JEE Main & Advanced Physics Transmission of Heat Question Bank Critical Thinking

  • question_answer
    One end of a copper rod of length \[1.0\ m\] and area of cross-section \[{{10}^{-3}}\] is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is \[92\ cal/m\text{-}s{{\text{-}}^{o}}C\] and the latent heat of ice is \[8\times {{10}^{4}}cal/kg\], then the amount of ice which will melt in one minute is [MNR 1994]

    A)            \[9.2\times {{10}^{-3}}kg\]    

    B)            \[8\times {{10}^{-3}}kg\]

    C)            \[6.9\times {{10}^{-3}}kg\]    

    D)            \[5.4\times {{10}^{-3}}kg\]

    Correct Answer: C

    Solution :

                       Heat transferred in one minute is utilised in melting the  ice so, \[\frac{KA({{\theta }_{1}}-{{\theta }_{2}})t}{l}=m\times L\]            \[\Rightarrow m=\frac{{{10}^{-3}}\times 92\times (100-0)\times 60}{1\times 8\times {{10}^{4}}}=6.9\times {{10}^{-3}}kg\]


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