Entropy and Endothermic Processes

[epsaliba]

I am a general chemistry student and I find thermodynamics fascinating. However, I have a hard time visualizing entropy. Can somebody please explain how an increase in entropy can make a process that is endothermic spontaneous? The typical demonstration of entropy that I have seen is on in which marbles are placed in beakers and the number of ways that they can be arranged. However, this only demonstrates an increase in entropy for a process in which ΔU=0. I was wondering if there is a good way to demonstrate how an increase in entropy can make something go against what its internal energy is telling it to do. I am familiar with most entropy equations, but I am looking for a description of what is actually going on. For example, the internal energy is equal to the sum of all of the kinetic energies of the particles in a system. If I had say three particles, how could I describe the entropy of those three particles? And how could I cause them to increase there internal energy simply by increasing the entropy? I seems to me that my lack of knowledge of the location and velocity of the particles doesn't have anything to do with whether they have the energy to do something or not. Thanks

 

[Borek]

Evaporation.

Imagine large, empty, thermally isolated tank. Add some water, wait. Tank gets colder, water evaporates.

 

[epsaliba]

Why though? I know that that would happen because the second law is one of those "it would be weird if it wasnt that way." My issue, I think, is how does the organization of the energy in a system drive the system against what it energetically wants to do. For example, how does an endothermic chemical reaction proceed as long as the entropy increases?

 

[Borek]

It is not entropy change and not enthalpy change that are driving force, but the change in Gibbs free energy, defined as ∆G=∆H-T∆S. So sometimes it is enthalpy that is a driving force of a process, and sometimes entropy that is responsible.

 

[epsaliba]

I guess what I am trying to ask is, is there a way to describe entropy in terms of Newtons laws of motion? For example, if there was some way for me to keep track of all of the equations of motion for every particle in a process, what would entropy represent in them? I guess I know what the equations are, but I do not really know what they are trying to convey. The way I view Gibbs free energy right now is that if I were to somehow link myself to some massive increase in entropy, I could walk up the stairs without performing any work.

 

[epsaliba]

I just realized that is not right. What I wanted to say is, how could I make something "falling up" the stairs spontaneous simply by increasing the entropy contribbution to the gibbs free energy change enough?

 

[Borek]

That's exactly the water evaporation example.

 

[epsaliba]

So does the entropy arise from the fact that not all of the water molecules are traveling at the same speed and some of them may have the energy necessary to evaporate?

 

[Borek]

Generally speaking when substance becomes gaseous its entropy is much higher than then it is a liquid or solid. Distribution of speeds definitely plays a role, but I don't feel well enough on the thermodynamic ground to quantify.