deltaS=nRln(V2/V1) vs. deltaS=Cln(T2/T1)

[Eunice Lee 1A]

So I know that you can derive deltaS=nRln(P2/P1) from deltaS=nRln(V2/V1) due to Boyle's law, but how do you get deltaS=Cln(T2/T1)? Where does the C come from?

[Tuong-Minh Tran 1C]

We already know that dS=dq(rev)/T. The C comes from the fact that it is related to dq(rev): dq(rev)=CdT. Through substitution, we get dS=CdT/T. With that, we can take the integral of the equation, which gives us ΔS=Cln(T2/T1).

If you're still confused, you can look up the process on pg. 300 in Section 4F.4 in the "How is that Done?" box, if you have the 7th edition textbook.