volume changes

[905934944]

I dont understand how the integral is derived. why does it make a difference is the volume is slowly changed bit by bit?

[Karen_Li_2D]

If you think of an integral, you are taking infinite sums of the very small changes in x for the area under a curve. If you apply that thinking to a reaction, the very small changes in x would translate to the very small changes in volume. This allows you to see to total change in work.

[Gregory_Kislik_2C]

If the volume is changing very slowly, it means that the deltaV in the w = -PdeltaV is not appropriate, since that represents a large change occurring in one instant/short period of time. It is also not reversible. For that reason, dV, or very small changes must be used instead, so the equation must be integrated. I hope this helps, please let me know if there are any errors.

[Janice Shin 1G]

In a reversible thermodynamic process, there is an infinitely small change in the external pressure. In a piston, changing the pressure will be caused by changing the volume since the piston is either moved in or out.

When external pressure is increased, the piston moves in and when the external pressure is reduced, the piston moves out. The goal is to expand against external pressure. In this case, external pressure must be reduced in small steps with the change in volume so that the external pressure is the same as the pressure of the gas.