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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 ........ $^oC$
$0$
$\frac{{100}}{l}$
$\frac{{100}}{{2l}}$
$100$
Solution
(a) Suppose temperature difference between $A$ and $B$ is $100°C$ 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.)
==> ${\theta _A} – {\theta _C} = {\theta _A} – {\theta _D}$ ==> ${\theta _C} = {\theta _D}$
i.e. temperature difference between $C$ and $D$ will be zero.
