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Question

Three rods made of the same material and having the same cross-section have been joined as shown in figure. Each rod is of the same length. The left and right ends are kept at 0C and 90C respectively. the temperature of the junction of the three rods will be.



Solution

The correct option is B


Let A and l be the area of cross-section and the length of each rod. If k is the coefficient of thermal conductivity and tC the temperature of the junction O, then the rates at which heat energy enters O from rods A and B are figure.

QA=kA(90t)land QB=kA(90t)l

The rate at which heat energy flows in rod C is

Qc=kA(t0)l

In the steady state, rate at which heat energy enters O = rate at which heat energy leaves O, i.e.

QA+QB=Qcor  kA(90t)l+kA(90t)l=kA(t1)l

or           (90 – t) + (90 – t) = t

or            3t = 180 or t = 60C. Hence the correct is (b)

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