JEE Main & Advanced Physics Transmission of Heat Question Bank Conduction

  • question_answer
    Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B \[i.e.\] \[{{r}_{A}}=2{{r}_{B}}\]. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

    A)            \[{{K}_{A}}=4{{K}_{B}}\] 

    B)            \[{{K}_{A}}=2{{K}_{B}}\]

    C)            \[{{K}_{A}}={{K}_{B}}/2\]

    D)            \[{{K}_{A}}={{K}_{B}}/4\]

    Correct Answer: D

    Solution :

               \[\frac{Q}{t}=\frac{KA\Delta \theta }{l}\Rightarrow \frac{{{K}_{A}}}{{{K}_{B}}}=\frac{{{A}_{B}}}{{{A}_{A}}}={{\left( \frac{{{r}_{B}}}{{{r}_{B}}} \right)}^{2}}=\frac{1}{4}\Rightarrow {{K}_{A}}=\frac{{{K}_{B}}}{4}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner