Proof of fundamental thermodynamics equation for open systems

AI Thread Summary
The discussion revolves around the confusion between two thermodynamic equations for open and closed systems. The first equation, de + dr = PdV = -du + TdS, is applicable to closed cycles, while the second equation, de + dr = vdP = -dH + TdS, is meant for open cycles. Participants debate the validity of the second equation and its derivation from the first. Clarification is sought on how to transition from the closed system equation to the open system equation. The conversation emphasizes the need for accurate representation and understanding of thermodynamic principles.
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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