Thermo: Dependence of pressure on entropy at a constant temperature

anwat21

1. The problem statement, all variables and given/known data
I was asked to prove that (dP/dS)T (subscript T ie, at a constant temperature) equals κPV ("kappa"PV, or, isothermal compressibility x pressure x volume).
By using the Maxwell relation -(dS/dP)T = (dT/dV)P I got an answer of -1/(alpha*volume) but cannot find out how to make this into kPV.. unless the question is wrong in the first place.



2. Relevant equations

Maxwell relation -(dS/dP)T = (dT/dV)P

3. The attempt at a solution

By using the Maxwell relation -(dS/dP)T = (dT/dV)P I got an answer of -1/(α*V) but cannot find out how to make this into κPV.. unless the question is wrong in the first place. Ty.