Why does formation of snow flakes not violate entropy law?

[low inhibition]

Sorry if this is a stupid question, I don't fully understand entropy. Snow flakes are highly structured, they form from water vapor which has very little structure. I must be misunderstanding entropy, my interpretation of it is that isolated system must evolve into more chaotic less structured states, which is not what happens with snow flakes. Can someone explain?

Also another question. Mods if you feel this is pseudoscience please just delete this paragraph instead of my whole thread. Does free will necessarily violate law of entropy? Because when I decide to raise my arm, something to switch on by itself in my brain and send electric signal to my arm, seemingly with no external influence. Again this must be my misunderstanding of entropy.

 

[Drakkith]

. I must be misunderstanding entropy, my interpretation of it is that isolated system must evolve into more chaotic less structured states, which is not what happens with snow flakes. Can someone explain?

A snowflake is not an isolated system. It is surrounded by an environment in which it can exchange energy.

Does free will necessarily violate law of entropy? Because when I decide to raise my arm, something to switch on by itself in my brain and send electric signal to my arm, seemingly with no external influence. Again this must be my misunderstanding of entropy.

Like snowflakes, we are not isolated systems. Just think of all that food and oxygen you consume just to keep yourself running!

 

[Khashishi]

A snowflake is just a fancy ice crystal. Ice has lower entropy but also lower energy than water vapor. Since energy is conserved, when water vapor frosts into ice, some heat is released, which normally heats some surrounding environment. When the environment is heated, the entropy of the environment increases.

Generally, whenever something loses energy, it loses some entropy. But the energy must go off somewhere else where it will increase the entropy.

 

[collinsmark]

A snowflake configuration of ice contains less energy than an amorphous configuration of the same mass. That means when the $\mathrm{H_2O}$ molecules spontaneously arrange themselves, one by one, into a snowflake formation, more energy is released into the environment than would otherwise happen, in say, and amorphous blob of ice. (I.e., less energy in the snowflake means more energy in the environment.)

Taken together, ice and the environment, there are more possible arrangements (of overall atoms/molecules configurations) in the case of the snowflake and the extra environmental energy than the case of the amorphous blob and less environmental energy. That extra environmental energy more than makes up for the fewer possible arrangements of the snowflake structure itself.

Thus the second law is not violated.

Regarding the second question, when you raise your arm, the chemical reactions involved in your muscles cause the molecules/atoms/chemical bonds in your arm, in you, and in the environment around you and your arm, to rearrange themselves in a fashion that ultimately has a higher number of possible arrangements.

Entropy is a measure of the number of ways to rearrange microstates such that a given macrostate is produced. In other words, it's a measure of how many microstates correspond to a given macrostate. And you need to take into account the whole system, not just a particular part of it.

 

[Demystifier]

To understand the formation of a snowflake, thermodynamics is not enough. Thermodynamics describes processes close to thermodynamic equilibrium, while the formation of a snowflake is a process far from equilibrium. The formation of a snowflake is an example of self-organization, and self-organization is studied by theory of complex systems. Another example of self-organized complex system is life. To explain the formation of a snowflake, it is not sufficient to say that thermodynamic entropy of the environment increases. It's much more complex than that.

In fact, since self-organization is a spontaneous process, some kind of entropy increases even of the snowflake itself (not only of its environment). But this entropy (which increases for the snowflake) is not thermodynamic entropy, because thermodynamic entropy is not a very useful concept for complex systems far from equilibrium.

 

[hilbert2]

At the freezing point of water, the heat released to the environment per mole of ice formed will increase the entropy of the surroundings by an amount equal to the entropy loss due to solid lattice formation per mole of ice. Both entropy changes have a magnitude

$\Delta S = \frac{Q}{T}$,

where $T = 273.15 K$ and $Q$ is the molar heat of fusion of water.

 

[Andy Resnick]

Sorry if this is a stupid question, I don't fully understand entropy. Snow flakes are highly structured, they form from water vapor which has very little structure. I must be misunderstanding entropy, my interpretation of it is that isolated system must evolve into more chaotic less structured states, which is not what happens with snow flakes. Can someone explain?

I think there are two parts to this question- the phase change and the dendritic growth pattern.

Clearly, nucleation and growth of a crystal (freezing) does not violate thermodynamics- thermokinetics is sufficient to explain this.

Dendritic growth is also known as 'diffusion limited aggregation' and also does not violate thermodynamics; Marty Glicksman did much of the seminal work on the topic, using succinonitrile (SCN) as a model system..

http://link.springer.com/chapter/10.1007/978-1-4419-7344-3_13#page-1
http://www.sciencedirect.com/science/article/pii/0025541684901976?via=ihub

Dendritic growth is a result of an instability between competing processes: capillary (interfacial energy) and thermal (phase change) and is, AFIAK, encoded in the Peclet number. The shape instability results from the interplay of the energetics of a curved interface and supercooling and also encodes the underlying crystal symmetry (hexagonal, in the case of ice).

 

[Ivanov]

Entropy is a very bad word. The first thing one thinks about is chaos. Rather it the tendency of all things to become leveled and calm. Structure, as opposed to entropy, implies something that is unlike the rest. For example, imagine you're tidying up your stones. You put the hot ones on the right side of the stone box and the cold ones on the left side. Eventually, the heat will even out, and that is entropy. It's called entropy because you tried having a nice, tidy pile of hot stones but you ended up with a boring lot of room temperature stones.
For the second question: although as you said moving requires putting order while things naturally tend to go towards disorder and I see how that could be confusing, don't forget that entropy starts creeping in when things are left on their own. When you move your arm you use energy, the neurons firing in your brain probably waste a good calorie themselves. To bring the stone analogy back - yes the hot ones would cool down but if we put one in the oven its red hot again.