Three rods of same dimensions have thermal conductivities $3 K$ , $2 K$ ,and $K$ , with their ends at $100 ° C$ , $50 ° C$ and $0 ° C$ respectively. They are arranged as shown in the diagram. The temperature of the junction $J$ in steady-state is

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Let T = temperature of the junction J L = length and A = area of each rod Heat conducted in first rod = heat conducted by second rod + heat conducted by third rod 3 K A 100 - T L = 2 K A T - 50 L + A K T - 0 L 3 100 - T = 2 T - 50 + T 400 = 6 T T = 200 3 ° C

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