Proof of fundamental thermodynamics equation for open systems

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SUMMARY

The discussion focuses on the derivation of fundamental thermodynamics equations for open systems, specifically the transition from the closed cycle equation de + dr = PdV = -du + TdS to the open cycle equation de + dr = vdP = -dH + TdS. Participants clarify that the correct form for enthalpy change is dH = TdS + vdP, emphasizing the distinction between closed and open systems. The conversation highlights the need for a proper understanding of these equations to facilitate accurate thermodynamic analysis.

PREREQUISITES
  • Understanding of thermodynamic concepts such as internal energy, enthalpy, and entropy.
  • Familiarity with the first and second laws of thermodynamics.
  • Knowledge of differential calculus as applied to thermodynamic equations.
  • Experience with closed and open thermodynamic cycles.
NEXT STEPS
  • Study the derivation of the first law of thermodynamics for open systems.
  • Learn about the implications of the second law of thermodynamics in open cycles.
  • Research the applications of enthalpy in real-world thermodynamic processes.
  • Explore advanced thermodynamic textbooks that cover the transition between closed and open systems.
USEFUL FOR

Students of thermodynamics, educators teaching thermodynamic principles, and professionals in engineering fields focusing on energy systems and fluid dynamics.

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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