A l = 2 m long wire of resistance R = 4 ohms and diameter d = 0.64 mm is coated with plastic of thickness Δ d = 0.06 mm. When a current of I = 5 A flows through the wire, find the temperature differen

Question

A l = 2 m long wire of resistance R = 4 ohms and diameter d = 0.64 mm is coated with plastic of thickness Δ d = 0.06 mm. When a current of I = 5 A flows through the wire, find the temperature difference across the plastic insulation in steady state. Thermal conductivity of plastic is k = 0.16 × 1 0 − 2 cal/s cm °C.

TestHub · Accepted Answer

Power = I 2 R = 100 W flows radially through the plastic cylinder, r 1 ​ = 0.32 mm, r 2 ​ = 0.38 mm. k = 0.16 × 1 0 − 2 × 4.2 × 100 = 0.672 W m⁻¹K⁻¹. Δ T = 2 πk L P ln ( r 2 ​ / r 1 ​ ) ​ = 2 π × 0.672 × 2 100 × 0.1719 ​ = 2.04 ∘ C.

Physics - Heat & Thermo Question with Solution | TestHub

Doubts & Discussion