# Extensive & intensive parmeters of TS

1. Apr 2, 2014

### sergiokapone

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?

2. Apr 3, 2014

### Staff: Mentor

external. They all depend on the amount of material.

3. Apr 3, 2014

### yuiop

Shouldn't that be extensive?

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.

Yes.

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.

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. Apr 3, 2014

### Staff: Mentor

Oops. Yes. I meant extensive.

Chet

5. Apr 4, 2014

### dauto

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

6. Apr 5, 2014

### sergiokapone

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. Apr 5, 2014

### yuiop

Where did you get that definition? Can you quote a source?

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?