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Question

Three rods of same dimensions have thermal conductivity 3K,2K and K. They are arranged as show in the figure below. Then the temperature of the junction in steady state is ________.
714045_7810530ec3f34b56b80c8c5946baa96c.jpg

A
1003C
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B
2003C
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C
75C
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D
503C
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Solution

The correct option is C 2003C
Given: Three rods of same dimensions have thermal conductivity 3K,2K and K. They are arranged as show in the figure below.
To find the temperature of the junction in steady state
Solution:
The amount of heat transmitted from one end to other end is
Q=KAT(t1t2)d
where T is the time, t1t2 is the temperature difference
Hence at the junction,
Q=Q1+Q23K(A)T(100t)d=2K(A)T(t50)d+KAT(t0)d
here t is the temperature of the junction
3(100t)=2(t50)+(t0)3003t=2t100+t6t=400t=4006=2003C
is the temperature of the junction in steady state

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