# Thermal Equilibrium

Hello,

What "path" do objects take to reach thermal equilibrium? Does heat from a hot part sitting in room temperature air like to travel through the most thermally conductive portions? My thought is that it is similar to current in a circuit taking the path of least resistance (where the most thermally conductive portions of a part offer the least "resistance" to reaching thermal equilibrium).

## Answers and Replies

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DEvens
Gold Member
Heat can travel through several processes.

One is conduction. This means a thermally conductive material allows heat to travel through itself. Different materials have very different thermal conductivities. But heat will try to go through every path. Keeping the electric circuit idea, it is somewhat similar to having several paths with very large resistances. The current will go through them to different degrees. However, an electric circuit model is only helpful to some degree. Heat is conducted by diffusion according to Fick's second law.

http://en.wikipedia.org/wiki/Fick's_laws_of_diffusion

Another method is convection. In this case, heating a material changes its properties, most often causing it to expand. Then the change in density causes buoyancy induced flow. This can be an important process in a variety of situations. It's part of what insulating your attic is about when you want to save on heating bills. An open air space will allow convection. An air space filled with some material with a lot of air pockets will resist this.

Another method is thermal radiation. This is usually not important until you get to temperatures of at least a few 100 C. Though if other methods are cut off (say by isolating an object in vacuum) then radiation could be the dominant method.

I seem to have the idea I'm forgetting one. But I'm forgetting it so...

Anyway, each of these is strongly affected by the details of the materials involved and the temperatures involved.

AkshayPitt
Merlin3189
Homework Helper
Gold Member
Hello,

What "path" do objects take to reach thermal equilibrium? ... My thought is that it is similar to current in a circuit taking the path of least resistance ....
Any and all paths, similar to current.
But note, current does not take the path of least resistance: it too takes any and all paths. If there were only two paths and one had twice the resistance of the other, then current would flow by both paths, but twice as much by the lower resistance path as by the higher resistance path.
Heat would pass similarly by both paths with twice as much heat flowing through the lower thermal resistance path as through the higher thermal resistance path.
Even if the ratio of resistances is 1:1000000 then current or heat still flows via both paths in inverse proportion to the resistance of that path.

Edit- just seen the #2 post and should say that I was only considering conduction, though heat will still travel by all paths, but the proportion will not be based on thermal conductivity for radiation or convection.

AkshayPitt
So assuming only conduction, heat will travel proportionately based on thermal conductivity (higher thermal conductivity means more heat traveling via that path).

Thanks for your responses!