LeChatelier's Principle

Another important set of thermodynamics concepts fall under the category of LeChatelier's principle. It is fundamentally an easy idea, but for some reason it is taught in fairly confusing ways.

The formal statement of LeChatelier's principle is something like this:

``If a body at equilibrium is disturbed by changing one of its environment's variables, then the body's internal variables will change so as to mitigate the change in environment.''

This is a pretty confusing statement for something that is fairly easy to understand. Perhaps, the following statement is easier? ``If a stimulus would produce an effect of magnitude 1 in a material that is constrained not to change its internal degrees of freedom, then an unconstrained material would have a response that is less than or equal to magnitude 1.'' No, not better? Oh, well.

Also, I've never found a good proof of this which leads to any additional physical enlightenment, so I won't disenlighten you by giving one (if you want to get confused, see the discussion by Landau and Lifshitz, Section 2.2; it is the best proof that I know of).

I think it best to give a few examples.

1. If the pressure is increased, the system will find an equilibrium that decreases its volume.

   Remember our friendly ideal gas reaction:

   $$\input{equations/16-3A}$$ (21-11)

   
   

   If we increase pressure, will the composition favor the reactants or products?

   $$\input{equations/16-3B}$$ (21-12)

   
   

   
   

   $$\input{equations/16-3C}$$ (21-13)

   
   

   
   

2. A crack in a material:

   Figure 21-2: A crack in a material--what is the response of the material to an increased load?

   

   If the load is increased, the stiffness decreases by propagating the crack.

3. Suppose that each homework set I give you is about the same amount of work. You spend an average of $\ensuremath{\langle h \rangle}$ hours per problem. If I were to assign ten times as many problems this week $\ensuremath{\langle h \rangle}$ would tend to decrease.

One last note about LeChatelier's principle: it pertains only for small changes applied to an equilibrium system that is not near a condition of instability. If a system is not in equilibrium, or the change in the external conditions are very great, then we should not expect LeChatelier's principle to apply.

As an example, consider a house with the wind blowing past it. The wind blows the door shut which seems like a violation of LeChatelier's Principle.

Figure 21-3: The stupid door doesn't care about LeChatelier's principle.

There is also the example of the ``Stupid Crack:''