Answer to Question #133338 in Physics for Pavan

Question

Calculate the temperature of a 4-in (0.1 m) piece of #12 copper wire at the end that is being heated by a 25-W (input power) soldering iron, and whose other end is clamped to a large metal vise (assume an infinite heat sink), if the ambient temperature is 25°C (77°F).

Answer 1

The thermal resistance of the copper wire:

$$\theta=\frac{L}{kA}=\frac{0.1}{(390)(3.31\cdot10^{-6})}=77.5\degree C$$

Then, rearranging the heat flow equation above yields (after assuming the heat energy actually transferred to the wire is around 10 W)

$$∆T = Pθ =(10)(77.5)=775\degree C$$

So the wire temperature at the hot end is

$$T_H=25+775=800\degree C$$