Thermo | Entropy and the 2nd Law of Thermodynamics
Though complex in its mathematics, entropy can be userstood from a conceptual level. To understand it we must talk about two related concepts, disorder and multiplicity. To explain these concepts imagine a container with two chambers that are seperated by a movable divider. The container will be our system and we can initiate the system by putting particles in either side. If I were to put 99 particles in the left side, and 1 in the right side, we would say that is a well ordered system (hold your questions). If the particles are identical you could exchange the single particle on the left with any one of the particles on the right. That means there are 99 different microscopic configurations that yield the same macroscopic state. We would consider that system of having a multiplicity of 99. Multiplicity is how many different ways you can rearrange the microcopic states (individual particles) to get the same overall macroscopic observable (99 on one side and 1 on the other). Entropy is a measure of this multiplicity.
Now if the divider is removed, and we picture these as particles of a gas, you would expect the system to not be in total equilibrium because some of the particles on the left would move to the right until there was about a 50/50 ratio - until there are about the same amount on each side. Now that the system is in equilibrium, what is the level of multiplicity? Well you can exchange one of the particles on the left with anyone of the 50 on the right, but can do that with anyone of the 50 particles on the left. That would be a multiplicity of 50x50 or 2500, it's actually much higher as we could talk about switching 2 or 3 or more at a time, but the point is the multiplicity increased as you moved from a state of non-equilibrium to a state of equilbrium.
So what about disorder? It's a tricky word but that's why I introduced the clearer word of multiplicity, because the original non-equilibrium state of the system was at a lower multiplicity, which also meant a more ordered state. More ordered in this sense meant there was only one particle at a time for me to change in the intial state and it would be much easier to keep track of the changes. In contrast, the high level of multiplicity in the equilibrium state makes it much harder to keep track of what changes can result in the same macroscopic 50/50 equilibrium state - there is a greater multiplicity. Thus we say the equilibrium state is less ordered. Since isolated systems drive towards equilbrium, they drive towards more disorder, a greater multiplicity, and a greater entropy.
The 2nd Law of Thermodynamics
The total entropy of an isolated system always increases over time until equilibrium is reached, wherein the entropy is maximum.
The second law of thermo, and the concept of entropy, are the only things in physics that have an arrow of time. They state that isolated systems go one way, but not the other. An example is in an isolated system, heat always flows from hot to cold and never the other way around (unless you put energy into the system, but then it is not isolated - think your refridgerator).
Entropy as it Relates to Heat: Normally I would not introduce an equation (Q=limΔs→0∑TΔsQ=limΔs→0∑TΔs) beyond the scope of this discussion, but in this case I want you see that heat (Q) is related to a change in entropy (ΔsΔs). If the heat transfer of your system is positive, which equates to energy entering your system, so is the change in entropy of the system. When the divider from the example above is removed, convection causes the particles to flow from the left to the right side. This results in a heat transfer and thus an increase in entropy. Perhaps a more concrete example is to consider a cube of ice melting. Energy is entering the system during the phase transition but the temperature does not change. The entropy of the ice is increasing because the heat is positive, but that heat energy is going into breaking the bonds and changing the configurational state of the system. And what about order? A solid with a well ordered crystalline lattice, is more ordered than the random motion of molecules rolling around each other, like in the case of a liquid.
Note that none of this discussion is impendent on temperature. If the particles on both sides of the chamber had the same average kinetic energy, the system was in thermal equilibrium, but it was not in total equilbrium because of the configurational change that entropy drives. This is why entropy is sometimes refered to configurational energy that is not available to do work, it's simply bound up in setting the most multiplicitive state possible.
Key Equations and Infographics
