Work of expansion

[Ernie Lee 3F]

I just wanted to clarify:
1. If there is a work of expansion hence a system's volume changes (not at equilibrium), the changes occurs in small steps and we use the equation of w that features the sum of the product of the external pressure and the volume change.
2.And when the volume change is infinitely small, we use the equation featuring the integral of the product of the external pressure and the derivative of the volume (since the change is small). However, what does the professor mean by infinite number of steps (do the infinitely small volume changes occur at an infinite number of steps?). Moreover, when we write the integral, are we solving the equation by using V as the variable?

[Vishal Reddy Kunam]

Hi, Ernie
1) I believe you're correct in your first point; however, I would say that we use the equation of w that features the negative sum of the product of specifically the "Pi" and ∆Vi from i = 1 to n.
2) I also believe that you are correct in your second point-- we use the integral while at equilibrium and infinitesimally small changes in volume are occurring. When we are writing the integral, I believe that we are solving the equation by using V as the variable (measuring from V1 to V2).

Hope this helped!