Re: lose energy, increase entropy

G'day Nelly, and greetings from the suburbs (we teach this stuff properly at La Trobe! ;-) )

In a textbook, it is said that water that runs downhill will lose the energy and therefore 
increases the entropy.

Your first question is tied up with the word "lose". The first law of thermodynamics says, in effect, 
that energy is conserved. Whatever energy we start out with is still there at the finish. So we cannot 
"lose" energy in the sense of the energy disappearing. What really happens is that we "lose" the 
energy in the sense of mislaying it, or spreading it very thinly around the environment. Another 
way of looking at the same thing is to regard the water as our "system" and everything else in the 
environment as the "surroundings", and we can say that energy is lost from the system to the 
surroundings.

Entropy is a measure of the uselessness of energy. A stream of rushing water is useful energy, or 
low entropy energy. You could use it, for example, to run a flour mill, or a hydroelectric generator. 
It is useful because all of the water molecules are moving in the same direction. If you took the 
water molecules from a stream, and gave them the same amount of extra kinetic energy, but in 
random directions instead of all in the same direction, all that would happen is that the 
temperature of the water would rise by a fraction of a degree, and there would be no way you 
could use the energy.

Now, suppose that you have water in a high lake flowing into a stream, and eventually arriving at a 
low lake. Any bit of water that makes this journey has clearly lost potential energy. And once the 
journey has finished in the lower lake, it does not appear to have gained kinetic energy (or 
chemical energy, or anything else!). But we know that energy is conserved, so what has happened 
to the energy? 

Well, some of it has disappeared into the sound of a rushing stream. Sound is the motion of air 
molecules that is originally in a coherent wave, but rapidly disperses into a simple tiny heating of 
the air. As the water rushes down the stream, there is friction between the water and the river bed, 
and within the water itself (a characteristic of viscous flow). So the water and the riverbed also 
warm up a little, but much too little to be reliably measured on a thermometer. Finally, when the 
water arrives in the lower lake, there is originally a current, then a swirl, and then the motion gets 
randomized. Again it amounts to heating, but only a tiny temperature rise. So the energy is lost -- 
mislaid or irretrievably dispersed -- even though it is conserved. And that is just what an entropy 
change means.

Also, it is said that decreasing the entropy will result in low solubility. Why?

The second law of thermodynamics says that we can never decrease the total entropy. Useful 
energy can be turned into more useless forms of energy, but useless energy is genuinely useless: 
you cannot restore it to a more useful form.

But that only applies to the total entropy of system plus surroundings. You can decrease the 
entropy of a system in any process where you consume useful energy to produce an even larger 
increase in the entropy of the surroundings.

Suppose that you have a substance in solution. It has to decide whether it will remain in solution, 
or whether to separate into crystals of a solid. A solid form af a substance is usually lower both in 
energy and entropy than its dissolved form. In order for crystals to form, the dissolved form has to 
have enough extra energy to produce the entropy decrease required.

If you can lower the entropy of the dissolved form, then you reduce the size of entropy decrease 
required, and you make it easier for the solid to be formed. That amounts to a decrease in 
solubility.

A slightly confusing thing about this explanation is that you cannot increase the available energy 
to drive the entropy decrease simply by warming the solution up. That does increase the energy 
available in the solution, but it increases the entropy of the solution by an even larger amount. 
Usually solids are more soluble in warmer solutions, not less soluble.