Two rods of lengths ℓ and 2ℓ, with thermal conductivities 2K and K respectively, are connected end to end. If their cross-sectional areas are equal, find the equivalent thermal conductivity of the system in units of K.
Physics · Mixed Chapter
JEE Main Practice

Question

Two rods of lengths ℓ and 2ℓ, with thermal conductivities 2K and K respectively, are connected end to end. If their cross-sectional areas are equal, find the equivalent thermal conductivity of the system in units of K.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Thermal resistances are R₁ = ℓ/(2KA) and R₂ = 2ℓ/(KA). Step 2: Combined resistance R = R₁ + R₂ = (ℓ/(KA))(½ + 2) = 5ℓ/(2KA). Step 3: Total length is 3ℓ; by definition R = 3ℓ/(Kₑff A). Step 4: Equate: 3ℓ/(Kₑff A) = 5ℓ/(2KA). Step 5: Kₑff = (6/5)K = 1.2K. Final answer in units of K: 1.2.