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Question

Three rods of same length and area of cross-section but of thermal conductivities K,2K and 3K are connected in series in the same order. The free end of the first rod is at 0C and the free end of the third rod is at 55C. Instead state, the temperature difference across the middle rod is:-

A
15C
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B
30C
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C
10C
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D
25C
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Solution

The correct option is A 15C
1keq=1k1+1k2+1k3 [ rods are in series ]
1keq=1k+12k+13k
1keq=6+3+26k
keq=6k11
So, Q=A(6k11)(550)2
=3×211×55Akl=OAkl
Let the temp difference across 2k rod be T, then
Q=A(2K)lT
30Akl=2Akl5
T=15oC
Option A is correct.


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