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