### Definition of degeneracy and relationship to entropy

Posted:

**Sun Jan 17, 2016 6:57 pm**I am still unsure as to what exactly degeneracy is, and how degeneracy is related to entropy.

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=128&t=9912

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Posted: **Sun Jan 17, 2016 6:57 pm**

I am still unsure as to what exactly degeneracy is, and how degeneracy is related to entropy.

Posted: **Sun Jan 17, 2016 8:21 pm**

So from our course reader it states that degeneracy is "the number of ways of achieving a given energy state." This basically means that there are different configurations and positions (ie number of ways) and these configurations determine the energy state. Gas will have a higher degeneracy because it takes the space of its container and will occupy a larger space than a solid or liquid which may only take the space of half a container. Because gas takes up the whole space of the container, there are a lot more possible configurations. Looking at the Boltzmann equation, you see that S=kBln(W). Because of the ln, entropy and degeneracy have a direct relationship. The larger the degeneracy, the larger the entropy. Therefore, gas has both the largest degeneracy and the largest entropy, while solids have the smallest degeneracy and the smallest entropy.

Posted: **Thu Jan 21, 2016 8:08 pm**

Degeneracy is the number of different ways that energy can exist, and degeneracy and entropy are directly related. This means that the higher that entropy is then there are potentially more ways for energy to be and so degeneracy is increased as well.

Posted: **Thu Jan 21, 2016 11:36 pm**

The formula kblnW for entropy and degeneracy is useful in theory but is not necessarily the best way to find Entropy. Use the other derived equations such as delta S=q/t and so on.

Posted: **Fri Jan 22, 2016 1:04 am**

The equation S=klnW is used to calculate statistical entropy (the entropy associated with large numbers of atoms and molecules). The equation delta S=q/T is used to calculate the thermodynamic entropy. In both cases, increasing the temperature or volume causes an increase in entropy because it would make more energy levels available to the molecules, so the molecules have more micro states that they can occupy.

Posted: **Fri Jan 22, 2016 2:11 am**

In basic chemical terms, degeneracy if it is unable to singularly conform to one energy state. It is labeled as degenerate when it has the ability to partake in more than one energy state and has several abundance availability in those. It can also be used to describe systems when the systems are of different states but equal in energy levels.

In the entropy equation, degeneracy is used because in simple terms, degeneracy is the measurement of the number of possible states. This relates to entropy because entropy uses degeneracy to show the change in entropy.

In the entropy equation, degeneracy is used because in simple terms, degeneracy is the measurement of the number of possible states. This relates to entropy because entropy uses degeneracy to show the change in entropy.

Posted: **Sat Jan 23, 2016 1:58 pm**

Degeneracy refers to the different states that energy can exist.