# What´s the temperature at a given distance from a heat source?

1. Apr 5, 2014

### ccbaye

This is not a homework. My physics training feels like having taken place in another life, so please show mercy :)
I would like to know what´s the formula to calculate the temperature at a given distance from a candle. I found this:

Thermal Conductivity = heat × distance / (area × temperature gradient)

λ = Q × L / (A × ΔT)

So..say I want to know the temperature at 2 m from the candle..

temperature gradient = heat x 2m x area / thermal conductivity of the air ?

Then I just have to know how hot is my candle to get the temperature at 2 m from the candle ?

I f I am right, where do I get Q and A?

Thanks!

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

2. Relevant equations

3. The attempt at a solution

2. Apr 5, 2014

### Staff: Mentor

This does not work for multiple reasons:

Obviously, the temperature anywhere depends on the remaining environment. If I light a second candle directly at the point where you want to measure, the temperature will be higher. If I place a wall in between, the temperature will be lower.
You could assume you just have air and nothing else, and consider the equilibrium temperature. But then you still run into multiple other problems:

Heat is transported by conductance, convection and radiation. For the candle, the latter two dominate, conductance (where your formula comes from) is negligible. Convection is hard to model - you basically need a full model of your candle and the air around it.

Radiation is relatively easy to model - if you know how hot and large the fire of your candle is. But then you have to consider absorption of this radiation by your body, and blackbody emission of the same body. They happen with a bit different wavelengths, so different materials can get different temperatures there. You can assume your object is a perfect blackbody, this should give a reasonable approximation - but then you still need the temperature and its distribution and size of your flame.

To summarize: this is much more complicated than just plugging in numbers in a formula.
For a simple candle, I would not expect temperature changes in a distance of 2 meters.

3. Apr 5, 2014

### ccbaye

ok thanks mfb!

4. Apr 5, 2014

### ccbaye

One more thing, can I say that if the heat-conductivity is maintained constant in the environment, then the temperature gradient stemming from a heat-source will be linear?

5. Apr 5, 2014

### Staff: Mentor

If your setup consists of parallel plates...
A very small source will show a nonlinear temperature/distance relation, as the area of conductance increases with distance.

6. Apr 5, 2014

### Staff: Mentor

Reality check: linear gradient forever means temperatures below absolute zero once you get far enough.

7. Apr 5, 2014

### ccbaye

:) very interesting point.