Proof of fundamental thermodynamics equation for open systems

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Discussion Overview

The discussion revolves around the fundamental thermodynamics equations for open systems, specifically the relationship between internal energy, enthalpy, work, heat, and entropy. Participants are exploring the differences between equations applicable to closed and open cycles.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant references a book stating the equation de + dr = PdV = -du + TdS applies to closed cycles.
  • Another participant mentions their teacher's equation de + dr = vdP = -dH + TdS, suggesting it pertains to open cycles.
  • There is a challenge to the correctness of the second equation, with a participant stating dH = TdS + vdP instead.
  • One participant acknowledges a potential miswriting of the equation and reiterates the form dH = TdS + vdP.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the validity of the second equation and its derivation from the first. There is no consensus on the correctness of the equations or the transition between them.

Contextual Notes

Participants have not fully resolved the assumptions or definitions underlying the equations, nor have they provided a clear proof for the transition between the two forms.

PHstud
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Hi !

I'm having a bit of trouble understanding something.
Let 'u' be internal energy, 'h' enthalpy, 'e' work and 'q' heat. ('r' are dissipations and 'S' entropy)

From a book , i read that de+dr=PdV= -du + TdS
This seems to stand for closed cycle.
Yet, my teacher uses the formula

de+dr=vdP= -dH + TdS

I guess this is different because it is an open cycle.But the thing is, how to go from one to another ? I can't find any proof of the second one.. So if someone could explain it to me ! Thank you
 
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PHstud said:
Hi !

I'm having a bit of trouble understanding something.
Let 'u' be internal energy, 'h' enthalpy, 'e' work and 'q' heat. ('r' are dissipations and 'S' entropy)

From a book , i read that de+dr=PdV= -du + TdS
This seems to stand for closed cycle.
Yet, my teacher uses the formula

de+dr=vdP= -dH + TdS

I guess this is different because it is an open cycle.But the thing is, how to go from one to another ? I can't find any proof of the second one.. So if someone could explain it to me ! Thank you
The second equation doesn't look correct. dH=TdS+vdP
 
Maybe I miswrote it, let's consider that dH=TdS+vdP then
 
PHstud said:
Maybe I miswrote it, let's consider that dH=TdS+vdP then
The ball is in your court.
 

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