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NEET Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Mock Test - Thermal Properties of Matter

  • question_answer
    The specific heat of a substance varies with temperature \[t({}^\circ Q)\]as \[c=0.20+0.14t+0.23{{t}^{2}}\](cal/g/ C) The heat required to raise the temperature of 2 g of substance from \[5{}^\circ C\]to \[15{}^\circ C\]will be

    A) 24 cal

    B) 56 cal

    C) 82 cal  

    D) 100 cal

    Correct Answer: C

    Solution :

    [c] Heat required to raise the temperature of m grams of substance by dT is given as \[dQ=mc\,dT\Rightarrow Q=\int{mcdT}\] Therefore, to raise the temperature of 2g of substance from \[5{}^\circ C\]to \[15{}^\circ C\] \[Q=\int\limits_{5}^{15}{2\times (0.2+0.14t+0.023{{t}^{2}})dT}\] \[=2\times {{\left[ 0.2t+\frac{0.14{{t}^{2}}}{2}+\frac{0.023{{t}^{3}}}{3} \right]}_{5}}^{15}=82cal\]


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