Extensive & intensive parmeters of TS

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Discussion Overview

The discussion revolves around the classification of thermodynamic parameters as extensive or intensive, and the distinction between internal and external parameters in thermodynamics. Participants explore the implications of these classifications on the internal energy and the basic thermodynamic identity.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that intensity and extensive thermodynamic parameters can only be internal parameters, with internal energy being an extensive parameter.
  • There is a claim that the internal energy is a function of temperature and external parameters, leading to questions about the classification of volume, entropy, and particle number in the thermodynamic identity.
  • One participant suggests that volume, entropy, and particle number should be considered external parameters, as they depend on the amount of material.
  • Another participant challenges the classification, arguing that extensive parameters are dependent on quantity while intensive parameters are independent, citing the ideal gas law as an example.
  • Confusion arises regarding the definitions of 'external' and 'internal' parameters, with participants providing differing interpretations and seeking clarification on these terms.
  • Some participants note that while entropy is typically extensive, it can be specific in certain contexts, and they discuss the implications of relativity on volume and other parameters.
  • A later reply indicates a potential misunderstanding between intensive/extensive and internal/external classifications.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between intensive/extensive and internal/external parameters, with no consensus reached on the definitions or classifications. The discussion remains unresolved with multiple competing interpretations presented.

Contextual Notes

Participants highlight the potential for confusion in terminology and the need for clear definitions, particularly regarding the classification of parameters in thermodynamics. There are unresolved interpretations of what constitutes internal versus external parameters.

sergiokapone
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As I understand it, The intensity and extensive thermodynamic system parameters can only be internal parameters. The internal energy is an extensive parameter. Caloric equation of state of matter states that the internal energy is a function of temperature and external parameters.
##U=U(T,a_1,a_2,...a_n)## where ##a_i## - external paraneters.
Basic thermodynamic identity asserts that
##dU=TdS-pdV+\Sigma_i \mu_idn_i##.
In this equation, the volume, entropy, and ##n_i## are external or internal parameters?
 
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sergiokapone said:
As I understand it, The intensity and extensive thermodynamic system parameters can only be internal parameters. The internal energy is an extensive parameter. Caloric equation of state of matter states that the internal energy is a function of temperature and external parameters.
##U=U(T,a_1,a_2,...a_n)## where ##a_i## - external paraneters.
Basic thermodynamic identity asserts that
##dU=TdS-pdV+\Sigma_i \mu_idn_i##.
In this equation, the volume, entropy, and ##n_i## are external or internal parameters?
external. They all depend on the amount of material.
 
Chestermiller said:
external. They all depend on the amount of material.

Shouldn't that be extensive?

sergiokapone said:
As I understand it, The intensity and extensive thermodynamic system parameters can only be internal parameters.
I am not sure that follows. Intensive parameters are independent of quantity and extensive parameters are dependent on quantity. In the equation ##PV=nRT## the number of molecules or moles (n) remains the same in any reference frame so n is not an internal quantity and n is clearly an extensive property. Volume is also an extensive property while temperature is an intensive property.

sergiokapone said:
The internal energy is an extensive parameter.
Yes.

sergiokapone said:
Caloric equation of state of matter states that the internal energy is a function of temperature and external parameters.
What exactly do you mean by 'external' parameters. Internal energy is the energy of the system in the reference frame in which the system is at rest. In a different reference frame there is additional energy due to the kinetic energy of the system as whole which is turn due the velocity of the system relative to the reference frame. I guess you could the kinetic energy, 'external' energy. There is potential for confusion here as when a boundary for a system is defined, energy outside the boundary could be called external energy.

sergiokapone said:
Basic thermodynamic identity asserts that
##dU=TdS-pdV+\Sigma_i \mu_idn_i##.
In this equation, the volume, entropy, and ##n_i## are external or internal parameters?
The title of your thread is about extensive and intensive parameters, but at some point the theme of your question has turned to external and internal parameters, so I can't help wondering if you have the terms confused with each other. Entropy is usually and extensive parameter except when quoted as specific entropy (entropy per unit mass). In relativity, volume is dependent on velocity but in classical physics, volume is independent of velocity and so classically volume is neither an external or internal quantity. The same goes for temperature, entropy and pressure.

An extended form of the thermodynamic identity is:

##dU=TdS-pdV+\Sigma_i \mu_idn_i + vdp##,

where v and p are the velocity and momentum. Normally I would think of these as external quantities if they apply to the system as a whole, but since the left side of the equation is internal energy (so an internal property) I can only assume that v and p are the average velocity and momentum of the individual gas particles relative to the rest frame of the system, which would be an internal property.
 
yuiop said:
Shouldn't that be extensive?]
Oops. Yes. I meant extensive.

Chet
 
sergiokapone said:
As I understand it, The intensity and extensive thermodynamic system parameters can only be internal parameters. The internal energy is an extensive parameter. Caloric equation of state of matter states that the internal energy is a function of temperature and external parameters.
##U=U(T,a_1,a_2,...a_n)## where ##a_i## - external paraneters.
Basic thermodynamic identity asserts that
##dU=TdS-pdV+\Sigma_i \mu_idn_i##.
In this equation, the volume, entropy, and ##n_i## are external or internal parameters?

You seem to be confusing intensive/extensive with internal/external.
 
dauto said:
You seem to be confusing intensive/extensive with internal/external.

I know the definition of that concept of intensive / extensive parameters apply only to the internal parameters. External parameters that affect the thermodynamic potentials are neither extensive nor intensive because they are external.
 
sergiokapone said:
I know the definition of that concept of intensive / extensive parameters apply only to the internal parameters.
Where did you get that definition? Can you quote a source?

sergiokapone said:
External parameters that affect the thermodynamic potentials are neither extensive nor intensive because they are external.
How exactly are you defining external and internal. In my last post a pointed out a couple of interpretations of those terms. Which interpretation are you using?
 

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