Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A composite slab is formed by pasting together two plates of thicknesses L₁ and L₂ and thermal conductivities K₁ and K₂ . The slabs possess equal cross-sectional area. Determine the equivalent conductivity of the composite slab.
Options
- AK₁ L₂ + K₂ L₁ L₁ + L₂
- BK₁ K₂ (L₁ + L₂) L₁ K₁ + L₂ K₂
- CK₁ L₁ + K₂ L₂ L₁ + L₂
- DK₁ K₂ (L₁ + L₂) L₁ K₂ + L₂ K₁
Correct answer
D. K₁ K₂ (L₁ + L₂) L₁ K₂ + L₂ K₁
Step-by-step solution
For a composite slab connected in series, the equivalent thermal resistance is the sum of the individual thermal resistances. R_ eq = R₁ + R₂ Using the formula for thermal resistance R = L KA , where A is the cross-sectional area: L₁ + L₂ K_ eq A = L₁ K₁ A + L₂ K₂ A L₁ + L₂ K_ eq = L₁ K₂ + L₂ K₁ K₁ K₂ K_ eq = K₁ K₂ (L₁ + L₂) L₁ K₂ + L₂ K₁