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