Why is VdP work if volume is constant?

[iScience]

i'm trying to relate the helmholtz and the gibbs free energy together. I thought that since the gibbs was just the W(other) and the helmholtz was the total work, that the following would be true.

F=G-PdV

because.. i thought that PdV was the work due to pressure, but it turns out that it's actually PdV+VdP which is just d(PV)

but i thought PdV was the only term that was the work due to pressure, how is VdP work due to pressure? V is constant!

 

[Nugatory]

it turns out that it's actually PdV+VdP which is just d(PV)

but i thought PdV was the only term that was the work due to pressure, how is VdP work due to pressure? V is constant!

V is not constant if dV is non-zero, right? Indeed, if V were constant the pressure wouldn't be doing any work (just as a weight sitting stationary on a rigid table does no work on the table).

 

[iScience]

i know dV isn't zero, this is what gives rise to a displacement in the system which ultimately gives rise to work.
i was referring to V, not dV. for the VdP term, i thought we were keeping V constant and varying P.