Snowflakes and Entropy

[Resha Caner]

Consider a system of water droplets and the formation of a snowflake from those droplets. Does the entropy of the system increase or decrease?

 

[pgp_protector]

Consider a system of water droplets and the formation of a snowflake from those droplets. Does the entropy of the system increase or decrease?

What system?

 

[Resha Caner]

What system?

Umm. As I said, the system of water droplets.

 

[pgp_protector]

Umm. As I said, the system of water droplets.

Water droplets be themselves don't form snowflakes. So a system of only water droplets won't create snow

 

[Resha Caner]

Water droplets be themselves don't form snowflakes. So a system of only water droplets won't create snow

Sigh. IMO an irrelevant detail for the question at hand. Yes, snowflakes generally form around a solid particle of some form, so include those in the system if it makes you feel better. Would your answer be different if the particles were clay dust vs. wood ash?

You also neglected to ask me what happens to the heat involved. If heat transfer occurs, is this a closed system? Let us consider that only a single snowflake forms, and there is an excess of water (and yes, solid particles) in the system such that any heat transfer occurs between material inside the system. Yet, aside from the formation of the snowflake, no other change occurs in the system.

How's that? So, does entropy increase or decrease?

 

[essentialsaltes]

Consider a system of water droplets and the formation of a snowflake from those droplets. Does the entropy of the system increase or decrease?

For the complete system (including the surrounding air) the entropy increases.

The transformation of water into ice (or a snowflake) decreases the entropy of the water. But water on its own can't go from unfrozen to frozen. It would have to be in contact with something else.

 

[Resha Caner]

For the complete system (including the surrounding air) the entropy increases.

I thought that would be the answer, but I wasn't sure. It somewhat violates my intuition. A snowflake represents the formation of a particular structure. Given that information theory uses the idea of entropy to indicate how much information is carried, an increase in entropy would mean a decrease in the potential information carried by the system. Yet, intuitively, forming a snowflake seems to be the opposite - an increase in information.

 

[essentialsaltes]

Yet, intuitively, forming a snowflake seems to be the opposite - an increase in information.

It is. But the increase in order in the snowflake is more than paid for by the increase in disorder in the air. So that the net entropy increases.

Similarly, when you clean your room, you increase the order in your room, but that decrease in entropy is more than counterbalanced by the increase of entropy in the rest of the system (all the energy you expend, the heat and energy lost in friction between your broom and the floor, etc. etc.)

 

[Resha Caner]

It is. But the increase in order in the snowflake is more than paid for by the increase in disorder in the air. So that the net entropy increases.

Ah, OK. That's a "Duh!" moment on my part. Thanks for clarifying.

 

[juvenissun]

Ah, OK. That's a "Duh!" moment on my part. Thanks for clarifying.

I think the problem is still on the definition of the system domain.

In your OP, the system does not include the air surrounds the water. In that case, the water system should have its entropy decreased.

If we define the domain as the water and the surrounding air, then the net change of energy in the system is zero. The snow flake gains information and the air loses information.

I am not sure how does the information theory handle the loss of information in the air. To me, I can not see the lost information. But I can clearly see the information gained in the snow flake.

 

[essentialsaltes]

I think the problem is still on the definition of the system domain.

In your OP, the system does not include the air surrounds the water. In that case, the water system should have its entropy decreased.

That is correct, as far as it goes.

This is not a violation of the 2nd law of thermodynamics because the water is not a closed system. It interacts with the air, so that the complete water and air system does obey the 2nd law, and the total entropy of *that* system increases. (Of course, this is exactly the same reason why evolution does not violate the 2nd law.)

If we define the domain as the water and the surrounding air, then the net change of energy in the system is zero.

That is correct. Energy is conserved.

The snow flake gains information and the air loses information.

'Information' is one way of loosely thinking of entropy not energy. Yes, the snowflake gains information and the air loses it, but they do not gain and lose the same amount. So the net change of energy is zero (1st law of thermodynamics) but the net change of entropy is positive (2nd law of thermodynamics).

I am not sure how does the information theory handle the loss of information in the air. To me, I can not see the lost information. But I can clearly see the information gained in the snow flake.

'Information' is not necessarily the best way to think of entropy. The air becomes more disordered, because heat flows from the water to the air when the water freezes into a snowflake. The warmer air has faster moving molecules, so it is more disordered, i.e. its entropy has increased.

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Microscopically, the change in entropy of a system is equal to the heat coming into it, divided by its temperature. ΔS = ΔQ/T

The heat leaving the water is the same in quantity as the heat entering the air. But since heat always flows from hot to cold, the temperature of the water is always warmer than the temperature of the air.

So ΔS(air) is a positive amount (heat is entering the air)
and ΔS(water) is a negative amount (heat is leaving the water)

But the total of the two will be positive, because of the difference in temperature. The larger (higher) temperature of the water, put into the denominator of the equation for entropy, means that the entropy change of the water is smaller in magnitude than the entropy change of the air.

 

[chilehed]

In every real process, the change in thermodynamic entropy is greater than or equal to zero.

Entropy NEVER decreases in a real process.

 

[chilehed]

I thought that would be the answer, but I wasn't sure. It somewhat violates my intuition. A snowflake represents the formation of a particular structure. Given that information theory uses the idea of entropy to indicate how much information is carried, an increase in entropy would mean a decrease in the potential information carried by the system. Yet, intuitively, forming a snowflake seems to be the opposite - an increase in information.

I think you may be misunderstanding the term "information" as it's used in information theory and thermodynamics: to say that thermodynamic entropy has increased IS to say that thermodynamic information has increased.

I've never herd the term "potential information" used in information theory. I have to admit that I'm far from being an expert in the field, but the term makes no sense to me given what the information function is.