## Entropy at 0 K

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Layal Suboh 1I
Posts: 61
Joined: Fri Sep 28, 2018 12:23 am

### Entropy at 0 K

Hello,

Is it possible to have 0 entropy? Also, what is the difference between residual, translational, vibrational, and transitional entropy?

Thanks

Becky Belisle 1A
Posts: 81
Joined: Fri Sep 28, 2018 12:18 am

### Re: Entropy at 0 K

At 0K, if the structure is perfectly ordered, then entropy is equal to zero. However, if there are still possible microstates, the entropy will not be equal to zero.

Christopher Anisi 2K
Posts: 30
Joined: Fri Sep 28, 2018 12:21 am

### Re: Entropy at 0 K

It is only possible to have entropy equal to 0 if the temperature is equal to 0K and if the substance in question is perfectly ordered.

Fayez Kanj
Posts: 62
Joined: Fri Sep 28, 2018 12:18 am
Been upvoted: 1 time

### Re: Entropy at 0 K

Hello.

when temperature reaches 0K, then entropy tends to zero. At 0K theoretically, a molecule/compound can still have positional entropy (number of micro-states). If it is perfectly ordered, then yes, entropy would theoretically be 0)

Fanny Lee 2K
Posts: 73
Joined: Fri Sep 28, 2018 12:29 am

### Re: Entropy at 0 K

When the entropy is at 0, it forms a perfect crystal. However, it still has some positional entropy. Higher entropy levels would result in higher rotational and vibrational entropy.

Danielle_Gallandt3I
Posts: 70
Joined: Fri Sep 28, 2018 12:24 am

### Re: Entropy at 0 K

The last 3 types of entropy you mentioned relate to the position and possible movement available to a molecule. The first type you mentioned, residual, relates to the residual entropy left in a molecule when it is at 0 K. At that point there is no entropy due to movement, but if the molecule has more than one possible position at 0 K then it will have residual entropy, which is why not all molecules will be at 0 entropy at 0 K.

JacobHershenhouse3G
Posts: 32
Joined: Thu Jan 10, 2019 12:17 am

### Re: Entropy at 0 K

Its possible to have 0 entropy, when there is no degeneracy at absolute zero. At higher temperatures, vibrational, translational, transitional entropy are spontaneous and add to the total entropy. This is why we have been considering entropy at 0 K because then the S= K In(W) holds true (does not include other types of entropy). Hope this helps :)

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