A 3 mm diameter and 5 m long copper wire is insu- lated using a 2 mm thick plastic cover whose thermal con- ductivity is `K = 0.15 Wm^(-1)K^(-1)`. The wire has a potential difference of 10 V between its ends and the current through it is 8A. The outer surface of the wire is at `30^(@)C`. Neglect convection.
(i) Calculate the temperature at the interface of the wire and the plastic cover.
(ii) Determine whether doubling the thickness of the plastic cover will increase or decrease the interface temperature. [Given `ln(2.33)=0.85`]

Answer

(i) `44.4^(@)C` (ii) increase