Proof of fundamental thermodynamics equation for open systems

In summary, the conversation discusses two different equations involving internal energy, enthalpy, work, heat, dissipations, and entropy, with one being for a closed cycle and the other for an open cycle. The discrepancy arises in the second equation, with the question of how to derive it and a possible correction being suggested.
  • #1
PHstud
12
0
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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  • #2
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
 
  • #3
Maybe I miswrote it, let's consider that dH=TdS+vdP then
 
  • #4
PHstud said:
Maybe I miswrote it, let's consider that dH=TdS+vdP then
The ball is in your court.
 

Related to Proof of fundamental thermodynamics equation for open systems

1. What is the fundamental thermodynamics equation for open systems?

The fundamental thermodynamics equation for open systems is the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

2. How is the fundamental thermodynamics equation for open systems different from that of closed systems?

The fundamental thermodynamics equation for open systems includes an additional term for the work done by the system, as the system can exchange both heat and work with its surroundings. In contrast, the equation for closed systems only includes the heat term.

3. What are the assumptions made in deriving the fundamental thermodynamics equation for open systems?

The fundamental thermodynamics equation for open systems is based on the following assumptions: the system is in a steady state, there is no change in kinetic or potential energy, and there is no energy transfer through mass flow.

4. How is the fundamental thermodynamics equation for open systems applied in real-world situations?

The fundamental thermodynamics equation for open systems is commonly used in engineering and scientific fields to analyze and predict the behavior of various open systems, such as power plants, refrigeration systems, and chemical reactions.

5. Can the fundamental thermodynamics equation for open systems be applied to all types of systems?

No, the fundamental thermodynamics equation for open systems is specifically applicable to open systems that allow for energy and mass exchange with their surroundings. It cannot be applied to closed or isolated systems, which have different equations that govern their behavior.

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