Answer:
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:
[tex]W=F\Delta x[/tex]
Where [tex]F[/tex] is the force that generates the change in [tex]x[/tex] ([tex]\Delta x[/tex]). The force is equal to the pressure applied times the area of application ([tex]F=PA[/tex]). Then:
[tex]W=(PA)\Delta x=P(A\Delta x)=P\Delta V[/tex]
Where [tex]\Delta V[/tex] is the change of volume and [tex]P\Delta V[/tex] is a rectangle in the PV diagram, when [tex]P[/tex] remains constant along the process, and this rectangle is the area under the curve, then the area under the curve is the work. If [tex]P[/tex] is a function of [tex]V[/tex], 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.
