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 $0^{\circ }Cand{90}^{\circ }C$ respectively. the temperature of the junction of the three rods will be.

• A.
• B.
• C.
• D.

Answer 1

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 $t^{\circ }C$ the temperature of the junction O, then the rates at which heat energy enters O from rods A and B are figure.

$Q_A=\frac{kA(90-t)}{l}and{Q}_B=\frac{kA(90-t)}{l}$

The rate at which heat energy flows in rod C is

$Q_c=\frac{kA(t-0)}{l}$

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

$Q_A+Q_B=Q_{c}or\frac{kA(90-t)}{l}+\frac{kA(90-t)}{l}=\frac{kA(t-1)}{l}$

or (90 – t) + (90 – t) = t

or 3t = 180 or t = ${60}^{\circ }C$. Hence the correct is (b)