DERIVATIONS FOR WORKDONE, ISOTHERMAL AND ADIABATIC PROCESSS

For Workdone

then workdone  = force x distance

workdone , W= F X dL

        =fdl

        but  P=F/A

        F =PA        

        W =PAdL        but AdL = V , volume

        thus W = PV

 for expansion from V1 to V2, an infinitesimal work has being done

w = PV

W =

W =

 =

W=P(V2-V1)

note replace k in the above equation with δ

For Adiabatic Process

from the first law of thermodynamics , , Q =0, 0 =U + W

U = -W

dU  =-W

W = PdV , but P =K

W=

W

W= 

but P1V1 =P2V2=K

 W =

NOTE  γ =a, replace into the above

For Isothermal Process