Proof of fundamental thermodynamics equation for open systems

[PHstud]

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

 

[Chestermiller]

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

 

[PHstud]

Maybe I miswrote it, let's consider that dH=TdS+vdP then

 

[Chestermiller]

Maybe I miswrote it, let's consider that dH=TdS+vdP then

The ball is in your court.