Q.
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
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a
45°C
b
60°C
c
30°C
d
20°C
answer is B.
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Detailed Solution
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).
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