What is the Issue with Extensive Properties of Entropy?

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Discussion Overview

The discussion revolves around the extensive properties of entropy, particularly in the context of an ideal gas as derived from statistical mechanics. Participants explore the implications of doubling the number of particles, volume, and energy on the entropy calculation.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the interpretation of entropy as an extensive property when doubling the number of particles, volume, and energy, suggesting that the entropy does not simply double due to the logarithmic nature of the equation.
  • Another participant argues that when considering the doubling of internal energy (U) and volume (V), the logarithmic terms will yield positive contributions that cancel out the negative contribution from the number of particles (N).
  • A later reply acknowledges the initial confusion and expresses gratitude for the clarification, indicating a shift in understanding.
  • One participant notes that the formula discussed is specific to a monoatomic gas, suggesting a limitation in the generality of the initial claim about ideal gases.

Areas of Agreement / Disagreement

Participants exhibit some disagreement regarding the interpretation of the entropy calculation, with differing views on how the logarithmic terms interact. The discussion remains unresolved as participants explore these differing perspectives.

Contextual Notes

There are limitations regarding the assumptions made about the nature of the gas and the specific conditions under which the entropy is calculated. The discussion also highlights the dependence on the definitions of extensive properties and the specific type of gas being considered.

Vectorcrust
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Hi to all!

The entropy is known as an extensive property. Here is an expression for the entropy of ideal gas derived by statistical mechanics methods:

sgas2.gif


Imagine that I multiply by 2 the number of particles, the volume of particles and the energy of particles(so the molar volume and molar energy and all other intensive properties are the same). According to this expression I'll never get entropy multiplied by 2 because of N that under ln expression.

Where am I wrong?

Thanks.
 
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Hi Vectorcrust, welcome to PF!

Vectorcrust said:
According to this expression I'll never get entropy multiplied by 2 because of N that under ln expression.

Sure you will, if you note that U and V get doubled as well and you work through the logarithms.
 
The U and V logarithms will give you positive ln(2) terms and the logarithm with N inside will give you -ln(2) terms. They will cancel.
 
Mapes said:
Sure you will, if you note that U and V get doubled as well and you work through the logarithms.


I see it now. Sorry for dumb question. Thanks a lot!
 
Vectorcrust said:
I see it now. Sorry for dumb question. Thanks a lot!

Not dumb! Stat. mech. requires a lot of staring at logarithm-filled equations no matter how smart you are. Stick around!
 
also note that the formula you posted is not for any "ideal gas", it is for a monoatomic gas. Just keep that in mind.
 

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