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 0∘C and 90∘C 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 t∘C the temperature of the junction O, then the rates at which heat energy enters O from rods A and B are figure. QA=kA(90−t)land QB=kA(90−t)l The rate at which heat energy flows in rod C is Qc=kA(t−0)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(90−t)l+kA(90−t)l=kA(t−1)l or           (90 – t) + (90 – t) = t or            3t = 180 or t = 60∘C. Hence the correct is (b)

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