Q 11-10-029NEETJEE MainEAMCET 2009 (Engineering)Medium
Three rods of the same dimensions have thermal conductivities $3K$, $2K$ and $K$. They are joined at one common point. The free end of the $3K$ rod is at $100°$C, that of the $2K$ rod at $50°$C and that of the $K$ rod at $0°$C. The temperature of the junction in the steady state is
Answer: (A) $\dfrac{200}{3}°$C
Concept. In the steady state the net heat flowing into the junction is zero; same dimensions, so each current $\propto K\times$ (temperature difference).
Step 1. Balance.
$$3K(100 - \theta) + 2K(50 - \theta) + K(0 - \theta) = 0$$
Step 2. Solve. $400 - 6\theta = 0 \Rightarrow \theta = \dfrac{200}{3}°$C.
Answer. $\dfrac{200}{3}°$C (Option A).
Solution by Sreeraj P, M.Sc Physics