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**Summary::**Basically the title: It seems that one of the formulas I use considers the pressure in PdV to be internal, when as far as I know, it is external.

So to my understanding, in w = PdV, the pressure is the external pressure.

However, I get tripped up because in my textbook, for a reversible adiabatic process, it states that:

U = -w (which makes sense)

and then goes to say that:

w = -PdV, but P = (nRT/V) from the ideal gas law and so they replace P with that expression in the integral and integrate from V1 to V2.

But wouldn't that really be the equivalent of looking at the change in volume of the external volume, given that the P comes from an external pressure? Assuming pretty common situations, shouldn't the external pressure always just be constant?

(Sorry about my lack of LaTeX, I haven't used the forums in a while and have completely forgot how to turn it on...)