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 \[{{100}^{o}}C\], then the temperature difference between the ends of other diagonal will be [MP PET 1989; RPMT 2002]

A)            \[{{0}^{o}}C\]

B)            \[\frac{100}{l}{{\ }^{o}}C\]; where l is the length of each rod

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

D)            \[{{100}^{o}}C\]

Correct Answer: A

Solution :

                   Suppose temperature difference between A and B is 100°C and qA > qB Heat current will flow from A to B via path ACB and ADB. Since all the rod are identical so (Dq)AC =(Dq)AD (Because heat current \[H=\frac{\Delta \theta }{R};\]here R = same for all.) Þ \[{{\theta }_{A}}-{{\theta }_{C}}={{\theta }_{A}}-{{\theta }_{D}}\] Þ \[{{\theta }_{C}}={{\theta }_{D}}\] i.e. temperature difference between C and D will be zero.