Physics · Heat Transfer

NEET (UG) 2025 — Question 18

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2 K while that in the middle has thermal conductivity $K$ . The left end of the combination is maintained at temperature $3 T$ and the right end at $T$ . The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_{1}$ and that at the right junction is $T_{2}$ . The ratio $T_{1} / T_{2}$ is

Option A:
$\frac{3}{2}$
Option B:
$\frac{4}{3}$
Option C:
$\frac{5}{3}$
Correct
Option D:
$\frac{5}{4}$

Answer: C

Step-by-step solution

In steady state $\Rightarrow\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_{1}=\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_{2}=\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_{3}$

$\frac{2 \mathrm{KA}\left(3 \mathrm{~T}-\mathrm{T}_{1}\right)}{\mathrm{L}}=\frac{\mathrm{KA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{L}}=\frac{2 \mathrm{KA}\left(\mathrm{T}_{2}-\mathrm{T}\right)}{\mathrm{L}}$

$6 \mathrm{~T}-2 \mathrm{~T}_{1}=\mathrm{T}_{1}-\widehat{\mathrm{T}_{2}}=2 \mathrm{~T}_{2}-2 \mathrm{~T}$

$6 \mathrm{~T}-2 \mathrm{~T}_{1}=\mathrm{T}_{1}-\mathrm{T}_{2}$

6 \mathrm{~T}+\mathrm{T}_{2}=3 \mathrm{~T}_{1} …(1)

$\mathrm{T}_{1}-\mathrm{T}_{2}=2 \mathrm{~T}_{2}-2 \mathrm{~T}$

2 \mathrm{~T}-3 \mathrm{~T}_{2}=-\mathrm{T}_{1} …(2)

Multiply equation (2) By '3'

6 \mathrm{~T}-9 \mathrm{~T}_{2}=-3 \mathrm{~T}_{1} …(3)

Equation (1) - (3)

$10 \mathrm{~T}_{2}=6 \mathrm{~T}_{1}$

$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{5}{3}$

Answer key and solution verified before publishing.

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Exam: NEET (UG) 2025
Paper: 2025 paper
Subject: Physics
Chapter: Heat Transfer
Topic: Introductory Heat transfer by Conduction