Path Independence of Entropy Change

[sigmaro]

Is there any way to prove that entropy change is independent from the path?


dS=dQ/T
dQ=dE+PdV
d(PV)=PdV+VdP
dS=nCd[ln(T)]+nR[ln(T)]-VdP/T
i go this far, but it is not very different from dS=nCd[ln(T)]+PdV/T

 

[sigmaro]

i think i got it
dS=dQ/T
dS=(nCdT+PdV)/T
PV=nRT
dS=nCd[ln(T)]+nRTdV/TV
dS=nCd[ln(T)]+nRd[ln(V)]
can somebody check?