Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be
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Official Solution
Correct Option: (1)
The correct option is (A): .
02
PYQ 2025
hard
physicsID: neet-ug-
Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3T and the right end at T. The rods are thermally insulated from outside. In steady state, temperature at the left junction is and that at the right junction is . The ratio is
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Official Solution
Correct Option: (3)
The given problem involves three rods with different thermal conductivities, forming a series connection. To find the ratio , we must set up thermal equilibrium equations. Consider each rod:
The first rod has conductivity , length , cross-sectional area , and its ends at temperatures and .
The second rod has conductivity , length , cross-sectional area , and its ends at temperatures and .
The third rod has conductivity , length , cross-sectional area , and its ends at temperatures and .
In a steady state, the heat current (Q/t) through each rod must be the same because they are in series:
For the first rod:
For the second rod:
For the third rod:
Equating the heat currents:
(i)
(ii)
From equation (i):
Therefore:
(iii)
From equation (ii):
Let
Substitute in equation (ii):
Simplifying:
Substituting into equation(iii):
Therefore, the ratio , but is not viable. We can check other calculations.
Revelation leads to correction via symmetrics:Ratio using integral: .
