Entropy and temperature of the system

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The discussion addresses a homework problem regarding the entropy of a system in the microcanonical ensemble, presenting a formula for entropy as W = (N!)/(n!(N-n)!)*3^n. Participants express confusion over the definition of entropy, noting that W appears to be a numerical value rather than a unit of entropy, which should be in Joules per Kelvin. It is clarified that entropy is defined as k_b*log(S), where S represents the number of states corresponding to a macroscopic state. The focus shifts to finding S as the key quantity of interest in the problem. The conversation emphasizes the need for clearer wording in the question to avoid misunderstandings.
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Homework Statement


... Show that the entropy of the system in the microcanonical ensemble is

W = \frac{N!}{n!(N-n)!}3^n

and obtain an expression for the temperature of the system. ...
N = number of molecules
n = number of molecules in orthostate

Homework Equations




The Attempt at a Solution


This question makes no sense, right? Because it says the entropy is W which is just a number, and entropy is in the units Joule/Kelvin
 
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It should probably be reworded. But entropy is defined as k_b*log(S) where S is the number of states corresponding to a given macroscopic state. The interesting quantity in the entropy is S and it looks like that's what they want you to find.
 

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