The work done in the expansion from an initial to a final state : a. is the negative of the area under the curve of a pvdiagram.
b. depends only on the end point.
c .is independent of the path.

a. is the negative of the area under the curve of a PV diagram.

Explanation:

The work in an expansion process is calculated according to  this expression:

Where is the force that generates the change in (). The force is equal to the pressure applied times the area of application (). Then:

Where is the change of volume and   is a rectangle in the PV diagram, when remains constant along the process, and this rectangle is the area under the curve, then the area under the curve is the work. If is a function of , not constant, the changes can be separated in infinitesimally thin rectangles for finding the area under the curve which represents the work. When the volume decreases the work is positive but when the volume increases the work is negative. In conclusion, the work in the expansion is the negative of the area under the curve in the PV diagram.

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