Arun
Last Activity: 5 Years ago
In an adiabatic process, No heat is exchanged
dQ=dU+PdV
0=dU+PdV
d(a+bPV)+PdV=0
bPdV+bVdP+PdV=0
(b+1)PdV+bVdP=0
(b+1)(dV/V) +b(dP/P) = 0
Integrating we get
(b+1)logV +b(logP)=constant
logV(b+1) +logPb=constant
log (V(b+1)xPb)= constant
V(b+1)xPb=constant
divide by
Vb and p(b-1) on both sides
PV((b+1)/b)= constant=PVr
r=((b+1)/b)