Understanding Entropy: Hot Water & Ice

[nyxynyx]

I'm having a problem understand entropy. From my book, it says the following:

It is a measure of the extent of disorder in a system or of the probability of the arrangement of parts of a system. Greater probability implies greater disorder and higher entropy.

There is an example that says that

In any isolated physical system the direction of spontaneous change is always from molecular order to disorder. A container of hot water, for example, undergoes spontaneous cooling as the energy of motion of its microscopic particles decreases

What I don't understand is if there is an increase in entropy, which is the increase in disorder, why does the hot water cool spontaneously when cooling the water makes the water molecules's movements more predictable, and move around slower, and eventually freeze into an ordered tetrahedral lattice in ice? To me, ice seems to have lesser disorder than liquid!

Thanks for any help!

 

[Andrew Mason]

What I don't understand is if there is an increase in entropy, which is the increase in disorder, why does the hot water cool spontaneously when cooling the water makes the water molecules's movements more predictable, and move around slower, and eventually freeze into an ordered tetrahedral lattice in ice? To me, ice seems to have lesser disorder than liquid!

My advice: ignore the concept of disorder to explain entropy. It is quite confusing and, depending on how you define disorder, simply WRONG. From a molecular point of view, entropy relates to the concept of equilibrium and the number of equivalent microstates that a system of N particles can have at equilibrium at a single temperature compared to the number of microstates that those same particles, with the same total energy, have when separated into different populations each at equilibrium but at different temperatures. Unless you use a very precise definition of disorder (one that refers to the number of microstates) it is WRONG. The example you gave illustrates perfectly why it is confusing.

Can we say that when we put a hot cup of water on an iceberg and watch as it freezes that the total disorder increases? Well, it certainly doesn't increase for the hot water and it is really not very clear that the magnitude of the increase the disorder, if any, for the iceberg would be greater than the magnitude of the decrease in disorder for the water.

Can we say that a greatly reduced disorder for the hot water molecules plus a slightly faster rate of vibration for the much larger number of molecules in ice represents a greater overall increase in disorder? You might, but I find that to be a rather unhelpful concept unless you tell me how I am supposed to measure "disorder".

Yet entropy increases overall because the entropy of the iceberg increases more than the entropy of the water decreases. (This is because the heat flow for the water occurs at a higher temperature than the ice, so the dQ/T, which is negative, has a smaller magnitude than dQ/T for the ice and entropy increases overall.)

AM