Question

Temperature difference of $120^{\circ}C$ is maintained between two ends of a uniform rod $AB$ of length $2L$. Another bent rod $PQ$, of same cross section as $AB$ and length $\frac{3L}{2}$ , is connected across $AB$ (See figure). In steady state, temperature difference between $P$ and $Q$ will be close to :

• A. $60^{\circ} C$
• B. $75^{\circ} C$
• C. $35^{\circ} C$
• D. $45^{\circ} C$

Answer 1

Answer: (D)

$45^{\circ} C$

Answer 2

$\frac{\Delta T}{R_{eq}} = I = \frac{\left(120\right)5}{8R} = \frac{120\times5}{8R}$

$\Delta T_{PQ} = \frac{120 \times5}{8R} \times\frac{3}{5}R = \frac{360}{8} = 45^{\circ}C$

$\text{Hence, the correct option is (D):}$ $45\degree\;C$