Understanding Entropy: Hot Water & Ice

In summary: EN! entropy increases overall because the entropy of the iceberg increases more than the entropy of the water decreases.
  • #1
nyxynyx
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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!
 
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  • #2
nyxynyx said:
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
 
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1. What is entropy?

Entropy is a measure of the randomness or disorder in a system. In thermodynamics, it is closely related to the amount of energy that is unavailable for work.

2. How does hot water turn into ice?

When hot water is cooled, the molecules within the water slow down and become more ordered. As the temperature drops, the molecules become more tightly packed and form a solid, which we know as ice.

3. Why does hot water freeze faster than cold water?

This phenomenon, known as the Mpemba effect, is still not fully understood. One explanation is that hot water has less dissolved gases, which can act as insulators and slow down the freezing process. Another theory is that hot water has a greater surface area, allowing for faster heat transfer and thus faster freezing.

4. How does entropy relate to the melting of ice?

As ice melts and transitions to liquid water, the molecules become more disordered and have more freedom of movement. This increase in randomness or disorder results in an increase in entropy.

5. Is entropy always increasing?

The second law of thermodynamics states that the total entropy of an isolated system will never decrease over time. However, within a closed system, local decreases in entropy can occur as long as there is an overall increase in the total entropy of the system and its surroundings.

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