derivation in thermodynamics

derivation for the equation of workdone

assuming a gas expand from volme  vi to volume V2 covering a distance dL

workdone =force x distance

        =F x dL

        =PAdL

        =PV

for expansion from V1 to V2 . the infinitesimal   work

kW = PkV

W =

W =

= P

W=  P(V2-V1)

when V is zero , workdone is 0, because there is no change in volume

REPLACE k WITH δ and redrive the equation