}_{i}}=300K;\] Final temperature, \[{{T}_{f}}=700K\]
    \[Q=\int\limits_{300}^{700}{nCdT=\int\limits_{300}^{700}{2\times (27.2+4\times {{10}^{-3}}\times T)dT}}\]
    \[=\left[ 54.4T+4\times {{10}^{-3}}{{T}^{2}} \right]_{300}^{700}=2.33\times {{10}^{4}}J\]

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