JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Heat & Thermodynamics

Temperature difference of

12 0^{\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{3 L}{2}

, is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:

Answer: (A)

Solution

Model the rods as thermal resistors whose resistance is proportional to length. The bent rod

P Q

bridges the stretch of

A B

between its two contact points, so the two sit in parallel there, and in steady state the full

12 0^{\circ}

C drop distributes across the series-parallel network in proportion to the resistances. Carrying the lengths through that division, with

A B = 2 L

and

P Q = \frac{3 L}{2}

, places the temperature difference between

P

and

Q

at close to

120 \times \frac{3}{8} = 4 5^{\circ}

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option