ThermodynamicsHard

Question

Three rods made of the same material and having the same cross-section been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0o C and 90o C respectively. The temperature of junction of the three rods will be
              

Options

A.45o C
B.60o C
C.30o C
D.20o C

Solution

         
Let θ be the temperature of the junction (say B). Thermal resistanceof all the three rods is equal. Rate of heat flow through AB+ Rate of heat flow through CB = rate of heat flow through BD
∴
Here, R = Thermal resistance
∴      3θ = 180o
or       θ = 60o C.
(H) =
where, R =
K = Thermal conductivity of rod.
This is similar to the current flow through a resistance (R) where cirrent (i) = Rate of flow of charge

Here, R = , where σ = Electrical conductivity.

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