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Question

Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown in the figure, with their ends at 100C,50C and 0C. The temperature of their junction point is:


A
75C
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B
2003C
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C
40C
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D
1003C
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Solution

The correct option is B 2003C
Let temperature of the junction be θ. As there are no sources and sinks at the junction, we can say that:
Net heat entering the junction = Net heat leaving the junction
Assume the direction of heat flow as shown below:


Then,
H1=H2+H3
3K(100θ)=2K(θ50)+K(θ0)
300K+3Kθ100K+2Kθ+Kθ=0
6θ=400
θ=4006=2003C
Hence, our initial assumption is correct and option (b) is the correct answer.

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