Three rods made of the same material and having the same cross-section have been joined as shown in Fig. 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

detailed solution

Correct option is B

Let A and I 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 (Fig.)       QA=kA(90−t)land QB=kA(90−t)lThe rate at which heat energy flows in rod C isQC=kA(t−0)lIn the steady state, rate at which heat energy entersO = rate at which heat energy leaves O, i.e.or  QA+QB=QCor  kA(90−t)l+kA(90−t)l=kA(t−0)lor  (90−t)+(90−t)=tor  3t=180 or t=60∘C. Hence the correct choice is (b).