[Pw_forum] a questoin about pressure and bulk modulus of system

[Stefano Baroni]

On Oct 15, 2010, at 11:27 AM, meysam pazoki wrote:

> 
> Dear  Stefano
> 
> Thanks for your good answer.I am an experimentalist and I learn good new things from your answer.
> My mistake was that I didnt know in calculation of pressure,we neglect electronic degrres of freedom(I will be thankfull to you,if you introduce a reference about this subject).

I am sorry to keep correcting you. I don't think I ever said that you can disregard the electronic degrees of freedom when calculating the pressure. I said you can neglect them *in the BO approximation*, when dealing with thermodynamics. I could have been more precise by saying that when doing thermodynamics in the BO approximation, you can safely assume that the "electronic temperature" is zero, i.e. that electrons can be considered in their ground state. In the BO approximations, electrons are kind of slaves who keep atoms together, but do participate in the (thermo) dynamics. The fact that they are slave does imply that you can do without them ...

> I have another question :Is these terms are right?
> E=-PV+uN+TS => dE=-PdV-VdP+udN+Ndu+Tds+SdT

NO - this is nonsense. Nor the energy, nor its differential are what you write. As said in my previous post, the energy is an extensive function of the three extensive quantities S,V,N: E=E(S,V,N) ≠ -PV+uN+TS. In calculating its differential, you should vary only the variables it depends upon (i.e., S,V,N).

> and we know from first law of thermodynamics that dE=-PdV+udN+Tds

This is correct, in fact it is different from the expression you gave before. Form this relation you can conclude that P=-∂E/∂V; T=∂E/∂S, μ=∂E/∂N. The first relation is what you need

> and we conclude that -VdP+Ndu+SdT=0

NO - see above

> and in zero temrature and fixed number of atoms
> we have dE=-PdV and P=-dE/dV

right, for the wrong reason (i.e. your conclusion is correct, the argument you use to derive it is not)

> Thanks

You are welcome. You asked a well posed question, and it is a pleasure to answer well posed questions. I think you should study some basic thermodynamics /  statistical mechanics. Chandler's book is a very good starting point.

Regards - SB

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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