• # 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) $2.33\times {{10}^{4}}J$

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