NEET 2025, Physics Q19: Heat Transfer

NEET2025Physics

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:

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

Solution

In steady state, the heat current through each rod is equal: $\frac{2 K A ( 3 T - T _{1} )}{L} = \frac{K A ( T _{1} - T _{2} )}{L} = \frac{2 K A ( T _{2} - T )}{L}$ .

From the first equality: $2 (3 T - T_{1}) = T_{1} - T_{2} \Rightarrow 6 T - 2 T_{1} = T_{1} - T_{2} \Rightarrow 6 T + T_{2} = 3 T_{1}$ . ...(1)

From the second equality: $T_{1} - T_{2} = 2 (T_{2} - T) \Rightarrow T_{1} = 3 T_{2} - 2 T$ , i.e. $2 T - 3 T_{2} = - T_{1}$ . ...(2)

From (1) $3 T_{1} - T_{2} = 6 T$ ;
From (2) $T_{1} - 3 T_{2} = - 2 T$ . Solving: $10 T_{2} = 6 T_{1} \Rightarrow T_{1} / T_{2} = 5/3$ .

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NEET 2025, Physics Q19: Heat Transfer

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