What does it mean that : "A perfect crystal at zero Kelvin has zero entropy"

Landon Caeli · Jun 29, 2023

I was just wondering what this means in regards to thermodynamics.

Occams Barber · Jun 29, 2023

Landon Caeli said:
I was just wondering what this means in regards to thermodynamics.

"A perfect crystal at zero degrees Kelvin has zero entropy" is a way of stating/visualising the third law of thermodynamics*.

Imagine a perfect crystal where all the molecules in the crystal lattice were exactly equidistant from each other. Now cool the crystal down to zero degrees Kelvin (aka 'absolute zero'). All molecular motion within the crystal would stop. With absolutely no heat and no motion there would be nothing happening within the crystal - no disorder, no chaotic movement - nothing. The 'entropy' within the system would be zero.

This is a way of visualising the third law. In real terms a perfect crystal is an impossibility as is reaching a temperature of zero degrees Kelvin.

*The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero. The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has.

OB

chevyontheriver · Jun 29, 2023

Landon Caeli said:
I was just wondering what this means in regards to thermodynamics.

There are no perfect crystals, only semi-perfect to mediocre ones. And there is no way to reach absolute zero in a laboratory or even in deep space. One can get really close but never actually get there. So this is not an empirical thing but a theoretical one.

Thermodynamics is an empirical science, so even if all the theories of the rest of chemistry and physics were disproven at least thermodynamics would still stand. And we could guess that a perfect crystal at true absolute zero would still have a zero entropy. The system that perfect crystal was in would nonetheless have delta S > 0 for the system as a whole. That is the empirical result of every system ever measured.

sjastro · Jun 29, 2023

Entropy can be defined using a simple example, a system composed of a partitioned box with four different molecules of gas in the left hand side of the box and none in the right hand side.
If we open a hole in the partition what would we expect regarding the distribution of the gas molecules.
Intuitively we might think the most likely configuration is to have two molecules on each side of the partition and this may in fact describe the thermodynamic macrostate of the system.
There are however 16 possible configurations as illustrated.

Each configuration is known as a microstate and the more microstates you have the greater the entropy or disorder.

In a real life scenario however there would be more than 4 molecules in the box, at a standard temperature and pressure 1 mole of gas occupies 22.4 litres and contains 6.02 X 10²³ molecules.
Using statistical mechanics we can define a formula defining the entropy S of a system given as:
S = k ln Ω
k is the Boltzmann constant, ln is the natural logarithm and Ω is the number of microstates.
This formula can be written S - S₀ = k ln Ω where S₀ is a baseline.

We can continue to cool a gas to lower temperatures as long as there exists distinguishable entropy states S ≠ S₀.
At absolute zero the entropy states are no longer distinguishable.
We define this state as a perfect crystal where there is only one possible microstate configuration
Ω = 1.
ln(1) = 0 hence S - S₀ = 0.

From a physical perspective and using the third law of thermodynamics the entropy of a perfect crystal of a pure substance approaches zero as T approaches zero but can never reach it.
There is only one possible microstate Ω = 1 as there is no ambiguity to the location and orientation of each part of the crystal.
Also as the energy of the crystal is reduced, the vibrations of the individual atoms are reduced to nothing, and the crystal becomes the same everywhere.
S₀ is the baseline describing a perfect crystal where the entropy is zero.

Landon Caeli · Jun 30, 2023

To be clear, when we talk about crystals, are we talking about the translucent kind found in stores? Or just crystallization in general?

Landon Caeli · Jun 30, 2023

Also, are bones and teeth crystalline in nature? And if so, would the laws of thermodynamics apply to bones and teeth?

GaryAnderson · Jun 30, 2023

What does it mean that : "A perfect crystal at zero Kelvin has zero entropy"

This usually means that a salesman is trying to sell you something.
Kinda like saying "Dark Web" or "AI". There is no such thing.

Entropy will win in the end when the universe experiences the cold death and the atom itself is torn apart. That's when Time ends too since there are no events happening forever.

partinobodycular · Jun 30, 2023

GaryAnderson said:
Entropy will win in the end when the universe experiences the cold death and the atom itself is torn apart. That's when Time ends too since there are no events happening forever.

Or is this where time begins, as reality continuously passes from aeon to aeon? After all everything that you see around you is the product of increasing entropy.

GaryAnderson · Jun 30, 2023

partinobodycular said:
Or is this where time begins, as reality continuously passes from aeon to aeon? After all everything that you see around you is the product of increasing entropy.

Yes, anything is possible at that point since we have no evidence for anything existential and that's where trusting in God is important for me as opposed to trusting theories of Multiverse, Matrix Theory or Holograms.

chevyontheriver · Jun 30, 2023

Landon Caeli said:
Also, are bones and teeth crystalline in nature? And if so, would the laws of thermodynamics apply to bones and teeth?

Thermodynamics applies to all matter, so yes. But bones are far far far from perfect crystals.

partinobodycular · Jun 30, 2023

GaryAnderson said:
Yes, anything is possible at that point since we have no evidence for anything existential and that's where trusting in God is important for me as opposed to trusting theories of Multiverse, Matrix Theory or Holograms.

WARNING
Incoherent rambling ahead. Proceed with caution.

Is the only difference between trusting in the 'Multiverse' and trusting in 'God' the fact that one is sentient and the other isn't. One responds to our needs and desires, but the other doesn't. One loves and cares about us, but the other doesn't. But is this true? Or are we simply anthropomorphizing God? Is humanity merely comforting itself with the notion that we're not just a serendipitous side effect of the laws of physics? But rather something chose to create us. Or have we as conscious beings simply created God in our image, to our ideal, because in a certain time and place we needed something greater than ourselves, to justify our laws and our morality, and console us against the brutality and indifference of life?

Did the knowledge of good and evil force humanity to create God? And is that really such a reprehensible idea? And are we now too afraid to let Him go, to loose the bonds of sin that we wrapped ourselves in, and realize that we, on our own, can rise above our prejudices and inequities, and fulfill the destiny that we once thought to be only the provenance of God.

I know, you think that such an idea is sacrilegious. Men believing themselves to be God. But it's not about us being Gods. It's about us fulfilling the potential that we were born with, whether that birth be by God or by the multiverse. But doesn't this make God irrelevant, if He can be replaced with a multiverse? Well, if it comforts you to believe that He's there, then by all means believe, in fact we may never know who we are, and where we came from, thus there may always be room for God.

Believing in God and accepting the existence of the multiverse aren't two irreconcilable ideas. What we should be focused on is fulfilling our potential and making our creator... whoever or whatever that may be... proud. To that end it doesn't matter who or what our creator is, it's about what we as sentient beings choose to make out of what we've been given.

So do justly, love mercy, and walk humbly with thy God. Then fate will do, whatever fate will do.

Halbhh · Jun 30, 2023

Fun behavior near zero kelvin.

Entropy such as most people think of it in the classical 3 laws of thermodynamics they learned about in high school or college for non physics majors -- they learn classical physics laws, for macro systems. So, typically it's a concept for engineering power plants, etc. -- big classically operating systems.

e.g. -- "The third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field. At absolute zero (zero kelvins) the system must be in a state with the minimum possible energy."

But nature is actually quantum, operating by quantum mechanics. Classical is only what usually we see at the macro level in commonplace temperatures, etc. People are accustomed to imagine classical physics is how things operate, and feel sure about it....but it's not really correct, but only usually reliable, because we can live and operate in the classical level. Power plants operate reliably.

So, getting near 'absolute zero' temperature, a fun thing that happens is that quantum effects become pronounced.

Quantum mechanics also means that the closer these researchers creep toward absolute zero, the weirder a substance’s properties become. At low enough temperatures, liquid helium, for example, morphs into a superfluid—a liquid that flows without the resistance of friction. As a result, it can spontaneously flow upwards and out of a container; seep through molecule-thin cracks; remain perfectly still while spinning at high speeds; and—most surprising to physicists—coalesce into one “super-atom,” known as a Bose-Einstein condensate. Working at around just 1 to 10 millikelvins, or thousandths of a kelvin, the Cavendish team is in the process of surveying a variety of other materials that also show funky quantum behavior. And the technology that the group uses to reach such frigid temperatures is almost as complicated as the behavior it’s trying to induce.

Racing toward Absolute Zero

A lab at the University of Cambridge is looking for materials that have weird quantum properties at the coldest temperatures possible

blogs.scientificamerican.com

Landon Caeli said:
I was just wondering what this means in regards to thermodynamics.

GaryAnderson · Jun 30, 2023

partinobodycular said:
WARNING
Incoherent rambling ahead. Proceed with caution.

Is the only difference between trusting in the 'Multiverse' and trusting in 'God' the fact that one is sentient and the other isn't. One responds to our needs and desires, but the other doesn't. One loves and cares about us, but the other doesn't. But is this true? Or are we simply anthropomorphizing God? Is humanity merely comforting itself with the notion that we're not just a serendipitous side effect of the laws of physics? But rather something chose to create us. Or have we as conscious beings simply created God in our image, to our ideal, because in a certain time and place we needed something greater than ourselves, to justify our laws and our morality, and console us against the brutality and indifference of life?

Did the knowledge of good and evil force humanity to create God? And is that really such a reprehensible idea? And are we now too afraid to let Him go, to loose the bonds of sin that we wrapped ourselves in, and realize that we, on our own, can rise above our prejudices and inequities, and fulfill the destiny that we once thought to be only the provenance of God.

I know, you think that such an idea is sacrilegious. Men believing themselves to be God. But it's not about us being Gods. It's about us fulfilling the potential that we were born with, whether that birth be by God or by the multiverse. But doesn't this make God irrelevant, if He can be replaced with a multiverse? Well, if it comforts you to believe that He's there, then by all means believe, in fact we may never know who we are, and where we came from, thus there may always be room for God.

Believing in God and accepting the existence of the multiverse aren't two irreconcilable ideas. What we should be focused on is fulfilling our potential and making our creator... whoever or whatever that may be... proud. To that end it doesn't matter who or what our creator is, it's about what we as sentient beings choose to make out of what we've been given.

So do justly, love mercy, and walk humbly with thy God. Then fate will do, whatever fate will do.

The main reason for me in believing in God is linked to Hope and Purpose.
I did however arrive At God after I examined the state of my existence.

1. The universe exists.
2. The fine-tuning argument exists.
3. The supernatural exists.
4. Jesus Christ was here.

A lot of details about existence remain a mystery and this is on purpose I think so we can make a free-willed choice about our Creator.

Halbhh · Jun 30, 2023

Here's a fun article I was just reading, with an inverted Maxwell Boltzmann distribution (of individual particle energies) where instead of most atoms at a given temperature having lower energy states and only a small portion in much higher energy (an idealized gas behavior that is usually seen in positive temperatures short of infinity), they created a system where this distribution of energies was inverted, which the researchers call 'negative temperature'

Atoms Reach Record Temperature, Colder than Absolute Zero

Researchers show they can achieve even lower temperatures than absolute zero for a strange realm of "negative temperatures."

www.livescience.com

One fun bit:
"...when objects with negative temperatures release energy, they can actually absorb entropy."

sjastro · Jun 30, 2023

Landon Caeli said:
To be clear, when we talk about crystals, are we talking about the translucent kind found in stores? Or just crystallization in general?

There is no such thing as a perfect crystal which is not only thermodynamically impossible as described in this thread but also violates quantum mechanics.
At absolute zero the atoms in a perfect crystal are stationary which means the position x of each atom is known with 100% certainty hence Δx = 0.
This violates Heisenberg's Uncertainty Principle Δx.Δp ≥ h/4π where p is the momentum and h is Planck's constant.

The unattainability of absolute zero also destroys the creation ex nihilo argument as there is no such thing as nothing.
Atoms cannot be stationary as the energy ground state Eₙ of a vacuum is not zero at n = 0, Eₙ = hω(n+1/2) = hω/2 ≠ 0 according to quantum field theory.
Fluctuations in the vacuum energy prevent the atoms from being perfectly stationary.

Occams Barber · Jun 30, 2023

Landon Caeli said:
To be clear, when we talk about crystals, are we talking about the translucent kind found in stores? Or just crystallization in general?

We're talking about crystals in general.

What makes a crystal a crystal is the regular, repeated, geometric layout of its atoms, with each atom in a fixed position relative to the others. This is different to say, a gas where the atoms/molecules are whizzing around all over the place.

This regularised layout is known as a 'lattice'.

These are some examples of crystal lattice structures (the blue dots are atoms):

OB

Occams Barber · Jun 30, 2023

Landon Caeli said:
Also, are bones and teeth crystalline in nature? And if so, would the laws of thermodynamics apply to bones and teeth?

Bones and teeth are a mixture of crystalised minerals and collagen (I just learned something new )

The laws of thermodynamics are universal - they apply to everything.

Crystals are mentioned in connection with the third law because their regular, fixed structure makes it easier to visualise the law.

OB

What does it mean that : "A perfect crystal at zero Kelvin has zero entropy"

I ♡ potato pancakes

Newbie

Well-Known Member

Newbie

I ♡ potato pancakes

I ♡ potato pancakes

Active Member

What does it mean that : "A perfect crystal at zero Kelvin has zero entropy"​

Well-Known Member

Active Member

Well-Known Member

Well-Known Member

Everything You say is Life to me

Active Member

Everything You say is Life to me

Newbie

Newbie

Newbie

Similar threads

Privacy & Transparency

Privacy & Transparency

What does it mean that : "A perfect crystal at zero Kelvin has zero entropy"