- #1

- 17

- 0

## Homework Statement

So I came down with something and missed some class and am making it up from others notes which arent entirely clear plus the long weekend for turkey day and I am really hoping someone can help me make some sense of this...

I am trying to come up with the derivations for

__irreversible adiabatic expansions/work__, ill try to explain as much as possible and hopefully it will be sufficient for someone to see what I am getting at give me a hand

## Homework Equations

The notes begin with adiabatic reversible work

Du=C

_{v,m}dT

dU=dq+dW -->q=0 for adiabatic so dU=dW

p

_{ex}=P

_{f}=nRT/V

∴nC

_{v,m}dT=-nRTdV/V

the notes then integrate each side wrt T & V end then exponentiate each side to arrive at v

_{1}T

_{1}

^{c}=v

_{2}T

_{2}

^{c}where c =C

_{v,m}/R

they then get sloppy to where i can't make anything of it and arrive at P

_{i}v

_{i}

^{[itex]\gamma[/itex]}P

_{f}v

_{f}

^{[itex]\gamma[/itex]}where[itex]\gamma[/itex]=Cpm/Cvm

Then there is a huge note that says DO NOT USE THIS IF WORK IS IRREV and that the instructor wants us to derive similar for irreversible work Hint: (it changes where dU=dw)

## The Attempt at a Solution

I tried working on this all morning and didnt make any progress...integrating dV/V to get the ln(vf/vi) is how we were taught to do reversible work and for non-reversible it was just w=-P

_{ex}ΔV

I don't see any way this could turn into similar expressions relate T,P&V

Someone please help! If i see a derivation a couple times they make sense but I can never figure this out solo.

Thank you so much