ThermodynamicsHard

Question

A cylinder of radius R made of a material of material of thermal conductivity K2 is surrounded by cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective conductivity of the system is

Options

A.K1 + K2
B.K1K2 / (K1 + K2)
C.(K1 + 3K2) / 4
D.(3K1 + K2) / 4

Solution

        
Let R1 and R2 be the thermal resistance of inner and outer portions. Since, temperature difference at both ends is same, the resistances are in parallel. Hence,
      
∴       
∴       
∴ Correct option is (c).

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