entropy equations

[WPING1A]

How are you able to find the value of W in the entropy equation S = kbxIn(w)? And what is the major difference between S = kbxln(w) and delta S = qrev/T?

[306060519]

It represents Boltzmann concept of degeneracy. Look up the Boltzmann equation to find out.

[Ishita S 2E]

W is equal to the number of orientations the molecule raised to the power of the number of molecules. S is the entropy of a substance while delta S is the change in entropy. We use S to calculate delta S of a reaction (entropy of products - entropy of reactants). Delta S is generally more useful than S as we can calculate changes in entropy for various processes

[Lexi Brownsberger 2E]

W is equal to the number of orientations to the power of the number of particles. The difference between the two equations is that the first is used to determine an exact value of entropy using Boltzmann's constant while the second equation determines a change in entropy using the heat of a reversible reaction over its temperature. You can determine which to use based on the information given in the question.

[Soobin Lim 2B]

To find W in S = kb ln(W):
Rearrange to get: W = e^(S/kb)

W depends on the entropy S and Boltzmann constant kb.
The major difference between the two equations:
S = kb ln(W) gives the total entropy of a system in terms of number of microstates W.
ΔS = qrev/T relates the entropy change ΔS to a reversible heat transfer qrev at temperature T.

The first defines total entropy, the second gives entropy change from a specific heat transfer process.

[Darya Pahlavan]

W is referring to the degeneration of the molecule we are looking at. W is equivalent to the number of positions to the power of the number of molecules. For example, if you have 4 molecules that have two different possible orientations, the W = 2^4.

Regarding those two different equations, it will be clear what to use given the information you are given. If they are telling you information about the orientation of the molecules and the number of molecules, use the W equation, but if they give you info about heat given off or time, use the qrev eq.

[305920501]

To figure out the ways that a molecule could be arranged (W), I think you have to consider the possible structures of the molecules. In the textbook, in the example with CO, they said there are 2 possible orientations, and a 1 mol of CO would have 2^(6.022x10^23) microstates to account for all of the possible arrangements for a mole of this molecule. S = k ln W is Boltsmann's Formula referring to the statistical entropy. Any formula with delta S is instead referring to the change in entropy over time.

[Valeria Perez 3J]

W is the number of available micro-states raised to the number of mols of the substance you are working with. However, oftentimes, you can use that same equation (S=kbln(w)) to figure out W since all you would need to know is the value of S, and would therefore not have to worry about figuring out the micro-states or moles. You can switch the equation around to be W= e^(S/kb). Also, this equation is referring to the entropy in relation to the number of microstates as its applied to a system, while deltaS=qrev/T deals more with the change in enthalpy as it relates to reversible processes, and is applied to situations where heat transfer occurs at a constant temp.

[806255289]

The difference between S=Kbln(W) and delta S= q/T is one deals with the relationship between entropy and micro states whilst the other deals with changes in entropy during the reversible process.