Question

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 temperture difference between the ends of other diagonal will be
(where $l$ is the length of each rod)

• A. $0^{\circ }C$
• B. $\frac{100}{l}{}^{\circ }C$
• C. $\frac{100^{\circ }}{2l}C$
• D. $100^{\circ }C$

Answer 1

Answer: (A)

Suppose temperature difference between $A$ and $B$ is $100^{\circ }C$ and ${\theta }_A>{\theta }_B$

Heat current will flow from $A$ to $B$ via path $ACB$ and $ADB$.
Since all the rod are identical, so, $(\Delta \theta {)}_{AC}=(\Delta \theta {)}_{AD}$
(Because heat current $H=\frac{\Delta \theta }{R}$; 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.