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BHU PMT BHU PMT (Mains) Solved Paper-2010

  • question_answer
    If\[\Delta G=\Delta H-T\Delta S\]and\[\Delta G=\Delta H-T{{\left[ \frac{d(\Delta G)}{dT} \right]}_{p}},\] then variation of emf of a cell, E with temperature, T is given by

    A)  \[\frac{\Delta H}{nF}\]                 

    B)  \[\frac{\Delta G}{nF}\]

    C)   \[\frac{\Delta S}{nF}\]                                

    D) \[\frac{-\Delta S}{nF}\]

    Correct Answer: C

    Solution :

                     \[\Delta G=\Delta H-T\Delta S\] \[\Delta G=\Delta H+T{{\left[ \frac{d(\Delta G)}{dT} \right]}_{p}}\] On comparing the above two equations, we get                 \[\Delta S=\frac{-d(\Delta G)}{dT}\]                 \[\Delta S=\frac{-d(-FE)}{dT}\]                                                 \[[\because \Delta G=-nFE]\]                 \[\Delta S=\frac{+dnFE}{dT}\]                 \[=nF\frac{dE}{dt}\] \[\Rightarrow \]               \[\frac{dE}{dt}=\frac{\Delta S}{nF}\]


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