JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    Same quantity of ice is filled in each of the two metal containers P and Q having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in P melts completes is Rune \[{{t}_{1}}\] whereas in Q takes a time \[{{t}_{2}}\]. The ratio of thermal conductivities of the materials of P and Q is :

    A)  \[{{t}_{2}}:{{t}_{1}}\]                                   

    B)  \[{{t}_{1}}:{{t}_{2}}\]

    C)  \[{{t}_{1}}^{2}:{{t}_{2}}^{2}\]                              

    D)  \[{{t}_{2}}^{2}:{{t}_{1}}^{2}\]

    Correct Answer: A

    Solution :

    Relation between temperature gradient (TG)and thermal conductivity (K) So, \[d\frac{\theta }{dt}=-KAd\frac{\theta }{dx}\,=-KA\,\times (TG)\] i.e., \[t\propto \,\frac{1}{K}\,\,\,\,\,\,or\,\,\,\,K\propto \,\frac{1}{t}\] \[{{K}_{1}}\propto \,\frac{1}{{{t}_{1}}}\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,{{K}_{2}}\propto \,\frac{1}{{{t}_{2}}}\] From eqs. (i) and (ii), we get \[\frac{{{K}_{1}}}{{{K}_{2}}}\,=\frac{1/{{t}_{1}}}{1/{{t}_{2}}}\] \[{{K}_{1}}:{{K}_{2}}\,={{t}_{2}}:{{t}_{1}}\]

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