Why entropy is an extensive quantity ?

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Discussion Overview

The discussion revolves around the question of why entropy is considered an extensive quantity, exploring its definition and implications in thermodynamics. Participants examine the relationship between entropy, volume, and the first law of thermodynamics, with a focus on the additivity of entropy across different systems.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that entropy increases with volume, suggesting that a gas occupying 2 m3 has double the entropy of a gas occupying 1 m3 at the same temperature and pressure.
  • Others question how one can know that "entropy increases by volume," seeking a definition-based understanding of entropy as an extensive quantity.
  • One participant references the first law of thermodynamics, stating that δQ is extensive because both dU and pdV are extensive, leading to the conclusion that δQ/T and its integral are also extensive.
  • Concerns are raised about the assumption that temperature is the same across different systems, with a participant arguing that while δQ is additive, it does not imply that entropy is additive without further justification.
  • Another participant emphasizes that the essence of an extensive quantity is its additivity, providing a mathematical expression for the entropy of two isolated systems.
  • Questions arise regarding the additivity of entropy, with participants discussing the implications of integrating δQ/T for different systems and whether this leads to a valid conclusion about entropy being additive.
  • A hypothetical scenario involving liquid water is presented to illustrate the concept of entropy additivity, prompting further discussion on how changes in temperature affect the total entropy of the integrated system.
  • One participant expresses gratitude for the step-by-step explanation that clarifies their understanding of why entropy is considered additive.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasons behind the additivity of entropy, with multiple competing views and questions remaining unresolved throughout the discussion.

Contextual Notes

Participants highlight limitations in their assumptions, particularly regarding temperature differences between systems and the implications of the first law of thermodynamics on entropy calculations.

abcdefg10645
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Why entropy is an extensive quantity ?
 
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Hi.
Entropy increase by volume. Gas of 2 m^3 have double entropy than gas of 1 m^3 in the same temperature and pressure.
Regards.
 
sweet springs said:
Hi.
Entropy increase by volume. Gas of 2 m^3 have double entropy than gas of 1 m^3 in the same temperature and pressure.
Regards.

But how do you know that "Entropy increase by volume. "

Let me restate my question :

How can ew know that entropy is an extensive quantity by its definition

dS=\int(dQ/T)
 
Hi.
First law of thermodynamics, about the conservation of energy: δQ=dU - dW =dU - pdV
δQ is extensive because dU and pdV are extenxive. δQ/T and ∫δQ/T are also extensive.
Regards.
 
sweet springs said:
Hi.
First law of thermodynamics, about the conservation of energy: δQ=dU - dW =dU - pdV
δQ is extensive because dU and pdV are extenxive. δQ/T and ∫δQ/T are also extensive.
Regards.

But for different systems , their temperature T may not be the same !

First Law sates that deltaQ=dU+deltaW

We can only infer that deltaQ is additive !

Please consider my comment~

Thanks
 
Hi.

abcdefg10645 said:
But for different systems , their temperature T may not be the same !
First Law sates that deltaQ=dU+deltaW
We can only infer that deltaQ is additive !

Thanks for correcting my sign mistake of deltaW.
You are right. Additive is the essence of extensive quantity. For isolated two different systems
S1 = ∫dQ1/T1, S2 = ∫dQ2/T2 and the entropy of total system is S = S1 + S2.
Regards.
 
sweet springs said:
Hi.



Thanks for correcting my sign mistake of deltaW.
You are right. Additive is the essence of extensive quantity. For isolated two different systems
S1 = ∫dQ1/T1, S2 = ∫dQ2/T2 and the entropy of total system is S = S1 + S2.
Regards.

Ha ha~never mind ~I believe that were just some typos

But , I cannot understand why entropy is additive ?
 
Hi.
Definition ∫　δQ/T is already addition of　δQ/T , isn't it ?
Why not additive you think?
Regards.
 
sweet springs said:
Hi.
Definition ∫　δQ/T is already addition of　δQ/T , isn't it ?
Why not additive you think?
Regards.

Using the integral to calculate the (delta)S "OF A SYSTEM" is to calculate the difference of entropy for a particular process , I want to ask why , for different systems , it can also be added ?
 
  • #10
Hi. How's that?

1 m^3 of liquid water of the room temperature and in standard pressure has entropy say S.
Let us remove half of water. Do you agree that the left water has entropy S/2 ?

We will bring removed water into another isolated room of the same temperature and pressure.
Do you agree that brought water has entropy S/2?

Water in the first room and water in the second room are different systems.
Do you agree that the integrated system of the two has entropy S?

In room 1 we increase the temperature then the entropy of water becomes S'/2
Do you agree that the integrated system of the two has entropy S/2 + S'/2 ?
Change of entropy ∫δQ/T for room 1 system is regarded as change of entropy in the integrated system, isn't it?

Please show your opinion so that I can surely get the core of your question.
Regards.
 
Last edited:
  • #11
Thank u ~

I can now fully understand the reason why entropy is additive by ur explaining steps by steps !
 

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