NEET2016PhysicsThermal Properties of MatterActual
A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a radius R and is made of material of thermal conductivity K , whereas a cylindrical shell has inner radius R and outer radius 2 R and is made of material of thermal conductivity twice as that of cylinder. Assuming the system in steady state and negligible heat loss across the cylindrical surface, find the effective thermal conductivity o
Options
- A3 K
- B2 3 K
- C7 K 4
- D5 K 4
Correct answer
C. 7 K 4
Step-by-step solution
R₁= L K₁ R^2 and aligned R₂ & = L K₂ (4 R^2- R^2 ) = L 3 K₂ R^2 R_ eq & = L K_ eq 4 R^2 aligned R₁ and R₂ are in parallel. 1 R_ eq = 1 R₁ + 1 R₂ aligned & & 4 R^2 K_ eq L & = R^2 K₁ L + 3 R^2 K₂ L & & 4 K_ eq & =K₁+3 K₂ aligned On putting values of K₁ and K₂ , we get aligned 4 K_ eq & =K+3(2 K) [ K₁=K, K₂=2 K ] K_ eq & = K+6 K 4 = 7 K 4 aligned