# Thermal Conductivity - Estimate Temperature

1. Apr 29, 2014

### unscientific

1. The problem statement, all variables and given/known data

Given an insulating case outer surface at 25C, radiates heat to surroundings at 20C. Find temperature inner surface.

2. Relevant equations

3. The attempt at a solution

The heat is conducted through a thickness of 2.5mm, with a temperature difference of 5oC. Thus $\frac{\partial T}{\partial z} = 2000$. Using $k = 0.02$:

We have a value for the flux:

$$J = k\frac{\partial T}{\partial z} = 40$$

Using Stefan's Law:

$$J = \sigma T^4$$

We get $T = 163K$, and boy that is one cold case!(-110oC)

2. May 1, 2014

### BvU

You seem to think the 5oC difference is between the iPod and the outside of the case.
Looks to me as if that temperature difference is to be calculated from the flux.
Stefan's law works two ways: 25 to 20 should be something like $$J = \sigma \left ( T_{\rm case}^4 - T_{\rm environment}^4 \right )$$

3. May 2, 2014

### unscientific

That's right, because $J$ is the net flux (caused by a temperature gradient). The answer turns out to be $26.8^o$, which looks right.