Is Log of Molecules a Thermodynamic State Variable?

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The discussion centers on whether the logarithm of the number of molecules (ln N) qualifies as a thermodynamic state variable. Participants agree that while the number of molecules (N) is a state variable, the logarithm may not be considered one since it is a mathematical function rather than a physical quantity. The conversation also touches on the nature of state variables, emphasizing that they describe inherent properties of a thermodynamic system. Additionally, there is a query about whether melting and boiling points are state variables, with some arguing they provide essential information about the system despite being uncontrollable. Overall, the distinction between physical quantities and their mathematical representations is a key focus.
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Is log (no of molecules) a state variable? I know that the no of molecules are a state variable so I assume the logarithm of this is still a state variable. Am I right?
 
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In what context did you bump into this question ? Why is ln N there ?
 
It was just a question I found in a thermodynamics question book. The full question is
"State whether these are state variables or not... (list of quantities)... logarithm of number of molecules"
 
What is a state variable ? You need to be sure about the notions before attempting an answer.
 
State Variables are parameters which describe a thermodynamic system.
Some are inherent in the system (eg specific heat capacity) and some we can control (eg heat capacity)

I suppose since we can control N then ln N is to an extent controlled, but I don't know if it counts as a state variable.

Also (quick question to check an answer I made) is the melting and boiling points of a material a bulk property state variable. As they cannot be controlled but still tell us about the system?
 
I would say that a state variable must be a physical quantity and not some mathematical function of it.

As for the melting and boiling point, what do you mean by <cannot be controlled> ?
 
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