Extensive & intensive parmeters of TS

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In summary, The intensity and extensive thermodynamic system parameters can only be internal parameters. The internal energy is an extensive parameter. The caloric equation of state of matter states that the internal energy is a function of temperature and external parameters, where the external parameters are neither extensive nor intensive. The basic thermodynamic identity asserts that the external parameters can affect the thermodynamic potential, but they are still not considered to be either extensive or intensive.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
yuiop said:
Shouldn't that be extensive?]
Oops. Yes. I meant extensive.

Chet
 
  • #5
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.
 
  • #6
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.
 
  • #7
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?
 

1. What is the difference between extensive and intensive parameters of thermodynamic systems?

Extensive parameters are properties of a thermodynamic system that depend on the size or amount of the system, such as mass, volume, or energy. Intensive parameters, on the other hand, are properties that are independent of the size of the system, such as temperature, pressure, or density.

2. How are extensive parameters related to the overall behavior of a thermodynamic system?

Extensive parameters play a crucial role in determining the overall behavior of a thermodynamic system. They can be used to calculate other properties of the system, and they also follow certain rules, such as additivity, which allow for a better understanding of the system's behavior.

3. Can you give an example of an extensive parameter and an intensive parameter?

An example of an extensive parameter is the mass of a gas in a container. As more gas is added to the container, the mass increases. An example of an intensive parameter is the temperature of the gas in the container. The temperature remains the same regardless of the amount of gas in the container.

4. How do extensive parameters change when a system undergoes a phase transition?

During a phase transition, extensive parameters such as volume and energy remain constant, while intensive parameters like temperature and pressure may change. For example, during the melting of ice, the mass of the ice remains the same, but the temperature changes from 0°C to 0.01°C.

5. Are there any exceptions to the rules governing extensive and intensive parameters?

While the distinction between extensive and intensive parameters is generally clear, there are some exceptions. For example, specific volume (volume per unit mass) is an extensive parameter, but it is also an intensive property of a substance. Additionally, certain properties can behave as both extensive and intensive parameters, depending on the conditions of the system.

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