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Question

Four identical rods AB, CD ,CF and DE are connected as shown in figure. The length, cross-sectional area and thermal conductivity of each rod are L, A, K respectively. The ends A, E, F are maintained at temperature T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, calculate the temperature at B [CB=BD].
(Consider T3 as higher temperature)


A
T1+T2+T33
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B
2T1+3T2+5T35
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C
3T1+2T2+2T37
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D
T1+2T2+3T35
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Solution

The correct option is C 3T1+2T2+2T37
Heat flow in the fiven system can be represented by following diagram


Let the temperature at B be x
In steady state ,
(Qt)3=(Qt)1+(Qt)2
(T3x)(3l2KA)=xT1lKA+(xT2)3l2KA [K and A gets cancelled]
T3x=32(xT1)+(xT2)
T3+T2+32T1=x+32x+x
2(T3+T2)+3T1=7x
Temperature at B is x=3T1+2T2+2T37

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