Equations

[Jenny Chau 1I]

I'm a bit confused but how do you know when to use -P(delta V) vs -(delta n)RT vs -nRTln(v2/v1) since they all account for work?

[Lea Baskin Monk 1F]

-P(delta V) and -(delta n)RT are both used for irreversible expansions. They are basically the same equation. I put the derivation below. The other equation, -nRTln(v2/v1), is used for reversible expansions. It can be derived from the the integral equation we covered in class.

Here is how to show that -P(delta V) = -(delta n)RT ...

PV = nRT
P(delta V) = (delta n)RT
delta V = (delta n)RT / P solve for delta V

Then ...
w = -P(delta V)
w = -P((delta n)RT / P) Plug the above solution for delta V in that was found from the PV = nRT equation
w = -(delta n)RT The pressure value (P) cancels out and we're left with the equation

Thus, -P(delta V) = -(delta n)RT

[Tanya Nguyen 1B]

In addition, I understand that work is the integral from v2 to v1 (-p(delta v)), but how does it also equal -nRTln(v2/v1)?

[Asia Yamada 2B]

You would use -P(delta V) when there is a constant external pressure. You use -nRTln(V2/V1) when the reaction is an isothermal, reversible one.

[Chinmayi Mutyala 3H]

it depends on whether pressure is constant or not. You can use -P(delta)V when external pressure is constant and the other when it isn't.