question_answer

Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is\[100{}^\circ C\], then the temperature difference between the ends of other diagonal will be (where / is the length of each rod)

A) \[0{}^\circ C\]

B) \[\frac{100}{l}{}^\circ C\]

C) \[\frac{100}{2l}{}^\circ C\]

D) \[100{}^\circ C\]

Correct Answer: A

Solution :

[a] Suppose temperature difference between A and B is \[100{}^\circ C\] and \[{{\theta }_{\Alpha }} > {{\theta }_{B}}\] Heat current will flow from A to B via path ACB and ADB. Since all therod are identical, so,\[{{(\Delta \theta )}_{Ac}}={{(\Delta \theta )}_{AD}}\]  (Because heat current \[\operatorname{H}=\frac{\Delta \theta }{R};\] here R = same for all) \[\Rightarrow {{\theta }_{A}}-{{\theta }_{C}}={{\theta }_{A}}-{{\theta }_{D}}\Rightarrow {{\theta }_{C}}={{\theta }_{D}}\] i.e., temperature difference between C and D will be zero.