# Simple Explaination of Temperature Difference

1. Aug 6, 2013

### recreated

This is not a homework question but a simple equation I want to make clear.

If temperature of gas on one side of a thin wall with negligible thickness is 20 decs c and on the other is 0 degs c how do you determine the temp. of the wall? Is it possible or do you need more information about the material of the wall?

Thank you,

2. Aug 6, 2013

### Aero51

You need to define the properties of the wall, most basically the conduction coefficient and thickness.

3. Aug 6, 2013

### 256bits

The wall is not the problem. The temperature gradient within a wall should follow be a linear relationship from one wall edge to the edge for a homogenous material and of suitable thickness.

But since your wall is thin, you could make a simple assumption that the wall temperature to be even across its width. You would also assume the temperature of the wall to be halfway between the two gas temperatures, and that the convection ( which it would be in most cases ) on either side is the predominate factor in determination of the heat flow.

If the amount of heat transfer by convection ( coeficient ) on either side of of wall is not the same, then the wall temperature will lean to towards the temperature of the hotter gas or the cooler gas.

Radiation could also be a factor if one side of the wall is facing a surface of different temperature than your gas. Your wall temperature could actually then be higher or lower than either temperature(s) of your gas(es).

4. Aug 6, 2013

### recreated

256bits, I know it is a simple assumption to make that the wall temp. is half way between t1 and t2, but what theory is it based on do you know? As I want to read more into it and find it hard to find where to start.

5. Aug 6, 2013

### 256bits

Fourier Law of Heat Conduction is linear.

See
http://www.chemeurope.com/en/encyclopedia/Heat_conduction.html
for the formula
For conduction, the heat flow is directly proportional to the surface area, directly proportional to the temperature difference, and indirectly proportional to the thickness.