Thermal Conductivity - Estimate Temperature

[unscientific]

Homework Statement

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

Homework Equations

The Attempt at a Solution

The heat is conducted through a thickness of 2.5mm, with a temperature difference of 5^oC. 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!(-110^oC)

 

[BvU]

You seem to think the 5^oC 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 $$J = \sigma \left ( T_{\rm case}^4 - T_{\rm environment}^4 \right )$$

 

[unscientific]

You seem to think the 5^oC 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 $$J = \sigma \left ( T_{\rm case}^4 - T_{\rm environment}^4 \right )$$

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.